Mathematicall recreations. Or a collection of sundrie problemes, extracted out of the ancient and moderne philosophers, as secrets in nature, and experiments in arithmeticke, geometrie, cosmographie, horolographie, astronomie, navigation, musicke, opticks, architecture, staticke, machanicks, chimestrie, waterworkes, fireworks, &c. ... Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent. And now delivered in the English tongue, with the examinations, corrections, and augmentations

MATHEMATICALL RECREATION .

PROBLEME . I. To finde a number thought upon .

BId him that hee Quadruple the Number thought upon , that is , multiply it by 4 and unto it bid him to adde , 6. 8. 10. or any Number at pleasure : and let him take the halfe of the summe , ●●en aske how much it comes to : for then if ●ou take away halfe the Number from it which ●ou willed him at first to adde to it , there ●hall remaine the double of the number ●●ought upon .

Example .

●he Number thought upon . 5. ●he Quadruple of it . 20. ●he 8. unto it , makes 28. ●he halfe of it is 14. Take away halfe the number added from it , viz. 4. the rest is 10. The double of the number thought upon , viz. 10.

Another way to finde what number was thought upon .

BId him which thinketh , double his Number , and unto that double adde 4. and bid him multiplie that same product by 5. and unto that product , bid him adde 12. and multiply that last number by 10. ( which is done easily by setting a Ciphar at the end of the number : ) then aske him the last number or product , and from it secretly subtract 320. the remainder in the hundreth place , is the number thought upon .

Example .

The number thought upon 7. For which 700. account onely but the number of the hundreds viz. 7. so have you the number thought upon . His double 14. To it adde 4 , makes 18. Which multiplied by 5. maks 90. To which ad 12 makes 102. This multiplied by 10 which is onely by adding a Ciphar to it , makes 1020. From this subtract 320. Rest 700.

To finde numbers conceived upon otherwise than the former .

BId the partie which thinkes the number , that he triple his thought , cause him to take the halfe of it : if it be odde take the least halfe and put one unto it : then will him to Triple the halfe and take halfe of it as before ; lastly , aske him how many nines there is in the last halfe , and for every 9. account 4. in your memorie , for that shall shew the number thought upon , if both the Triples were even : but if it be odde at the first Triple , and even at the second , for the one added unto the least halfe keepe one in memorie : if the first Triple be even and the second odde , for the one added unto the least halfe keepe two in memorie : lastly if at both times in tripling , the numbers be odde , for the two added unto the least halfes , keepe three in memorie , these cautions observed and added unto as many fowe●s as the partie sayes there is nines contained in the last halfe , shall never faile you to declare , or discerne truly what number was thought upon .

Example .

The number thought upon , 4. or 7. The Triple 12. or 21. The halfe there of 6. or 10. 1 put to it makes 11. The Triple of the halfe 18. or 33. The halfe 6. or 16. 1 put to it maks 17. The number of nines in the last halfe 1. or 1.

The first 1. representeth the 4. number thought upon , and the last 1. with the caution makes 7. the other number thought upon .

Note .

Order your method so that you bee not discovered : which to helpe you may with dexteritie , and industrie make additions , subtractions , multiplications , divisions , &c. and in stead of asking how many nines there is : you may aske how many eights , tens , &c. there is , or subtract 8. 10. &c. from the number which remaines , for to finde out the number thought upon .

Now touching the Demonstrations of the former directions , and others which follow , they depend upon the 2. 7. 8. and 9. Booke of the Elements of Euclid : upon which 2. Booke and 4. proposition this may bee extracted for these which are more learned for the finding of any number that any one thinketh on .

Bid the partie that thinkes , that hee breake the number thought upon into any two parts , and unto the squares of the parts , let him adde the double product of the parts : then aske what it amounteth unto , so the Root Quadrat shall be the number thought upon .

The number thought upon 5. the parts suppose 3. and 2.

The square of 3. maks 9. The summe of these three numbers 25. the square Root of which is 5. the number thought upon . The square of 2. maks 4 The product of the parts viz. 3. by 2. makes 6. which 2. doubled makes 12

Or more compendiously , it may be delivered thus ,

Breake the number into two parts , and to the product of the parts , adde the square of halfe the difference of the parts , then the Root Quadrate of the aggregate is halfe the number conceived .

EXAMINATION .

THe Problemes which concern Arithmetick , we examine not , for these are easie to any one which hath read the grounds and principles of Arithmeticke : but we especially touch upon that , which tends to the speculations of Physicke , Geometrie and Optickes , and such others which are of more difficultie , and more principally to be examined and considered .

PROBLEM . II. How to represent to these which are in a chamber that which is without , or all that which passeth by .

diagram

But heere note , that they may be Represented right two manner of wayes ; first with a concave glasse , ●econdly , by helpe of another convex glasse : disposed or placed be●weene the paper and the other Glasse : as may be seene here by the figure .

Now I will adde here onely by passing by , for such which affect painting , and portraiture , that this experiment may excellently helpe them , in the lively painting of things perspective wise , as Topographicall cards , &c. and for philosophers , it is a fine secret to explaine the organ of the sight , for the hollow of the eye is taken as the close Chamber , the balle of the Aple of the eye , for the hole of the Chamber , the Crystalline humor at the small of the Glasse and the bottome of the eye , for the wall , or leafe of Paper .

EXAMINATION .

IT is false that the species being pressed together or contracted doth performe it upon a wall , for the species of any thing doth represent it selfe not onely in one hole of a window , but in infinite holes ; even unto the whole Spheare , or at least unto a Hemispheare ( intellectuall in a free medium ) if the beames or reflections be not interposed , & by how much the hole is made lesse to give passage to the species , by so much the more lively are the Images formed .

In convexe , or concave Glasses the Images will be disproportionable to the eye , by how much they are more concave , or convexe , and by how ●●●h the parts of the Image comes neare to the ●s , for these that are neare are better propor●ated , than these which are farther off .

But to have them more lively , and true , a●●ording to the imaginarie conicall section , let ●ole be no greater than a pins head made 〈◊〉 a peece of thinne Brasse , or such like , ●ch hole represents the top of the Cone , and the ●e thereof the terme of the species : this ●ctice is best when the Sunne shines upon the 〈◊〉 , for then the objects which are opposite to 〈◊〉 plaine , will make two like Cones , and will lively represent the things without , in a perfect inversed perspective , which drawne by the Pensell of some artificiall Painter , turne the paper upside ●ne , and it will be direct , and to the life .

But the apparences may be direct , if you place ●ther hole opposite unto the former so that the ●ctator be under it ; or let the species reflect ●●on a Concave Glasse , and let that Glasse reflect ●n a paper , or some white thing .

PROBLEM . III. To tell how much waighs the blow of ones fist , of a Mallet , Hatchet or such like , or resting without giving the blow .

〈◊〉 Caliger in his 331. exercise against Cardan , 〈◊〉 relates that the Mathematitians of Maximillian the Emperour did propose upon a day this Question , and promised to give the re●●lution ; notwithstanding Scaliger delivered 〈◊〉 not , and I conceive it to be thus . Take a Bala●● and let the fist , the Mallet or Hatchet rest up● the Scale or upon the beame of the Ballan● and put into the other scale , as much wei●● as may counterpoyse it ; then charging or l●ing more waight into the Scale , and striking 〈◊〉 on the other end : you may see how much 〈◊〉 blow is heavier than another , and so co●quently how much it may waygh : for as A●stotle saith ; the motion that is made in strike ads great waight unto it , and so much 〈◊〉 more , by how much it

diagram is quicker : therefore in effect if there were placed a thousand mallets , or a thousand pound waight upon a stone , nay though it were exceedingly pressed downe by way of a vice , by levers or other mechanick Ingine , it would be nothing to the rigor and violence of a blow .

Is it not evident that the edge of a knife lai● upon butter , and a hatchet upon a leafe of P●per , without striking makes no impression , o● at least enters not ; but striking upon the wo● a little , you may presently see what effect it hath which is from the quicknesse of the motion which breakes and enters without resistance extreame quicke , as experience shewes ●he blowes of Arrows , of Cannons , Thun●ts , and such like .

EXAMINATION .

His Probleme was extracted from Scaliger , who had it from Aristotle , but somewhat refractory compiled , and the strength of the ●he sayes depends onely in the violence of ●otion ; then would it follow that a little ●hammer upon a peece of wood being quick●ed to smite , would give a greater blow and ●ore hurt than a great sledge striking soft ; 〈◊〉 absurd , and contrary to experience : there●●● consists not totally in the motion , for if two ●all hammers , the one being 20. times hea●●● than the other , should move with like quick● the effect would be much different : there ●n some thing else to be considered besides the ●on which Scaliger understood not , for if should have asked him , what is the reason 〈◊〉 stone falling from a window to a place 〈◊〉 at hand is not so forceable , as if it fell far● downe ; and when a bullet flying out of a 〈◊〉 and striking the marke neare at hand , ●ot make such an effect as striking the marke ●her off : but wee suppose that Scaliger and ●anus who handles this subject , would not bee lesse troubled to resolve this , than they h●● beene in that .

PROBLEM . IIII. How to breake a staffe which is laid upon 〈◊〉 Glasses full of water , without breaking the Glasse , spilling the water , or upon two Reeds or Strawes without breaking of them .

FIrst place the Glasses which are full of n● upon two joynt stooles , or such like , 〈◊〉 one as high as the other from the ground , 〈◊〉 distant one from another by 2. or 3. foote , t● place the ends of the staffe upon the edges of 〈◊〉 two Glasses so that they bee sharpe ; this d●● with all the force you can , with another st● strike the staffe which is upon the two Gla● in the middle , and it

diagram will breake without breaking the Glasses or spilling the water . In like manner may you doe upon two Reeds , held in the aire without breaking them : thence Kitchin-boyes often breake bones of mutton upon their hand , or with a 〈◊〉 without any hurt , in onely striking up●●e middle of the bone , with a knife .

N●w in this act the two ends of the staffe in ●ing slides away from the Glasses , upon 〈◊〉 they were placed ; hence it commeth ●●e Glasses are no wise indangered , no more ●he knee upon which a staffe is broken , 〈◊〉 much as in breaking it presseth not : as ●otle in his Mechanicke questions obser● .

EXAMINATION .

〈◊〉 were necessary here to note , that this thing ●ay be experimented , first , without Glasses , ●acing a small slender Staffe upon two props , ●hen making tryall upon it , by which you may ●ow the Staffe will either breake , bow , or de● from his props : and that eyther directly , ●bliquely : But why by this violence , that 〈◊〉 Staffe striking another , ( which is supported ●o Glasses ) will bee broken without offending 〈◊〉 Glasses , is as great a difficultie to be resol● as the former .

PROBLEM . V. How to make a faire Geographicall Card in Garden Plot , fit for a Prince , or great personage .

IT is usuall amongst great men to have 〈◊〉 Geographicall mappes , large Cards , and g● Globes , that by them they may as at once h● a view of any place of the world , and so ●nish themselves with a generall knowled● not onely of their owne kingdomes fo● situation , Longitude , Latitude , &c. but o● other places in the whole Vniverse , with t● Magnitudes , Positions , Climats , and distanc●

Now I esteeme that it is not unworthy 〈◊〉 the meditations of a Prince , seing it ca● with it many profitable and pleasant cont●ments : if such a Card or Mappe by the ad● and direction of an able Mathematitian 〈◊〉 Geographically described in a Garden 〈◊〉 forme , or in some other convenient place , 〈◊〉 in stead of which generall description mi● particularly , and Artificially be prefigured 〈◊〉 whole kingdomes and dominions , the Mo●taines and Hils being raised like small hill● 〈◊〉 with curfes of earth , the vallies somewhat 〈◊〉 cave ; which will be more agreeable & pleas● to the Eye , than the description in p●● Mapps and Cards , within which may be pre●ted , the townes , villages , Castles , or other re●keable edifices in small greene Mossie ban● or springworke proportionall to the plat for● forrests and woods represented according to ●ir forme and capacitie , with hearbs and ●abs , the great rivers , lakes and ponds , to dilate ●mselves according to their course from ●●e Artificiall fountaine made in the Garden ●passe through Chanels ; then may there bee ●●posed walkes of pleasure , Ascents , places 〈◊〉 repose adorned with all varietie of de●●tfull hearbs & flowers , both to please the eye , other sences . A Garden thus accommodated ●ll farre exceede that of my Lo. of Verulams ●cified in his Essayes ; that being onely for ●ight and plasure , this may have all the pro●ties of that , and also for singular use , by ●hich a Prince may in little time personally ●ite his whole kingdome , and in short time ●ow them distinctly , and so in like manner ●y any particular man Geographically prefi●e his owne possession , or heritage .

PROBLEM . VI. ●w three staves , knives , or like bodies may be conceaved to hang in the Aire , without being supported by any thing , but by themselves .

TAke the first staffe A. B. raise up in the Aire , the end B. and upon him croswise ●ce the staffe C. B. then lastly in Triangle wise ●ce the third staffe E.F. in such manner that may be under A. B. and yet upon C. D. I 〈◊〉 that these staves so disposed cannot fall , and the space C. B. E. is made the stronger , 〈◊〉 how much the more it is pressed downe , if th● staves breake not , or sever themselves fro● the triangular forme ▪

diagram so that alwayes the Center of gravitie be in the Center of the Triangle : for A. B. is supported by E. F. and E. F. is helde up by C. D. and C. D. is kept up from falling by A. B therefore one of these staves cannot fall , and so by consequence none .

PROBLEM VII . How to dispose as many men , or other thing in such sort that rejecting , or casting away the 6. 9. 10. part , unto a certaine number , there shall remaine these which you would have .

ORdinarily the proposition is delivere● in this wise : 15. Christians and 15. Turke● being at Sea in one Shippe , an extreame tempel being risen , the Pilot of the Shippe say it is necessary to cast over board halfe of the number of Persons to disburthen the Shippe , an● to save the rest : now it was agreed to bee done by lot and therefore they consent to put themselves in ranke , counting by nine and nine the ninth Person should alwayes be cast into the Sea , untill there were halfe throwne over board ; Now the Pilote being a Christian indeavoured to save the Christians , how ought hee therefore to dispose the Christians , that ●he lot might fall alwayes upon the Turkes , ●nd that none of the Christians be in the ninth place ?

The resolution is ordinarily comprehended in this verse , Populeam virgam mater regina ferebat :

For having respect unto the vowels , making 〈◊〉 one , e two , i three , o foure and u five : o the ●●rst vowell in the first word sheweth that ●●ere must bee placed 4. Christians , the next ●owell u , signifieth that next unto the 4. Christi●●s must be placed 5. Turkes , and so to place ●oth Christians and Turkes according to the ●antitie and value of the vowels in the words 〈◊〉 the verse , untill they be all placed : for then ●unting from the first Christian that was ●aced , unto the ninth , the lot will fall upon 〈◊〉 Turke , and so proceede . And here may be ●rther noted that this Probleme is not to bee ●●ited , seeing it extends to any number and ●●er whatsoever , and may many wayes bee ●full for Captaines , Magistrats , or others ●ich have divers persons to punish , and would ●stise chiefely the unruliest of them , in taking ● 10. 20. or 100. person , &c. as we reade was commonly practised amongst the ancient Romans : herefore to apply a generall rule in counting the third , 4. 9. 10. &c. amongst 30. 40. 50. persons , and more or lesse ; this is to bee observed : take as many unites as there are persons , and dispose them in order privately : as for example , let 24. men bee proposed to have committed some outrage , 6. of them especially are found accessary : and let it be agreed that counting by 8. and 8. the eight man should be alwayes punished : Take therefore first 24. unites , or upon a peece of paper write downe twenty foure Ciphars , and account from the beginning to the eighth , which eighth marke , and so continue counting alwayes marking the eighth , untill you have markt 6. by which you may easily perceive how to place those 6. men that are to bee punished , and so of others . It is supposed that Iosephus the Author of the Iewish History , escaped the danger of death by helpe of this Probleme ; for a worthy Author of beliefe reports in his eighth Chapter of the third Booke of the destruction of Ierusalem , that the Towne of Iotapata being taken by maine force by Vespatian ; Iosephus being governour of that Towne accompained with a troope of 40. Souldiers , hid themselves in a Cave in which they resolved rather to famish than to fall into the hands of Vespatian : and with a bloody resolution in that great distresse would have butchered one another for sustenance : had not Iosephus perswaded them to die by lot , and order , upon which it should fall : Now seeing that Iosephus did save himselfe by this Art : It is thought that his industrie was exercised by the helpe of this Probleme ; so that of the 40. persons which hee had , the third was alwayes killed . Now by putting himselfe in the 16. or 31. place he was saved , and one with him which hee might kill , or easily perswade to yeeld unto the Romans .

PROBLEM . VIII Three things , and three persons proposed , to finde which of them hath either of these three things .

LEt the three things bee a Ring , a peece of Gold , and a peece of Silver , or any other such like , and let them bee knowne privatly to your selfe , by these three vowels , a e i : or let there bee three persons that have different names , as Ambrose , Edmond and Iohn ; which privately you may note or account to your selfe once knowne by the aforesaid vowels , which signifie for the first vowell 1. for the second vowell 2. for the third vowell 3.

Now if the sayd three persons should by the mutuall consent of each other privatly change their names , it is most facill by the course and excellencie of numbers , distinctly to declare each ones name , so interchanged : or of three persons in private , the one should take a Ring , the other a peece of Gold , and the third should take a peece of Silver ; it is easie to finde which hath the Gold , the Silver , or the Ring , and it is thus done .

Take 30. or 40. Counters ( of which there is but 24. necessary ) that so you may conceale the way the better , and lay them downe before the parties , and as they sit or stand give to the first 1. Counter , which signifieth a the first vowell , to the second 2. Counters which represents e the second vowell , and to the third 3. Counters which stands for i. the third vowell : then leaving the other Counters upon the Table , retire apart , and bid him which hath the Ring , take as many Counters as you gave him , and hee that hath the Gold , for every one that you gave him , let him take 2. and he that hath the Silver for every one that you gave him let him take 4. this being done , consider to whom you gave one Counter , to whom two , and to whom three ; and marke what number of Counters you had at the first , for there are necessarily but 24. as was sayd before , the surpluse you may privately reject . And then there will be left either 1. 2. 3. 5. 6. or 7. & no other number can remaine , which if there be , then they have failed in taking according to the directions delivered : but if either of these numbers doe remaine , the resolution will bee discovered by one of these 6. words following , which ought to be had in memory , viz.

Salve , certa , anima , semita , vita , quies . 1. 2. 3. 5. 6. 7.

As suppose 5. did remaine , the word belonging unto it is semita , the vowels in the first two sillables are e and i , which sheweth according to the former directions that to whom you gave 2. Counters he hath the Ring ( seeing it is the second vowell represented by two as before ) and to whom you gave the 3. Counters he hath the Gould , for that i represents the third vowell , or 3. in the former direction , and to whom you gave one Counter , he hath the Silver , and so of the rest : the varietie of changes in which exercise , is layd open in the Table following .

diagram

rest men hid rest men hid 1 1 a 5 1 e 2 e 2 i 3 i 3 a 2 1 e 6 1 i 2 a 2 a 3 i 3 e 3 1 a 7 1 i 2 i 2 e 3 e 3 a

This feat may be done also without the former words by helpe of the Circle A. for having divided the Circle into 6. parts , write 1. within and 1. without , 2. within and 5. without , &c. the first 1. 2. 3. which are within with the numbers over them , belongs to the upper semicircle ; the other numbers both within and without , to the under semicircle ; now if in the Action there remaineth such a number which may bee found in the upper semicircle without , then that which is opposite within shewes the first , the next is the second , &c. as if 5. remaines , it shewes to whom hee gave 2. hee hath the Ring , to whom you gave 3. hee hath the Gould , &c. but if the remainder bee in the under semicircle , that which is opposite to it , is the first ; the next backwards towards the right hand is the second , as if 3. remaines , to whom you gave 1. he hath the Ring ; he that had 3. he had the Gould , &c.

PROBLEM . IX . How to part a vessell which is full of wine containing 8. Pints , into two equall parts , by two other vessels which contained as much as the greater vessell ; as the one being 5. Pints , and the other 3. Pints .

LEt the 3. vessels be represented by A. B. C. A. being full , the other two being emptie ; first powre out A. into B. untill it bee full : so there will be in B. 5. Pints and in A. but 3. Pints ; then powre out of B. into C. untill it bee full : so in C. shall be 3. Pints , in B 2. Pints , and in A. 3. Pints ; then powre the wine which is in C. into A. so in A. will be 6. Pints , in B 2. Pints , and in C. nothing : then powre out the wine which is in B. into the pot C. so in C. there is now 2. Pints , in B. nothing and in A. 6. Pints . Lastly , powre out of A. into B. untill it be full , so there will

diagram bee now in A. onely 1. Pint , in B. 5. Pints , and in C. 2. Pints : But it is now evident that if from B. you powre in unto the pot C. untill it bee full , there will remaine in B. 4. Pints , and if that which is in C. viz. 3 Pints bee powred into the vessell A. which before had 1. Pint , there shall bee in the vessell A. but halfe of its liquor that was in it at the first , viz 4. Pints as was required . Otherwise powre out of A. into C. untill it be full , which powre into B then powre out of A. into C. againe untill it bee full , so there is now in A. onely 2. Pints , in B. 3. and in C 3. then powre from C into B. untill it bee full , so in C. there is now but 1. Pint , 5. in B. and 2. in A. powre all that is in B. into A. then powre the wine which is in C. into B. so there is in C. nothing , in B. onely 1 Pint , and in A. 7. Pints : Lastly out of A. fill the pot C. so there will remaine in A. 4. Pints , or be but halfe full : then if the liquor in C. bee powred into B. it will bee the other halfe . In like manner might bee taken the halfe of a vessell which containes 12. Pints , by having but the measures 5. and 7. or 5. and 8. Now such others might be proposed , but wee omit many , in one and the same nature .

PROBLEM . X. To make a sticke stand upon the tipp of ones finger , without falling .

FAsten the edges of two knives or such like of equall poise , at the end of the sticke , leaning out somewhat from the sticke , so that they may counterpoise one another ; the sticke being sharpe at the end and held upon the top of the finger , will there rest without supporting : if it fall it must fall together , and that perpendicular or

diagram plumbe wise , or it must fall side-wise or before one another ; in the first manner it cannot : for the Center of gravitie is supported by the top of the finger : and seeing that each part by the knives is counter-poysed it cannot fall sidewise , therefore it cannot fall no wise .

In like manner may great peeces of Timber as Ioists &c. be supported , if unto one of the ends be applyed convenient proportionall counterpoises , yea a Lance or Pike , may stand perpendicular in the Aire upon the top of ones finger : or placed in the midst of a Court by helpe of his Center of gravitie .

EXAMINATION .

THis Proposition seemes doubtfull for to imagine absolutely , that a Pike , or such like , armed with two knives , or other things shall stand upright in the Ayre , and so remaine without any other support , seeing that all the parts hath an infinite difference of propensitie to fall ; and it is without question that a staffe so accommodated upon his Center of gravitie , but that it may incline to some one part without some remedie be applyed , and such as is here specified in the Probleme will not warrant the thing , nor keepe it from falling ; and if more knives should be placed about it , it should cause it to fall more swiftly , for asmuch as the superiour parts ( by reason of the Centricall motion ) is made more ponderous and therefore lesse in rest .

To place therefore this prop really , let the two knives , or that which is for counterpoise , be longer alwaies than the staffe and so it will hang together as one body : and it will appeare admirable if you place the Center of gravitie , neare the side of the top of the finger or point ; for it will then hang Horizontall , and seeme to hang onely by a touch , yet more strange if you turne the point or top of the finger upside downe .

PROBLEM . XI . How a milstone or other Ponderositie , may be supported by a small needle , without breaking or any wise bowing the same .

LEt a needle be set perpendicular to the Horizon , and the center of gravitie of the stone , be placed on the top of the Nedle : it is evident that the stone cannot fall , for asmuch as it hangs in aequilibra , or is counterpoysed in all parts alike ; and moreover it cannot bow the Needle more on the one side , than on the other , the Needle will not therefore be eyther broken or bowed ; if otherwise , then the parts of the Needle must penitrate and sinke one with another : that which is absurd and impossible to nature : therefore it shall be supported . The experiments which are

diagram made upon trencher plates , or such like lesser thing doth make it most credible in greater bodies .

But here especially is to bee noted that the Needle ought to be uniforme in matter and figure , and that it be erected perpendicular to the Horizon , and lastly that the Center of gravitie be exactly found .

PROBLEM . XII . To make three knives hang and move upon the point of a Needle .

FIt the three knives in forme of a ballance , and houlding a Needle in your hand , and place the backe of

diagram that knife which lies crossewise to the other two , upon the point of the Needle : as the figure here sheweth you ; for then in blowing softly upon them , they will easily turne & move upon the point of the needle without falling .

PROBLEM . XIII . To finde the weight of smoake , which is exhaled of any combustible body whatsoever .

LEt it be supposed that a great heape of Fagots , or a load of straw waying 500. l should be fired , it is evident that this grosse substance will bee all inverted into smoake and Ashes : now it seemes that the smoake waighes nothing ; seeing it is of a thinne substance now delated in the Aire , notwithstanding if it were gathered and reduced into the thickest that it was at first , it would bee sensibly waighty : waigh therefore the ashes which admit 50 pound , now seeing that the rest of the matter is not lost , but is exhaled into smoke , it must necessarily bee , that the rest of the waight ( to wit ) 450 pound , must bee the waight of the smoke required .

EXAMINATION .

NOw although it bee thus delivered , yet here may be noted , that a ponderositie in his owne medium is not waightie : for things are sayd to be waighty , when they are out of their place , or medium : and the difference of such gravitie , is according to the motion : the smoke therefore certainely is light being in its true medium ( the ayre ) if it should change his medium , then would we change our discourse .

PROBLEM . XIIII . Many things being disposed circular , ( or otherwise ) to find which of them , any one thinkes upon .

Suppose that having ranked 10 things , as A B C D E F G H I K , Circular ( as the figure showeth ) and that one had touched or thought upon G. which is the 7 : aske the partie at what letter he would begin to account ( for ●●count he must , otherwise it cannot bee done ) which suppose , at E which is the 5 place , then ●●d secretly to this 5. 10. ( which is the number of the Circle ) and it makes 15 , bid him account 15. backward from E , beginning his account with that

diagram number hee thought upon , so at E hee shall account to himselfe , 7 , at D account 8 , at C account 9 &c. So the account of 15 will exactly fall upon G , the thing or number thought upon : and so of others : but to conceale it the more , you may will the party from E to account 25. 35 &c. and it will be the same .

There are some that use this play at cards , turned up side downe , as the ten simple Cards , with the King and Queene , the King standing for 12 , and the Queene for 11 , and so knowing the scituation of the Cards : & thinking a certaine houre of the day : cause the partie to account from what Card hee pleaseth : with this Proviso , that when you see where hee intends to account set 12. to that number , so in counting as before , the end of the account shall fall upon the Card : which shall denote or shew the houre thought upon , which being turned up will give grace to the action , and wonder to those that are ignorant in the cause .

PROBLEM . XV. How to make a dore , or a Gate , which shall open on both sides .

ALL the skill and subtiltie of this , rests in the artificiall disposer of 4 plates of Iron , two at the higher end , and two at the lower end of the Gate : so that one side may move upon the hookes or hindges of the Posts , and by the other end may be made fast to the Gate , and so moving upon these hindges , the Gate will open upon one side with the aforesayd plates , or hookes of Iron : and by helpe of the other two plates , will open upon the other side .

PROBLEM . XVI . To shew how a Ponderositie , or heavie thing , may be supported upon the end of a staffe ( or such like ) upon a Table , and nothing holding or touching it .

TAke a paile which hath a handle , and fill it full of water ( or at pleasure : ) then take a staffe or sticke which may not rowle upon the Table as E C , and place the handle of the Paile upon the staffe ; then place another staffe , or sticke , under the staffe C E , which may reach from the bottome of

diagram the Paile unto the former staffe C E , perpendicular wise : which suppose F. G , then shall the Paile of water hang without falling , for if it fall it must fall perpendicularly , or plumbe wise : and that cannot bee seeing the staffe C E , supports it , it being parallel to the Horizon and sustained by the Table , and it is a thing admirable that if the staffe C E , were alone from the table , and that end of the staffe which is upon the Table were greater and heavier than the other : it would be constrained to hang in that nature .

EXAMINATION .

NOw without some experience of this Probleme , a man would acknowledge either a possibility or impossibilitie ; therefore it is that very touchstone of knowledge in any thing , to discourse first if a thing bee possible in nature , and then if it can bee brought to experience and under sence without seeing it done . At the first , this proposition seemes to be absurd , and impossible at the first . Notwithstanding , being supported with two stickes as the figure declareth , it is made facill : for the Horizontall line to the edge of the Table , is the Center of motion ; and passeth by the Center of gravitie , which necessarily supporteth it .

PROBLEM . XVII . Of a deceitfull Bowle to play withall .

MAke a hole in one side of the Bowle , and cast moulten Lead therein , and then make up the hole close , that the knavery or deceit be not perceived : you will have pleasure to see , that notwithstanding the Bowle is cast directly to the play , how it will turne away side-wise : for that on that part of the Bowle which is heavier upon the one side than on the other , it never will goe truly right , if artificially it bee not corrected ; which will hazard the game to those which know it not : but if it bee knowne that the leady side in rowling , be alwayes under or above , it may goe indifferently right ; if otherwise , the weight will carry it alwayes sidewise .

PROBLEM . XVIII . To part an Apple into 2. 4. or 8 like parts , without breaking the Rind .

Passe an needle and threed under the Rind of the Apple ; and then round it with diverse turnings , untill you come to the place where you began : then draw out the thred gently , and part the Apple into as many parts as you thinke convenient : and so the parts may bee taken out betweene the parting of the Rind , and the rind remaining alwayes whole .

PROBLEM . XIX . To finde a number thought upon without asking of any questions , certain operations being done .

BId him adde to the number thought ( as admit 15 ) halfe of it , if it may bee , if not the greatest halfe that exceede the other but by an unite , which is 8 ; and it makes 23 : Secondly , unto this 23. adde the halfe of it if it may bee , if not the greatest halfe viz 12. makes 35. in the meane time ; note that if the number thought upon cannot be halfed at the first time as here it cannot : then for it keepe 3. in the memory , if at the second time it will not be equally halfed , reserve 2. in memory , but if at both times it could not be equally halved , then may you together reserve five in memory : this done , cause him from the last summe , viz. 35. subtract the double of the number thought , viz. 30. rest 5. will him to take the halfe of that if he can , if not , reject 1. and then take the halfe of the rest : which keepe in your memory : then will him to take the halfe againe if he can , if not take one from it , which reserve in your memory , and so perpetually halveing untill 1. remaine : for then marke how many halfes there were taken , for the first halfe account 2 , for the second 4 , for the third 8 , &c. and adde unto those numbers the ones which you reserved in memory , so there being 5 remaining in this proposition , there were 2 halfeings : for which last I account 4 , but because it could not exactly be halved without rejecting of 1 : I adde the 1 therefore to this 4 , makes 5 , which halfe or summe alwayes multiplyed by 4 , makes 20 : from which subtract the first 3 and 2 , because the halfe could not bee formerly added , leaves 15 , the number thought upon .

Other examples .

the number thought upon The number thought 79 The greatest halfe 40 3 The summe 119 The number thought 12 The greatest halfe of which is 60 2 The halfe of it 6 The summe of it is 179 The summe 18 The double of 79 is 158 The halfe of it 9 Which taken from it , rests 21 The summe of it 27 The lesser half 10. which halve : The double of the number 24 The halfe of this is 5 which makes Which taken away , rests 3 The halfe of it 1 The half of this is 2 which is 10 For which account 2 The half of this is 1 , with 10 and 11 is 21. this 21 which is the double of the last halfe with the remainder being multiplied by 4 makes 84 , from which take the aforesaid 3 and 2 , rest 79 , the number thought upon . and 1 put to it because the 3 could not bee halfed , makes 3 this multiplied by 4 makes 12

PROBLEM . XX. How to make an uniforme , & an inflexible body , to passe through two small holes of divers formes , as one being circular , & the other square , Quadrangular , and Triangularwise , yet so that the holes shall be exactly filled .

THis Probleme is extracted from Geometricall observations , and seemes at the first somewhat obscure , yet that which may be extracted in this nature , will appeare more difficult and admirable . Now in all Geometricall practices , the lesser or easier Problemes doe alwayes make way to facilitate the greater : and the aforesaid Probleme is thus resolved . Take a Cone or round Pyramedie , and make a Circular hole in some boord , or other hard materiall , which may bee equall to the bases of the Cone , and also a Triangular hole , one of whose sides may be equall to the Diamiter of the circle , and the other two sides equall to the length of the Cone : Now it is most

diagram evident that this Conicall or Pyramidall body , will fill up the Circular hole , and being placed side-wise will fill up the Triangular hole : moreover if you cause a body to be turned , which may be like to two Pyramides conjoyned , then if a Circular hole bee made , whose Diamiter is equall to the diamiter of the Cones conjoyned , and a Quadrangular hole , whose slopeing sides bee equall to the length of each side of the Pyramidie , and the bredth of the hole equall to the diamiter of the Circle , this conjoyned Pyramidie shall exactly fill both the Circular hole , and also Quadrangle hole .

PROBLEME . XXI . How with one uniforme body or such like to fill three severall holes : of which the one is round , the other a just square ; and the third an ovall forme .

THis proposition seemes more subtill than the former , yet it may bee practised two wayes : for the first , take a Cilindricall body as great or little as you please : Now it is evident that it will fill a Circular hole , which is made equall to the basis of it : if it bee placed downe right , and will also fill a long square ; whose sides are equall unto the Diamiter and length of the Cylinder , and

diagram according to Pergeus , Archimedes , &c. in their Cylindricall demonstrations , a true Ovall is made when a Cylinder is cut slopewise , therefore if the Ovall have bredth equall unto the Diamiter of the Basis of the Cylinder , & any length whatsoever : the Cylinder being put into his owne Ovall hole shall also exactly fill it .

The second way is thus , make a Circular hole in some board , and also a square hole , the side of which Square may bee equall to the Diamiter of the Circle : and lastly make a hole Ovall wise whose bredth may be equall unto the diagonall of the Square ; then let a Cylindricall body bee made , whose Basis may be equall unto the Circle , and the length equall also to the same : Now being placed downe right shall fall in the Circle , and flat-wise will fit the Square hole , and being placed sloping-wise will fill the Ovall .

EXAMINATION .

YOu may note upon the last two Problemes farther , that if a Cone bee cut Eclipticke-wise , it may passe through an Issocele Triangle through many Scalen Triangles , and through an Ellipsis ; and if there be a Cone cut scalen wise , it will passe through all the former , onely for the Ellipsis place a Circle : and further if a sollid Colume be cut Eclipticke-wise it may fill a Circle , a Square , divers Parallelogrames , and divers Ellipsis , which have different Diamiters .

PROBLEM XXII . To finde a number thought upon after another manner , than that which is formerly delivered .

BId him that he multiply the number thought upon , by what number he pleaseth , then bid him divide that product by any other number , and then multiply that Quotient by some other number ; and that product againe divide by some other , and so as often as he will : and here note that he declare or tell you by what number he did multiply and devide . Now in the same time take a number at pleasure , and secretly multiply and divide as often as he did : then bid him devide the last number by that which hee thought upon . In like manner doe yours privately , then will the Quotient of your devisor be the same with his , a thing which seemes admirable to those which are ignorant of the cause . Now to have the number thought upon without seemeing to know the last Quotient , bid him adde the number thought upon to it , and aske him how much it makes : then subtract your Quotient from it , there will remaine the number thought upon . For example , suppose the number thought upon were 5 , multiply it by 4 makes 20 : this divided by 2 , the Quotient makes 10 , which multiplyed by 6 makes 60 , and divided by 4 makes 15 : in the same time admit you thinke upon 4 , which multiplyed by 4 makes 16 , this divided by 2 makes 8 , which multiplyed by 6 makes 48 , and divided by 4 makes 12 ; then divide 15 by the number thought which was 5 , the Quotient is 3 ; divide also 12 by the number you tooke , viz. 4 , the Quotient is also 3 as was declared ; therefore if the Quotient 3 bee added unto the number thought viz 5 , it makes 8 , which being known the number thought upon is also knowne .

PROBLEM . XXIII . To finde out many numbers that sundry persons , or one man hath thought upon .

IF the multitude of numbers thought upon be odde , as three numbers , five numbers , seaven &c. as for example let 5 numbers thought upon be these , 2 , 3 , 4 , 5 , 6. Bid him declare the sum of the first and second , which will be 5 ; the second and third which makes 7 , the third and fourth which makes 9 , the fourth and fifth which makes 11 , and so alwayes adding the two next together ; aske him how much the first and last makes together , which is 8 : then take these summes and place them in order , and adde all these together which were in the odde places : that is the first , third , and fifth , viz. 5. 9 , 8 , makes 22. In like manner adde all these numbers together which are in the even places , that is in the second and fourth places , viz. 7 and 11 makes 18 , subtract this from the former 22 , then there will remaine the double of the first number thought upon , viz. 4 , which knowne the rest is easily knowne : seeing you know the summe of the first and second ; but if the multitude of numbers bee even as these sixe numbers , viz. 2 , 3 , 4 , 5 , 6 , 7 , cause the partie to declare the summe of each two , by antecedent and consequent , and also the summe of the second and last which will bee 5 , 7 , 9 , 11 , 13 , 10 , then adde the odde places together , except the first that is 9 , and 13 , makes 22 ; adde also the even places together , that is 7 , 11 , 10 , which makes 28 ; subtract the one from the other , there shall remaine the double of the second number thought upon , which knowne all the rest are knowne .

PROBLEM . XXIIII . How is it that a man in one and the same time , may have his head upward , and his feet upward , being in one and the same place .

THe answere is very facill , for to bee so he must be supposed to be in the center of the earth : for as the heavens is above on every side , Coelum undique sursum , all that which lookes to the heavens being distant from the center is upward ; and it is in this sense that Maurolyeus in his Cosmographie , and first dialogue , reported of one that thought hee was led by one of the Muses to hell , where hee saw Lucifer sitting in the middle of the world , and in the center of the earth as in a Throne : having his head and feete upward .

PROBLEM . XXV . Of a Ladder by which two men ascending at one time ; the more they ascend the more they shall be asunder , notwithstanding one being as high as another .

THis is most evident , that if there were a Ladder halfe on this side of the Center of the earth , and the other halfe on the other side : and that two at the Center of the world at one instant , being to ascend the one towards us , and the other towards our Antipodes , they should in ascending goe farther and farther , one from another ; notwithstanding both of them being of like height .

PROBLEM . XXVI . How it is that a man having but a Rode or Pole of land ; doth bragge that he may in a right line passe from place to place above 3000 miles .

THe opening of this is easie , forasmuch as he that possesseth a Rode of ground possesseth not only the exterior surface of the earth , but is master also of that which extends even to the center of the earth , and in this wise all heritages and possessions are as so many Pyramides , whose summets or points meete in the center of the earth , and the basis of them are nothing else but each mans possession , field , or visible quantitie ; and therefore if there were made or imagined so to be made , a descent to goe to the bottome of the heritage , which would reach to the center of the earth ; it would bee above 3000 miles in a right line as before .

PROBLEM . XXVII . How it is that a man standing upright , and looking which way he will , he looketh true North or South .

THis happeneth that if the partie be under either of the Poles , for if he be under the North pole , then looking any way hee looketh South , because all the Meridians concurre in the Poles of the world , and if he be under the South pole , hee lookes directly North by the same reason .

PROBLEM . XXVIII . To tell any one what number remaines after certaine operations being ended , without asking any question .

BId him to thinke upon a number , and will him to multiply it by what number you thinke convenient : and to the product bid him adde what number you please , provided that secretly you consider , that it may be divided by that which multiplied , and then let him divide the sum by the number which he first multiplied by , and subtract from this Quotient the number thought upon : In the same time divide apart the number which was added by that which multiplied , so then your Quotient shall bee equall to his remainder , wherefore without asking him any thing , you shall tell him what did remaine , which will seeme strange to him that knoweth not the cause : for example , suppose he thought 7 , which multiplied by 5 makes 35 , to which adde 10 , makes 45 , which divided by 5 yeeldes 9 ; from which if you take away one the number thought , ( because the Multiplier divided by the divisor gives the Quotient 1 , ) the rest will be 2 , which will be also proved , if 10 the number which was added , were divided by 5 , viz. 2.

PROBLEM . XXIX . Of the play with two severall things .

IT is a pleasure to see and consider how the science of numbers doth furnish us , not one●y with sports , to recreate the spirits , but al●o bring us to the knowledge of admirable ●hings , as shall in some measure bee shewen in this ensuing progression . In the meane time to produce alwaies some of them : suppose that a man hold divers things in his hand , as Gould and Silver , and in one hand he held the Gould , and in the other hand hee held the Silver : to know subtilly , and by way of divination , or artificially in which hand the Gold or Silver si ; attribute to the gould , or suppose it have a certaine prise , & so likewise attribute to the Silver another price , conditionally that the one be od and the other even : as for example , bid him that the Gould be valued at 4. Crownes , or shillings , and the Silver at 3. Crownes or 3. Shillings or any other number so that one be odde , and the other even as before : then bid him triple that which is in the right hand , and double that which is in the left hand , and bid him adde these two products together , and aske him if it be even or odde , if it be even then the Gould is in the right hand , if odde the Gould is in the left hand .

PROBLEM . XXX . Two numbers being proposed unto two severall parties , to tell which of these numbers is taken by each of them .

AS for example : admit you had proposed unto two men whose names were Peter , and Iohn , two numbers , or peeces of money , the one even , and the other odde , as 10. and 9. and let the one of them take one of the numbers , and the other partie take the other number , which they place privatly to themselves : how artificially , according to the congruitie , and excellency of numbers , to finde which of them did take 10. and which 9. without asking any question : and this seemes most subtill , yet delivered howsoever differing little from the former , and is thus performed : Take privately to your selfe also two numbers , the one even and the other odde , as 4. and 3. then bid Peter that he double the number which he tooke , and doe you privately double also your greatest number ; then bid Iohn to triple the number which he hath , and doe you the like upon your last number : adde your two products together , and marke if it be even or odde , then bid the two parties put their numbers together , and bid them take the halfe of it , which if they cannot doe , then immediatly tell Peter hee tooke 10. and Iohn 9. because the aggregate of the double of 4. and the triple of 3. makes odde ; and such would be the aggregate or summe of ●he double of Peters number and Iohns number , ●f Peter had taken 10. if otherwise , then they might have taken halfe , and so Iohn should have taken 10. and Peter 9. as suppose Peter had taken 10. the double is 20 , and the triple of ●9 . the other number is 27. which put together makes 47. odde : in like manner the double of your number conceived in minde , viz. 4. makes 8. and the triple of the 3. the other number , makes 9. which set together makes 17. odde : Now you cannot take the halfe of 17. nor 47. which argueth that Peter had the greater number , for otherwise the double of 9. is 18. and the triple of 10. is 30. which set together makes 48. the halfe of it may be taken : therefore in such case Peter tooke the lesse number : and Iohn the greater , and this being done cleanly carries much grace with it .

PROBLEM . XXXI . How to describe a Circle that shall touch 3. Points placed howsoever upon a plaine , if they be not in a right line .

LEt the three points bee A. B. C. put one foot of the Compasse upon A. and describe an Arch of a Circle at pleasure : and placed at B. crosse that Arke in the two points E. and F. and placed in C. crosse the Arke in G. and H. then lay a ruler upon G.H. and draw a line , and place a Ruler upon E.

diagram and F. cut the other line in K. so K. is the Center of the Circumference of a Circle , which will passe by the said three points A. B. C. or it may bee inverted having a Circle drawne , to finde the Center of that Circle . Make 3. points in the circumference , and then use the same way : so shall you have the Center a thing most facill , to every practitioner in the pinciples of Geometrie .

PROBLEM . XXXII . How to change a Circle into a square forme .

MAke a Circle upon pastboard or other materiall , as the Circle A. C. D. E. of which A. is the Center ; then cut it into 4. quarters and dispose them so , that A. at the center of the Circle may alwaies be at the Angle of the square , and so the foure quarters of the Circle being placed

diagram so , it will make a perfect square , whose side A.A. is equall to the diamiter B. D. Now here is to bee noted that the square is greater than the Circle by the vacuity in the middle , viz. M.

PROBLEM . XXXIII . With one and the same compasses , and at one and the same extent , or opening , how to describe many Circles concentricall , that is , greater or lesser one than another .

IT is not without cause that many admire how this proposition is to bee resolved ; yea in the judgement of some it is thought impossible : who consider not the industrie of an ingenious Geometritian , who makes it possible , and that most facill , sundry wayes ; for in the first place if you make a Circle upon a fine plaine , and upon the Center of that Circle , a small pegge of wood be placed , to bee raised up and put downe at pleasure by helpe of a small hole made in the Center , then with the same opening of the Compasses , you may describe Circles Concentricall :

diagram that is , one greater or lesser than another : for the higher the Center is lifted up , the lesser the Circle will be . Secondly , the compasse being at that extent upon a Gibus body , a Circle may bee described , which will be lesse than the former , upon a plaine , and more artificially upon a Globe , or round bowle : and this againe is most obvious upon a round Pyramide , placing the Compasses upon the top of it which will be farre lesse than any of the former ; and this is demonstrated by the 20. Pro. of the first of Euclids , for the Diamiter E.D. is lesse than the line A D. A E. taken together , and the lines A D. A E. being equall to the Diamiter B C. because of the same distance or extent of opening the Compasses , it followes that the Diamiter E D. and all his Circles together is much lesse than the Diamiter , and the Circle B C. which was to be performed .

PROBLEM . XXXIIII . Any numbers under 10. being thought upon , to finde what numbers they were .

LEt the first number be doubled , and unto it adde 5. and multiplyed that summe by 5. and unto it adde 10. and the next number thought upon ; multiplye this same againe by 10. and adde unto it the next number , and so proceede : now if he declare the last summe ; marke if he thought but upon one figure , for then subtract onely 35. from it , and the first figure in the place of tens is the number thought upon : if he thought upon two figures , then subtract 35. also , and the 2. also the said 35. from his last summe , and the two figures which remaines are the number thought upon : if he thought upon three figures , then subtract 350. and then the first 3. figures are the numbers thought upon , &c. so if one thought upon these numbers 5.7 . 9 , 6. double the first , makes 10. to which adde 5. makes 15. this multiplyed by 5. makes 75. to which adde 10. makes 85. to this adde the next number , viz. 7. makes 92. this multiplyed by 10. makes 920. to which adde the next number , viz. 9. makes 929. which multiplyed by 10. makes 9290. to which adde 6. makes 9296. from which subtract 3500. resteth 5796. the foure numbers thought upon . Now because the two last figures are like the two numbers thought upon : to conceale this bid him take the halfe of it , or put first 12. or any other number to it , and then it will not be so open .

PROBLEM . XXXV . Of the Play with the Ring .

AMongst a company of 9. or 10. persons , one of them having a Ring , or such like : to finde out in which hand : upon which finger , joynt it is ; this will cause great astonishment to ignorant spirits , which will make them beleeve that he that doth it workes by magicke , or witchcraft : But in effect it is nothing else but an nimble act of Arithmeticke , founded upon the precedent Probleme : for first it is supposed that the persons stand or sit in order that one is first , the next second , &c. likewise there must be imagined that of these two hands the one is first and the other second : and also of the five fingers the one is first , the next is second , and lastly of the joynts , the one is as 1. the other as 1. the other is as 2. the other as 3. &c. from whence it appeares that in performing this Play there is nothing else to be done than to thinke 4. numbers : for example if the forth person had the Ring in his left hand : and upon the fift finger and third joynt , and I would divine and finde it out thus : I would proceede as in the 35. Probleme : in causing him to double the first number : that is , the number of persons , which was 4. and it makes 8. to which ad 5. makes 13. this multiplyed by 5. makes 65. put 10. to it , makes 75. unto this put 2. for the number belonging to the left hand , and so it makes 77. which multiplyed by 10. makes 770. to this adde the number of the fingers upon which the Ring is , viz. 5. makes 775. this multiplyed by 10 makes 7750. to which adde the number for the joynt upon which the Ring is viz. the third joynt , makes 7753. to which cause him to adde 14. or some other number , to conceale it the better : and it makes 7767. which being declared unto you , subtract 3514. and there will remaine 4. 2. 5. 3. which figures in order declares the whole mystery of that which is to bee knowne , 4. signifieth forth person , 2. the left hand , 5. the fifth finger , and 3. the third joynt of that finger .

PROBLEM . XXXVI . The Play of 3 4. or more Dice .

THat which is said of the two precedent Problemes may be applyed to this of Dice ( and many other particular things ) to finde what number appeare upon each Dice being cast be some one , for the points that are upon any side of a Dice are alwayes lesse than 10. and the points of each side of a Dice may be taken for a number thought upon : therefore the Rule will be as the former : As for example , one having throwne three Dice & you would declare the numbers of each one , or how much they make together , bid him double the points of one of the Dice , to which bid him adde 5. then multiply that by 5. and to it adde 10. and to the summe bid him adde the number of the second Dice : and multiplie that by 10. lastly , to this bid him adde the number of the last Dice , and then let him declare the whole number : then if from it you subtract 350. there will remaine the number of the three Dice throwne .

PROBLEM . XXXVII . How to make water in a Glasse seeme to boyle and sparkle .

TAke a Glasse neare full of water or other liquor ; and setting one hand upon the foote of it , to hould it fast : turne slightly one of the fingers of your other hand upon the brimme , or edge of the Glasse ; having before privatly wet your finger : and so passing softly on with your finger in pressing a little : for then first the Glasse will begin to make a noyse : secondly the parts of the Glasse will sencibly appeare to tremble , with notable rarification and condensation : thirdly the water will shake , seeme to boyle : fourthly it will cast it selfe out of the Glasse , and leape out by small drops , with great astonishment to the standers by ; if they be ignorant of the cause of it , which is onely in the Rarifaction of the parts of the Glasse : occasioned by the motion and pressure of the finger .

EXAMINATION .

THe cause of this , is not in the rarifaction of the parts of the Glasse , but it is rather in the quicke locall motion of the finger , for reason sheweth us that by how much a Body draweth nearer to a qualitie , the lesse is it subject or capable of another which is contrary unto it : now condensation , and rarifaction are contrary qualities and in this Probleme there is three bodies considered , the glasse , the water , and the ayre ; now it is evident that the Glasse being the most solid , and impenitrable Body , is lesse subject , and capable of rarifaction than the water , the water is lesse subject than the ayre , and if there be any rarifaction , it is rather considerable in the ayre than in the water , which is inscribed by the Glasse , and above the water , and rather in the water than in the Glasse : the agitation , or the trembling of the parts of the Glasse to the sence appeares not : for it is a continued body ; if in part why then not in the whole ; and that the water turnes in the Glasse this appeares not , but onely the upper contiguous parts of the water : that at the bottome being lesse subject to this agitation , and it is most certaine that by how much quicker the circular motion of the finger upon the edge of the Glasse is , by so much the more shall the Ayre be agitated , and so the water shall receive some apparant affection more or lesse from it , according to that motion : as wee see from the quicknesse of winde uppon the Sea , or calme thereof , that there is a great or lesser agitation in the water ; and for further examination , we leave it to the search of these which are curious .

PROBLEME XXXVIII . Of a fine vessell which holds wine or water , being cast into it at a certaine height , but being filled higher , it will runne out of its owne accord .

LEt there be a vessell A. B. C. D. in the middle of which place a Pipe ; whose ends both above at E , and below at the bottome of the vessell as at F. are open ; let the end E. be somewhat lower than the brimme of the Glasse : about this Pipe place another Pipe as H. L , which mounts a little above E , and let it most diligently be closed at H. that no Aire enter in thereby , and this Pipe at the bottome may have a small hole to give passage unto the water : then powre in water or wine , and as long as it mounts not above E , it is safe ; but if you powre in the water so that it mount above it , farewell all : for it will not cease untill it be all gone out : the same may be

diagram done in disposing any crooked Pipe in a vessell in the manner of a faucet or funnell , as in the figure H : for fill it , under H. at pleasure , and all will goe well ; but if you fill it unto H. you will see fine sport , for then all the vessell will bee empty incontinent , and the subtiltie of this will seeme more admirable , if you conceale the Pipe by a Bird , Serpent , or such like , in the middle of the Glasse . Now the reason of this is not difficult to these which know the nature of a Cocke or Faucet ; for it is a bowed Pipe one end of which is put into the water or liquor , and sucking at the other end untill the Pipe be full , then will it runne of it selfe ; and it is a fine secret in nature to see , that if the end of the Pipe which is out of the water be lower than the water , it will runne out without ceasing : but if the mouth of the Pipe bee higher than the water or levell with it , it will not runne , although the Pipe which is without be many times bigger than that which is in the water : for it is the property of water to keepe alwayes exactly levell .

EXAMINATION .

HEre is to be noted that if the face of the water without be in one and the same plain , with that which is within , though the outtermost Pipe bee ten times greater than that which is within : the water naturally will not runne , but if the plaine of the water without be any part lower than that which is within , it will freely runne : and here may be noted further that if the mouth of the Pipe which is full of water , doth but onely touch the superficies of the water within , although the other end of the Pipe without be much lower than that within , the water it will not run at all : which contradicts the first ground ; hence we gather that the pressure or ponderositie of the water within , is the cause of running in some respect .

PROBLEM . XXXIX . Of a Glasse very pleasant .

SOmetimes there are Glasses which are made of a double fashion , as if one Glasse were within another , so that they seeme but one , but there is a little space betweene them . Now powre wine or other liquor betweene the two edges by helpe of a Tunnell , into a little hole left to this end : so will there appeare two fine delusions or fallacies ; for though there be not a droppe of wine within the hollow of the Glasse , it will seeme to these which behold it that it is an ordinary Glasse full of wine , and that especially to these which are sidewise of it ; and if any one moove it , it will much confirme it , because of the motion of the wine : but that which will give most delight , is that if any one shall take the Glasse , and putting it to his mouth shall thinke to drinke the wine ; instead of which hee shall suppe the aire : and so will cause laughter to these that stand by : who being deceived , will hold the Glasse to the light ; and thereby considering that the rayes or beames of the light are not reflected to the eye , as they would bee if there were a liquid substance in the Glasse : hence they have an assured proofe to conclude , that the hollow of the Glasse is totally empty .

PROBLEM . XL. If any one should hold in each hand , as many peeces of money as in the other , how to finde how much there is .

BId him that holdes the money that hee put out of one hand into the other what number you thinke convenient : ( provided that it may be done , ) this done , bid him that out of the hand that he put the other number into , that he take out of it as many as remaine in the other hand , and put it into that hand : for then be assured that in the hand which was put the first taking away : there will be found just the double of the number taken away at the first . Example , admit there were in each hand 12 Shillings or Counters , and that out of the right hand you bid him take 7 and put it into the left : and then put into the right hand from the left as many as doth remaine in the right , which is 5 : so there will bee in the left hand 14 , which is the double of the number taken out of the right hand , to wit 7 : then by some of the rules before delivered , it is easie to finde how much is in the right hand , viz. 10.

PROBLEM . XLI . Many Dice being cast , how artificially to discover the number of the points that may arise .

SVppose any one had cast three Dice secretly , bid him that he adde the points that were upmost together : then putting one of the Dice apart , unto the former summe adde the points which are under the other two , then bid him throw these two Dice , and marke how many points a paire are upwards , which adde unto the former summe : then put one of these Dice away not changing the side , marke the points which are under the other Dice , and adde it to the former summe : lastly throw that one Dice , and whatsoever appeares upward adde it unto the former summe ; and let the Dice remaine thus : this done , comming to the Table , note what points doth appeare upward upon the three Dice which adde privately together , and unto it adde 21 or 3 times 7 : so this Addition or summe shall be equall to the summe which the party privately made of all the operations which hee formerly made . As if hee should throw three Dice , & there should appeare upward 5 , 3 , 2. the sum of them is 10 : & setting one of them aparte as 5. unto 10 , adde the points which are under 3 and 2 , which is 4 and 5 ; and it makes 19 : then casting these two Dice suppose there should appeare 4 and 1 , this added unto 9 makes 24 : and setting one of these two Dice aparte as the 4. unto the former 24 , I adde the number of points which is under the other Dice , viz. under 1 , that is 6 , which makes 30. Last of all I throw that one Dice , and suppose there did appeare 2 , which I adde to the former 30 , and it makes 32 : then leaving the 3 Dice thus , the points which are upward will be these , 5 , 4 , 2 , unto which adde secretly 21 , ( as before was said ) so have you 32 the same number which he had : and in the same manner you may practice with 4 , 5 , 6 , or many Dice or other bodies , observing onely that you must adde the points opposite of the Dice : for upon which depends the whole demonstration or secret of the play ; for alwayes that which is above and underneath makes 7 : but if it make another number , then must you adde as often that number .

PROBLEM . XLII . Two mettals as Gold and Silver , or of other kind weighing alike , being privately placed into two like Boxes , to finde which of them the Gold or Silver is in .

diagram

But because that this experiment in water hath diverse accedents , and therefore subject to a caution ; and namely because the matter of the chest , mettle , or other things may hinder :

Behold here a more subtill and certaine invention to finde and discover it out without weighing it in the water : Now experience and reason sheweth us that two like bodies or magnitudes of equall weight , and of divers mettalls , are not of equall quantity : & seeing that gold is the heaviest of all mettalls , it will occupie lesse roome or place ; from which will follow that the like weight of lead in the same forme , will occupie or take up more roome or place . Now let there be therfore presented 2 globes or chests of wood or other matter alike , and equall one to the other , in one of which in the middle there is another Globe or body of lead weighing 12 pound ( as C , ) and in the other a Globe or like body of gold weighing 12 pound ( as B. ) Now it is supposed that the wooden globes or chests are of equall weight , forme , and magnitude● and to discover in which the gold or lead is in , take a broade paire of Compasses and clip one of the coffers or globes somewhat from the middle as at D ; then fixe in the chest or globe a small peece of iron between the feet of the compasses , as E K , at the end of which hang a weight G so that the other end may be counterpoysed , and hang in aequilibro : & doe the like to the other chest or globe . Now if that the other chest or globe being clipsed in like distant from the end , and hanging at the other end the same weight G. there be found no difference : then clipse them nearer towards the middle , that so the points of the Compasse may bee against some of the mettell which is inclosed : or just against the extremitie of the gold as in D , and suppose it hang thus in aequilibrio ; it is certaine that in the other coffer is the lead ; for the points of the Compasses being advanced as much as before , as at F. which takes up a part of the lead , ( because it occupies a greater place than the gold ) therefore that shall helpe the weight G to weigh , and so will not hang in aequilibrio except G be placed neare to F : hence we may conclude that there is the lead ; and in the other chest or globe there is the gold .

EXAMINATION .

IF the two Boxes being of equall magnitude weighed in the aire be found to bee of equall weight , they shall necessarily take up like place in the water , & therefore weigh also one as much as another : hence there is no possibilitie to finde the inequallitie of the mettells which are inclosed in these Boxes in the water : the intention of Archimedes was not upon contrary mettells inclosed in equall Boxes , but consisted of comparing mettels , simple in the water one with another : therefore the inference is false and absurd .

PROBLEM : XLIII . Two Globes of diverse mettles , ( as one gold and the other copper ) yet of equall weight being put into a boxe as B. G. to finde in which end the gold or copper is .

THis is discovered by the changing of the places of the two Bowles or Globes having the same counterpoyse H. to bee houng at the other side as in N. and if the Gould which is the lesser Globe were before the nearest to the handle D.E. having now changed his place will bee farthest from the handle D. E. as in K. therefore the Center of gravitie of the two Globes taken together , shall bee farther separate from the midle of the

diagram handle ( under which is the Center of gravitie of the Box ) than it was before , and seeing that the handle is alwayes in the midle of the box , the waight N. must bee augmented , to keepe it in aequilibria : and by this way one may know , that if at the second time , the counterpoise bee too light , it is signe that the Gould is farthest off the handle , as at the first triall it was nearest .

PROBLEM . XLIIII . How to represent diverse sorts of Rainebowes here below .

THe Rainebow is a thing admirable in the world , which ravisheth often the eyes and spirits of men in consideration of his rich intermingled colours which are seene under the cloudes , seeming as the glistering of the starres , pretious stones , & ornaments of the most beautious flowers : some part of it as the resplendant stars , or as a rose , or burning cole of fire : in it one may see dies of sundry sorts , the violet , the blew , the orion , the saphir , the jacint , and the emeraud colours , as a lively plant placed in a greene soyle : and as a most rich treasure of nature , it is a high worke of the Sunne who casteth his rayes or beames as a curious Painter drawes strokes with his pensell , and placeth his colours in an exquisite situation ; and Salomon saith , Eccles. 43. it is a chiefe and principall worke of God. Notwithstanding there is left to industrie how to represent it from above , here below , though not in perfection yet in part , with the same intermixture of colours that is above .

Have you not seene how by Oares of a Boate it doth exceeding quickly glide upon the water with a pleasant grace ? Aristotle sayes that it coloureth the water and makes a thousand atomes , upon which the beames of the Sunne reflecting makes a kinde of coloured Rainebow : or may we not see in houses or gardens of pleasure artificiall fountaines , which powre forth their droppie streames of water , that being betweene the Sunne and the fountaine , there will be presented as a continuall Rainebow ? But not to goe farther , I will shew you how you may doe it at your doore , by a fine and facill experiment .

Take water in your mouth , and turne your backe to the Sunne , and your face against some obscure place , then blow out the water which is in your mouth , that it may bee sprinkled in small drops and vapours : you shall see these atomes vapours in the beames of the Sunne to turne into a faire Rabinebow , but all the griefe is that it lasteth not but soone is vanished .

But to have one more stable and permanent in his colours , take a Glasse full of water and expose it to the Sunne , so that the rayes that passe through strike upon a shadowed place , you will have pleasure to see the fine forme of a Rainebow by this reflexion . Or take Trigonall Glasse or Cristall Glasse of diverse Angles , and looke through it , or let the beames of the Sunne passe through it , or with a candle let the appearances be received upon a shadowed place : you will have the same contentment .

PROBLEM . XLV . How that if all the Powder in the world were inclosed within a bowle of paper or glasse , and being fired on all parts , it could not breake that bowle .

IF the bowle and the powder be uniforme in all his parts , then by that means the powder would presse and move equally on each side , in which there is no possibilitie whereby it ought to begin by one side more than another . Now it is impossible that the bowle should bee broken in all his parts : for they are infinite .

Of like finenes or subtiltie may it be that a bowle of iron from a high place upon a plaine pavement of thin Glasse , it were impossible any wise to breake it ; if the bowle were perfectly round , and the Glasse flat and uniforme in all his parts : for the bowle would touch the Glasse but in one point , which is in the middle of infinite of parts which is about it : neither is there any cause why it ought more on one side than on another , seeing that it may not be done with all his sides together ; it may bee concluded as speaking naturally , that such a bowle falling upon such a glasse will not break it . But this matter is meere Metaphysicall , and all the workemen in the world cannot ever with all their industrie make a bowle perfectly round , or a Glasse uniforme .

PROBLEM . XLVI . To finde a number which being divided by 2 there will remaine 1 , being divided by 3 , there will remaine 1 ; and so likewise being divided by 4 , 5 , or 6. there would still remaine 1 : but being divided by 7 , there will remaine nothing .

IN many Authors of Arithmeticke this Probleme is thus proposed : A woman carrying egges to market in a basket , mett an unruly fellow who broake them ; who was by order made to pay for them : and she being demanded what number she had , she could not tell : but she remembred that counting them by 2 , & 2 ; there remained 1 : likewise by 3 and 3 , by 4 and 4 , by 5 and 5 , by 6 and 6 ; there still remained 1 : but when she counted them by 7 and 7 , there remained nothing : Now how may the number of egges be discovered ?

Finde a number which may exactly be measured by 7 , and being measured by 2 , 3 , 4 , 5 , and 6 ; there will still remaine a unity : multiply these numbers together , makes 702 , to which adde 1 ; so have you the number , viz. 721 : in like manner 301 will be measured by 2 , 3 , 4 , 5 , 6 ; so that 1 remaines : but being measured by 7 , nothing will remaine ; to which continually adde 220 , and you have other numbers which will doe the same : hence it is doubtfull what number shee had , therefore not to faile it must be knowne whether they did exceed 400 , 800 , &c. in which it may bee conjectured that it could not exceed 4 or 5 hundred , seeing a man or woman could not carry 7 or 8 hundred egges ; therefore the number was the former 301. which shee had in her basket : which being counted by 2 and 2 , there will remaine 1 , by 3 and 3 , &c. but counted by 7 and 7 , there will remaine ● .

PROBLEME XLVII . One had a certaine number of crownes , and counting them by 2 and 2 , there rested 1 : counting them by 3 and 3 , there rested 2 : counting them by 4 and 4 , there rested 3 : counting them by 5 and 5 , there rested 4 : counting them by 6 and 6 , there rested 5 : but counting them by 7 and 7 , there remained nothing : how many crownes might hee have .

THis Question hath some affinitie to the precedent , and the resolution is almost in the same manner : for here there must be found a number , which multiplied by 7 , and then divided by 2 , 3 , 4 , 5 , 6 ; there may alwayes remaine a number lesse by 1 than the divisor : Now the first number which arives in this nature is 119 , unto which if 420 be added , makes 539 , which also will doe the same : and so by adding 420 , you may have other numbers to resolve this proposition .

PROBLEM . XLVIII . How many sorts of weights in the least manner must there be to weigh all sorts of things betweene 1 pound and 10 pound , and so unto 121 , and 364 pound .

TO weigh things betweene 1 and 40 : take numbers in triple proportion , so that their summe be equall , or somewhat greater than 40 , as are the numbers 1. 3. 9. 27. I say that with 4 such weights , the first being of 1 pound , the second being 3 pound , the third being 9 pound , and the fourth being 27 : any weight betweene 1 and 40 pound may bee weighed . As admit to weigh 21 pound , put unto the thing that is to be weighed the 9 pound weight , then in the other ballance put 27 pound and 3 pound which doth counterpoise 21 pound and 9 pound : and if 20 pound were to be weighed , put to it in the ballance 9 and 1 , and in the other ballance put 27 and 3 , and so of others .

In the same manner take those 5 weights , 1 , 3 , 9 , 27 , 81 , you may weigh with them betweene 1 pound , and 121 pound : and taking those 6 weights , as 1 , 3 , 9 , 27 , 81 , 243 , you may weigh even from 1 pound unto 364 pound : this depends upon the property of continued proportionalls , the latter of which containing twice all the former .

PROBLEM . XLIX . Of a deceitfull ballance which being empty seemes to be just , because it hangs in aequilibrio : notwithstanding putting 12 pound in one ballance , and 11 in the other , it will remaine in aequilibrio .

ARistotle maketh mention of this ballance in his mechanicke Questions , and saith that the Merchants of purpose in his time used them to deceive the world : the subtiltie or craft of which is thus , that one arme of the ballance is longer than another , by the same proportion , that one weight is heavier than another : As if the beame were 23 inches long , and the handle placed so that 12 inches should be on one side of it ,

diagram and 11 inches on the other side : conditionally that the shorter end should be as heavy as the longer , a thing easie to bee done : then afterwards put into the ballance two unequall weights in such proportion as the parts of the beame have one unto another , which is 12 to 11 ; but so that the greater be placed in the ballance which hangs upon the shorter part of the beame , and the lesser weight in the other ballance : it is most certaine that the ballances will hang in aequilibrio , which will seeme most sincere and just ; though it bee most deceitfull , abominable , and false .

The reason of this is drawne from the experiments of Archimedes , who shewes that two unequall weights will counterpoyse one another , when there is like proportion betweene the parts of the beame ( that the handle separates ) and the weights themselves : for in one and the same counterpoise , by how much it is farther from the Center of the handle , by so much it seemes heavier ; therefore if there be a diversitie of distance that the ballances hang from the handle , there must necessarily bee an inequallity of weight in these ballances to make them hang in aequilibrio , and to discover if there be deceite , change the weight into the other ballance , for as soone as the greater weight is placed in the ballance that hangs on the longer parts of the beame : it will weigh downe the other instantly .

PROBLEM . L. To heave or lift up a bottle with a straw .

TAke a straw that is not bruised , bow it that it make an Angle , and put it into the bottle : so that the greatest

diagram end bee in the necke ; then the Reede being put in the bowed part will cast sidewise , and make an Angle as in the figure may bee seene ; then may you take the end which is out of the bottle in your hand , and heave up the bottle : and it is so much surer , by how much the Angle is acuter or sharper ; and the end which is bowed approacheth to the other perpendicular parts which comes out of the bottle .

PROBLEM . LI. How in the middle of a wood or desert , without the sight of the Sunne , Starres , Shaddow or Compasse , to finde out the North or South , or the foure Cardinall points of the world , East , West , &c.

IT is the opinion of some , that the windes are to be observed in this : if it be hot , the South is found by the windes that blow that way , but this observation is uncertaine and subject to much error : nature will helpe you in some measure to make it more manifest than any of the former from a tree , thus : cut a small tree off even to the ground , and marke the many circles that is about the sap or pith of the tree , which seeme nearer together in some part than in other , which is by reason of the sunnes motion about the tree : for that the humiditie of the parts of the tree towards the South by the heat of the Sunne is rarified and caused to extend : and the Sunne not giving such heat towards the North part of the tree , the sap is lesser rarified but condensed ; by which the circles are nearer together on the North part , than on the South part : therefore if a line bee drawne from the widest to the narrowest

diagram part of the circles , it shall shew the North and South of the world : Another experiment may bee thus , take a small needle such as women worke with : place it gently downe flatwise upon still water and it will not sinke , ( which is against the generall tenet that iron will not swimme ) which needle will by little and little turne to the North and South points . But if the needle bee great and will not swimme , thrust it through a small peece of corke or some such like thing , and then it will doe the same : for such is the propertie of iron when it is placed in aequlibrio , it strives to finde out the Poles of the word , or points of North and South : in a manner as the magnes doth .

EXAMINATION .

HEre is observable that the moysture which aydeth to the growth of the tree , is dilated and rarified by the Meridionall heat , and contracted by the Septentrionall cold : this rarifaction workes upon the part of the humour or moysture that is more thinne , which doth easily dissipate and evaporate : which evaporation carries a part of the salt with it ; and because that solidation or condensation , so that there is left but a part of the nourishment which the heat bakes up and consumes : so contrarily on the other side the condensation and restrictive quality of the moysture causeth lesse evaporation and perdition : and so consequently there remaines more nourishment , which makes a greater increase on that side than on the other side : for as trees have their growth in winter , because their powers , and these of the earth are shut up : so in the spring when their powers are open , and when the sappe and moysture is drawne by it , there is not such cold on the North side that it may bee condensed at once : But contrarily to the side which is South , the heate may be such , that in little time by continuance , this moysture is dissipated greatly : and cold is nothing but that which hardneth and contracteth the moysture of the tree , and so converteth it into wood .

PROBLEM . LII . Three persons having taken Counters , Cards , or other things , to finde how much each one hath taken .

CAuse the third party to take a number which may be divided by 4 , & as often as he takes 4 , let the second party take 7 , and the first take 13 , then cause them to put them all together and declare the summe of it : which secretly divide by 3 , and the Quotient is the double of the number which the third person did take . Or cause the third to give unto the second and first , as many as each of them hath ; then let the second give unto the first and third , as many as each of them hath : lastly let the third give unto the second and first , as many as each of them hath ; and then aske how much one of them hath : ( for they will have then all alike , ) so halfe of that number is the number that the third person had at the first : which knowne all is knowne .

PROBLEME LIII . How to make a consort of musicke of many parts with one voyce , or one instrument onely .

THis Probleme is resolved , so that a singer or player upon an instrument , be neare an Echo which answereth his voice or instrument ; and if the Echo answereth but once at a time , he may make a double ; if twice , then a triple ; if three times , then an harmonie of foure parts ; for it must be such a one that is able to exercise both tune and note as occasion requires . As when he begins ut , before the Echo answere , he may begin sol , and pronounce it in the same tune that the Echo answereth , by which meanes you have a fift , agreeable consort of musicke : then in the same time that the Echo followeth , to sound the second note sol , hee may sound forth another sol higher or lower to make an eight ; the most perfect consort of musicke , and so of others ; if he will continue his voyce with the Echo : and sing alone with two parts . Now experience sheweth this to be true , which often comes to passe in many Churches ; making one to beleeve that there is many more parts in the musicke of a Quier , than in effect truly there is , because of the resounding and multiplying of the voyce , and redoubling of the Quire.

PROBLEM . LIIII . To make or describe an Ovall forme , or that which neare resembles unto it , at one turning with a paire of a common Compasses .

THere is many fine wayes in Geometricall practices , to make an Ovall figure or one neare unto it , by severall centers : any of which I will not touch upon ; but shew how it may be done promptly upon one center only . In which I will say nothing of the Ovall forme which appeares , when one describeth circles with the points of a common compasses , somewhat deepe upon a skinne stretched forth hard : which contracting it selfe in some parts of the skinne maketh an Ovall forme . But it will more evidently appeare upon a columne or cylinder : if paper be placed upon it , then with a paire of Compasses describe as it were a circle upon it , which paper afterwards being extended , will not bee circular but ovall-wise : and a paire of Compasses may be so accommodated that it may be done also upon a plain thus . As let the length of the Ovall be H. K , fasten 2 pinnes or nayles neare the end of that line as

diagram F. G , and take a threed which is double to the length of G. H , or F. K : then if you take a Compasse which may have one foot lower than another , with a spring betweene his legges : & placing one foot of this Compasse in the Center of the Ovall , and guiding the threed by the other foot of the Compasses , and so carrying it about : the spring will helpe to describe and draw the Ovall forme . But in stead of the Compasses it may be done with ones hand onely , as in the figure may appeare .

PROBLEM . LV. Of a purse difficult to be opened .

IT is made to shut and open with ring first at each side there is a strap or string , as A B and CD , at the end of which are 2 rings , B & D , and the string C D passeth through the ring B , so that it may not come out againe ; or be parted one from another : and so that the ring B , may slide up and downe upon the string C D , then over the purse there is a peece of leather E. F. G. H. which covers the opening of the purse , and there is another

diagram peece of leather A. E. which passeth through many ringes : which hath a slitte towards the end I. so great that the string B. C. may slide into it : Now all the cunning or craft is how to make fast or to open the purse , which consists in making the string B.C. slide through the side at I ; therefore bring downe B. to I , then make the end I. passe through the ring B : and also D. with his string to passe through the slit I , so shall the purse be fast ; and then may the strings be put as before : and it will seeme difficult to discover how it was done . Now to open the purse , put through the end I. through the ring B , and then through the slit I ; by which you put through the string D C : by this way the purse will be opened .

PROBLEM . LVI . Whether it is more hard and admirable without Compasses to make a perfect circle , or being made to finde out the Center of it .

IT is said that upon a time past , two Mathematicians meete , and they would make tryall of their industry : the one made instantly a perfect circle without Compasses , and the other immediately pointed out the center thereof with the point of a needle : now which is the chiefest action : it seemes the first : for to draw the most noblest figure upon a plaine Table without other helpe than the hand , and the minde , is full of admiration : to finde the center is but to finde out only one point , but to draw a round , there must be almost infinite points , equidistant from the center or middle : that in conclusion it is both the circle and the center together . But contrarily it may seeme that to finde the center is more difficult , for what attention , vivacitie , and subtiltie must there be in the spirit , in the eye , in the hand , which will chuse the true point amongst a thousand other points ? He that makes a circle keepes alwayes the same distance , and is guided by a halfe distance to finish the rest ; but he that must finde the center , must in the same time take heed to the parts about it , and choose one onely point which is equall distant from an infinite of other points which are in the circumference : which is very difficult . Aristotle confirmes this amongst his moralls , and seemes to explaine the difficultie which is to be found in the middle of vertue ; for it may want a thousand wayes and be farre separated from the true center of the end of a right mediocritie of a vertuous action : for to doe well it must touch the middle point which is but one , and there must be a true point which respects the end , and that s but one onely . Now to judge which is the most difficults as before is said , either to draw , the round or to finde the center ; the round seemes to be harder than to finde the center , because that in finding of it , it is done at once , and hath an equall distant from the whole : But as before to draw a round there is a visible point imagined , about which the circle is to bee drawne . I esteeme that it is as difficult therefore if not more , to make the circle without a center , as to finde the middle or center of that circle .

PROBLEM . LVI . Any one having taken 3 Cards , to finde how many points they containe .

THis is to bee exercised upon a full packe of Cards of 52 , then let one choose any three at pleasure secretly from your sight : and bid him secretly account the points in each Card : and will him to take as many Cards as will make up 15 to each of the points of his Cards ; then will him to give you the rest of the Cards , for 4 of them being rejected , the rest shewes the number of points that his three Cards which he tooke at the first did containe . As if the 3 Cards were 7 , 10 , and 4 ; now 7 wants of 15 , 8 : take 8 Cards therefore for your first Card : the 10 wants of 15. 5 , take 5 Cards for your second Card : lastly 4 wants of 15 , 11 , take 11 Cards for your third Card , and giving him the rest of the Cards , there will be 25 ; from which take 4 , there remaines 21 : the number of the three Cards taken , viz. 7 , 10 , and 4.

Whosoever would practise this play with 4 , 5 , 6 , or more Cards , and that the whole number of Cards be more or lesse than 52 ; and that the terme be 15 , 14 , 12 , &c. this generall rule ensuing may serve : multiply the terme by the number of Cards taken at first : to the product adde the number of Cards taken , then subtract this summe from the whole number of Cards ; the remainder is the number which must bee subtracted from the Cards , which remaines to make up the game : if there remaine nothing after the substraction , then the number of cards remaining doth justly shew the number of points which were in the Cards chosen . If the substraction cannot be made , then subtract the number of Cards from that number , and the remainder added unto the Cards that did remaine , the summe will be the number of points in the Cards taken , as if the Cards were 7 , 10 , 5 , 8 , and the terme given were 12 ; so the first wants 5 , the second wants 2 , the third wants 7 , and the fourth wants 4 Cards , which taken , the party gives you the rest of the Cards : then secretly multiply 12 by 4 , makes 48 ; to which adde 4 the number of Cards taken , makes 52 , from which 52 should bee taken , rest nothing : therefore according to the direction of the remainder of the Cards which are 30 , is equall to the points of the foure Cards taken , viz. 7 , 10 , 5 , 8. Againe let these five Cards bee supposed to be taken , 8 , 6 , 10 , 3 , 7 ; their differences to 15 , the termes are 7 , 9 , 5 , 12 , 8 , which number of Cards taken , there will remaine but 6 Cards : then privatly multiply 15 by 5 , makes 75 , to which adde 5 makes 80 , from this take 52 the number of Cards , rest 28 , to which adde the remainder of Cards , make 34 : the summe with 8 , 6 , 10 , 3 , 7.

PROBLEM . LVII . Many Cards placed in diverse rankes , to finde which of these Cards any one hath thought .

TAke 15 Cards and place them in 3 heapes in ranke-wise , 5 in a heape : now suppose any one had thought one of these Cards in any one of the heapes , it is easie to finde which of the Cards it is , and it is done thus : aske him in which of the heapes it is , which place in the middle of the other two : then throw downe the Cards by 1 and 1 into three severall heapes in ranke-wise , untill all be cast downe ; then aske him in which of the rankes his Card is : which heape place in the middle of the other two heapes alwayes ; and this doe foure times at least , so in putting the Cards altogether , looke upon the Cards , or let their backe bee towards you , and throw out the eight Card : for that was the Card thought upon without faile .

PROBLEM . LVIII . Many Cards being offered to sundry persons , to finde which of those Cards any one thinketh upon .

ADmit there were 4 persons , then take 4 Cards and shew them to the first : bid him think one of them , & put these 4 away ; then take 4 other Cards and shew them in like manner to the second person , and bid him thinke any one of these Cards : and so doe to the third person , and so the fourth , &c. Then take the 4 Cards of the first person , and dispose them in 4 rankes : and upon them the 4 Cards of the second person , upon them also these of the third person , & lastly upon them these of the fourth person : then shew unto each of these parties each of these rankes , and aske him if his Card be in it which he thought : for infallibly that which the first partie thought upon will bee in the first ranke , and at the bottome ; the Card of the second person will bee in the second ranke : the Card of the third thought upon will be in the third ranke , and the fourth mans Card will be in the fourth ranke ; and so of others : if there bee more persons use the same methode . This may be practised by other things , ranking them by certaine numbers : allotted to peeces of money , or such like things .

PROBLEM . LIX . How to make an instrument to helpe hearing , as Gallileus made to helpe the sight .

THinke not that the Mathematickes ( which hath furnished us with such admirable helpes for seeing ) is wanting for that of hearing : it s well knowne that long trunkes or pipes makes one heare well farre off , and experience shewes us that in certaine places of the Arcades in a hollow vault , that a man speaking but softly at one corner thereof , may be audibly understood at the other end : notwithstanding these which are betweene the parties cannot heare him speake at all : And it is a generall principle , that pipes doe greatly helpe to strengthen the activitie of naturall causes : we see that fire contracted in a pipe , burnes 4. or 5. foot high , which would scarce heat , being in the open aire : the rupture or violence of water issuing out of a fountaine , shewes us that water being contracted into a pipe , causeth a violence in its passage . The Glasses of Gallileus makes us see how usefull pipes or trunkes are to make the light and species more visible , and proportionable to our eye . It is said that a Prince of Italy hath a faire hall , in which he can with facility heare distinctly the discourses of these which walke in the adjacent gardens , which is by certaine vessels and pipes that answere from the garden to the hall . Vitruvius makes mention also of such vessels and pipes , to strengthen the voyce and action of Comedians : and in these times amongst many noble personages , the new kinde of trunkes are used to helpe the hearing , being made of silver , copper , or other resounding materiall ; in funnell-wise putting the widest end to him which speaketh , to the end to contract the voyce , that so by the pipe applyed to the eare it may be more uniforme and lesse in danger to dissipate the voyce , and so consequently more fortified .

PROBLEM . LX. Of a fine lampe which goes not out , though one carry it in ones pocket : or being rouled upon the ground will still burne .

IT must be observed that the vessell in which the oyle is put into , have two pinnes on the sides of it one against another , being included within a circle : this circle ought to have two other pinnes , to enter into another circle of brasse , or other sollid matter : lastly this second circle hath two pinnes which may hang within some box to containe the whole lampe , in such manner , that there be 6 pinnes in different position : Now by the aide of these pegges or pinnes , the lampe that is in the middle will bee alwayes well scituated according to his Center of gravity , though it

diagram bee turned any way : though if you endeavour to turne it upside downe , it will lie levell : which is pleasant and admirable to behold to these which know not the cause : And it is facill from this to make a place to rest quiet in , though there bee great agitation in the outward parts .

PROBLEM . LXI . Any one having thought a Card amongst many Cards , how artificially to discover it out .

TAke any number of Cards as 10 , 12 , &c. and open some 4 or 5 to the parties sight , and bid him thinke one of them , but let him note whether it be the first , second , third , &c. then with promptnesse learne what number of Cards you had in your hands , and take the other part of the Cards , & place them on the top of these you hold in your hand ; and having done so , aske him whether his Card were the first , second , &c. then before knowing the number of Cards that were at the bottome , account backwards untill you come to it : so shall you easily take out the Card that he thought upon .

PROBLEM . LXII . Three women A. B. C. carryed apples to a market to sell , A. had 20 , B. 30 , and C. 40 ; they sold as many for a penny , the one as the other : and brought home one as much money as another , how could this be .

THe answere to the Probleme is easie , as suppose at the beginning of the market : A. sold her apples at a

diagram penny an apple : and sold but 2. which was 2 pence , and so shee had 18 left : but B. sold 17. which was 17 pence , and so had 13. left : C. sold 32 which was 32 pence , and so had 8 apples left : then A. said she would not sell her apples so cheape , but would sell them for 3 pence the ●●eece , which shee did : and so her apples came ●o 54 pence , and B. having left but 13 apples sold them at the same rate which came to 39 ●ence : and lastly C. had but 8 apples , which at the same rate came to 24 pence : these summes of money which each others before received come to 56 pence , and so much each one received ; and so consequently brought home one as much as another .

PROBLEM . LXIII . Of the properties of some numbers .

FIrst , any two numbers is just the summe of an number that have equall distance from the halfe of that number : the one augmenting , and the other diminishing , as 7 and 7 , of 8 and 6 , of 9 and 5 , of 10 and 4 , of 11 and 3 , of 12 and ● , of 13 and 1 : as the one is more than the halfe the other is lesse .

Secondly , it is difficult to finde two numbers whose summe and product is alike , ( that is ) if the numbers be multiplyed one by another , and added together , will be equall : which two numbers are 2 and 2 , for to multiply 2 by 2 makes 4 , and adding 2 unto 2 makes the same : this property is in no other two whole numbers , ●ut in broken numbers there are infinite , whose summe and product will bee equall one to another . As Clavius shewes upon the 36 Pro. of the 9th booke of Euclide .

Thirdly , the numbers 5 and 6 are called circular numbers , because the circle turnes to the point from whence it begins : so these numbers multiplyed by themselves , doe end alwayes in 5 and 6 , as 5 times 5 makes 25 , that againe by 5 makes 125 ; so 6 times 6 makes 36 , and that by 6 makes 216 , &c.

Fourthly , the number 6 , is the first which Arithmeticians call a perfect number , that is , whose parts are equall unto it , so the 6 part of it is 1 , the third part is 2 , the halfe is 3 , which are all his parts : now 1 , 2 , and 3 , is equall to 6. It is wonderfull to conceive that there is so few of them , and how rare these numbers are , so of perfect men : for betwixt 1 & 1000000000000 numbers there is but ten , that is ; 6 , 28 , 486. 8128. 120816. 2096128. 33550336. 536854528.8589869056 , & 137438691328 : with this admirable property , that alternately they end all in 6 and 8 , & the twentieth perfect number is 151115727451553768931328.

Fiftly , the number 9 amongst other priviledges carries with it an excellent property , for take what number you will , either in grosse or in part : the nines of the whole or in its parts rejected , and taken simply will be the same , as 27 it makes 3 times 9 , so whether the nines bee rejected of 27 , or of the summe of 2 and 7 , it is all one : so if the nines were taken away of 240. it is all one , if the nines were taken away of 2 , 4 , and 0 ; for there would remaine 6 in either : and so of others .

Sixtly , 11 being multiplyed by 2 , 4 , 5 , 6 , 7 , 8 , or 9 , will end and begin with like numbers ; ●0 11 multiplyed by 5 makes 55 : if multiplyed by 8 , it makes 88 , &c.

Seventhly , the numbers 220 and 284 being unequall , notwithstanding the parts of the one number doth alwayes equallise the other number : so the alliquot parts of 220 are 110 , 54 , 44 , 22 , 20 , 11 , 10 , 5 , 4 , 2 , 1 , which together makes 284 : the alliquot parts of 284 are 142 , 71 , 4 , 2 , 1 , which together makes 220 , a thing rare and admirable , and difficult to finde in other numbers .

diagram

If one bee taken from any square number which is odde , the square of halfe of it being added to the first square , will make a square number .

The square of halfe any even number ✚ . 1 being added to that even number makes a square number , and the even number taken from it leaves a square number .

If odde numbers bee continually added from the unitie successively , there will bee made all square numbers , and if cubicke numbers bee added successively from the unitie , there will bee likewise made square numbers .

PROBLEM . LXV . Of an excellent lampe which serves or furnisheth it selfe with oyle , and burnes a long time .

diagram

But that which I here deliver is more ingenious , the principall peece of which is a vessell as C. D : which hath neare the bottome a hole , and a funnell or pipe C : & then a bigger funnell which passeth through the middle of the vessell , having an opening at D. neare the E top , and another at the bottome as at E , neare the vessell under it , so that the pipe touch it not : the vessell being thus made , fill it with oyle , and opening the hole C. the oyle running out will stop the hole at E : or throwing in oyle into the vessell underneath , untill E. bee stopped ; then the oyle at C. will not runne : because no aire can come into the pipe D. E. Now as the oyle burneth and consumeth in the vessell A. B. the hole at E , will begin to be open , then immediatly will C. begin to runne to fill up A B : and E being stopped with the oyle , the oyle at C. ceaseth to run .

It is certaine that such a lampe the Athenians ●ed , which lasted a whole yeare without being touched : which was placed before the statue of Minerva , for they might put a certaine quantitie of oyle in the lampe C. D , and a match to burne without being consumed : such as the naturallists write of , by which the lampe will furnish it selfe and so continue in burning : and here may be noted that the oyle may be powred in at the top of the vessell at a little hole , & then made fast againe that the aire get not in .

PROBLEM . LXV . Of the play at Keyles or nine Pinnes .

YOu will scarce beleeve that which one bowle and at one blow playing freely , one may strike downe all the Keyles at once : yet from Mathematicall principles it is easie to bee demonstrated , that if the hand of him that playes was so well assured by experience , as reason induceth one thereto : one might at one blow strike downe all the Keyles , or at least 7 or 8 , or such a number as one pleaseth .

For they are but 9 in all disposed or placed in a perfect square , having three every way . Let us suppose then that a good player beginning to play at 1 somewhat low , should so strike it , that it should

diagram strike down the Keyles 2 and 5 , and these might in their violence strike down the Keyles 3 , 6 , and 9 : and the bowle being in motion may strike downe the Keyle 4 , and 7 ; which 4 Keyle may strike the Keyle 8 : and so all the 9 Keyles may bee striken downe at once .

PROBLEM . LXVI . Of Spectacles of pleasure .

SImple Spectacles of blew , yeallow , red or greene colour , are proper to recreate the sight , and will present the objects died in like colour that the Glasses are , onely those of the greene doe somewhat degenerate ; instead of shewing a lively colour it will represent a pale dead colour , and it is because they are not dyed greene enough , or receive not light enough for greene : and colour these images that passe through these Glasses unto the bottome of the eye .

EXAMINATION .

IT is certaine that not onely Glasses dyed green , but all other Glasses coloured , yeeldes the appearances of objects strong or weake in colour according to the quantity of the dye , more or lesse , as one being very yellow , another a pale yellow ; now all colours are not proper to Glasses to give colour , hence the defect is not that they want facultie to receive light , or resist the penetration of the beames , for in the same Glasses those which are most dyed , gives alwayes the objects more high coloured and obscure , and those which are lesse dyed gives them more pale and cleare : and this is dayly made manifest by the painting of Glasse , which hinders more the penetration of the light than dying doth , where all the matter by fire is forced into the Glasse , leaving it in all parts transparant .

Spectacles of Crystall cut with diverse Angles dimond-wise doth make a marvelous multiplication of the appearances , for looking towards a house it becomes as a Towne , a Towne becomes like a Citie , an armed man seems as a whole company caused soly by the diversity of refractions , for as many plaines as there are on the outside of the Spectacle , so many times will the object be multiplyed in the appearance , because of diverse images cast into the eye .

These are pleasurable Spectacles for avaritious persons that love gold and silver , for one peece will seeme many , or one heape of money will seeme as a treasury : but all the mischiefe is , he will not have his end in the injoying of it , for indeavoring to take it , it will appeare but a deceitfull image , or delusion of nothing . Here may you note that if the finger be directed by one and the same ray or beam , which pointeth to one & the same object , then at the first you may touch that visible object without being deceived : otherwise you may faile often in touching that which you see .

Againe there are Spectacles made which doe diminish the thing seene very much , and and brings them to a faire perspective forme , especially if one looke upon a faire garden plot , a greater walke , a stately building , or great court , the industry of an exquisite Painter cannot come neare to expresse the lively forme of it as this Glasse will represent it ; you will have pleasure to see it really experimented , and the cause of this is , that the glasses of these Spectacles are hollow & thinner in the middle , than at the edges by which the visuall Angle is made lesser : you may observe a further secret in these Spectacles , for in placing them upon a window one may see those that passe to and fro in the streets , without being seene of any ; for their property is to raise up the objects that it lookes upon .

Now I would not passe this Probleme without saying something of Gallileus admirable Glasse , for the common simple perspective Glasses give to aged men , but the eyes or sight of young men , but this of Gallileus gives a man an Eagles eye , or an eye that pearceth the heavens : first it discovereth the spottie and shaddowed opacous bodies that are found about the Sunne , which darkeneth and diminisheth the splendor of that beautifull and shinining Luminary : secondly , it shewes the new planets that accompany Saturne and Iupiter : thirdly , in Venus is seene the new , full , and quartall increase ; as in the Moone by her separation from the Sunne : fourthly , the artificiall structure of this instrument helpeth us to see an innumerable number of stars , which otherwise are obscured by reason of the naturall weakenesse of our sight , yea the starres in via lactea are seene most apparantly ; where there seemes no starres to be , this instrument makes apparantly to be seene , and further delivers them to the eye in their true and lively colour , as they are in the heavens : in which the splendor of some is as the Sunne in his most glorious beauty . This Glasse hath also a most excellent use in observing the body of the Moone in time of Eclipses , for it augments it manifold , and most manifestly shewes the true forme of the cloudy substance in the Sunne ; and by it is seene when the shaddow of the earth begins to eclipse the Moone , and when totally shee is overshaddowed : besides the celestiall uses which are made of this Glasse , it hath another noble property ; it farre exceedeth the ordinary perspective Glasses , which are used to see things remote upon the earth , for as this Glasse reacheth up to the heavens and excelleth them there in his performance , so on the earth it claimeth preheminency : for the objects which are farthest remote , and most obscure , are seene plainer than those which are neere at hand , scorning as it were all small and triviall services , as leaving them to an inferiour helpe : great use may be made of this Glasse in discovering of Shippes , Armies , &c. Now the apparell or parts of this instrument or Glasse , is very meane or simple , which makes it the more admirable ( seeing it performes such great service ) having but a convex Glasse thickest in the middle , to unite and amasse the rayes , and make the object the greater : to augmenting the visuall Angle , as also a pipe or truncke to amasse the Species , and hinder the greatnes of the light which is about it : ( to see well , the object must be well inlightened , and the eye in obscuritie ; ) then there is adjoyned unto it a Glasse of a short fight to distinguish the rayes , which the other would make more confused if alone . As for the proportion of those Glasses to the Trunke though there be certaine rules to make them , yet it is often by hazard that there is made an excellent one , there being so many difficulties in the action , therefore many ought to be tryed , seeing that exact proportion , in Geometricall calculation cannot serve for diversity of sights in the observation .

PROBLEME LXVII . Of the Adamant or Magnes , and the needles touched therewith .

WHo would beleeve if he saw not with his eyes , that a needle of steel being once touched with the magnes , turnes not once , not a yeare , but as long as the world lasteth ; his end towards the North and South , yea though one remove it , and turne it from his position , it will come againe to his points of North and South . Who would have ever thought that a brute stone blacke and ill formed , touching a ring of iron , should hang it in the aire : and that ring support a second , that to support a third , and so unto 10 , 12 , or more , according to the strength of the magnes ; making as it were a chaine without a line , without souldering together , or without any other thing to support them onely ; but a most occult and hidden vertue , yet most evident in this effect : which penitrateth insencibly from the first to the second , from the second to the third , &c.

diagram

What is there in the world that is more capable to cast a deeper astonishment in our mindes , than a great massie substance of iron to hang in the aire in the midest of a building without any thing in the world touching it , only but the aire ? And histories assure us , that by the aide of a magnes or adamant , placed at the roofe of one of the Turkish Synagogues in Meca : the sepulcher of that infamous Mahomet rests suspended in the aire ; and Plinie in his naturall historie writes that the Architecter Dinocrates did begin to vault the Temple of Arsinoe in Alexandria , with store of magnes to produce the like deceit , to hang the sepulcher of that Goddesse likewise in the aire .

I should passe the bounds of my counterpoise , if I should divulge all the secrets of this stone , and should expose my selfe to the laughter of the world : if I should brag to shew other the cause how this appeareth , than in its owne naturall sympathy , for why is it that a magnes with one end will cast the iron away , and attract it with the other ; from whence cometh it that all the magnes is not proper to give a true touch to the needle , but onely in the two Poles of the stone : which is knowne by hanging the stone by a threed in the aire untill it be quiet , or placed upon a peece of Corke in a dish of water , or upon some ●hinne board , for the Pole of the stone will then turne towards the Poles of the world , and point out the North and South ; and so shew by which of these ends the needle is to be touched .

From whence comes it that there is a variation in the needle , and pointeth not out truly the North and South of the world , but onely in some place of the earth .

How is it that the needle made with pegges and inclosed within two Glasses , sheweth the height of the Pole , being elevated as many degrees as the Pole is above the Horizon .

What s the cause that fire and Garlicke takes away the propertie of the magnes : There are many great hidden misteries in this stone , which have troubled the heads of the most learned in all ages ; and to this time the world remaines ignorant of declaring the true cause thereof .

Some sayes that by helpe of the Magnes persons which are absent may know each others minde , as if one being here at London , and another at Prage in Germany : if each of them had a needle touched with one magnes , then the vertue is such that in the same time that the needle which is at Prage shall moove , this that is at London shall also ; provided that the parties have like secret notes or alphabets , and the observation be at a set houre of the day or night ; and when the one party will declare unto the other , then let that party move the needle to these letters which will declare the matter to the other , and the mooving of the other parties needle shall open his intention .

The invention is subtile , but I doubt whether in the world there can be found so great a stone , or such a Magnes which carries with it such vertue : neither is it expedient , for treasons would be then too frequent and open .

EXAMINATION .

THe experimentall difference of rejection , and attraction proceedes not from the different nature of stones , but from the quality of the iron , and the vertue of the stone consisteth onely and especially in his Poles ; which being hanged in the aire , turnes one of his ends alwayes naturally towards the South , and the other towards the North : but if a rod of iron be touched with one of the ends thereof , it hath the like property in turning North and South , as the magnes hath : notwithstanding the end of the iron rod touched , hath a contrary position to that end of the stone that touched it ; yet the same and will attract it , and the other end reject it : and so contrarily this may easily be experimented upon two needles touched with one or different stones , though they have one and the same position ; for as you come unto them apply one end of the magnes neare unto them , the North of the one will abhorre the North of the other , but the North of the one will alwayes approach to the South of the other : and the same affection is in the stones themselves . For the finding of the Poles of the magnes , it maybe done by holding a small needle betweene your fingers softly , and so mooving it from part to part over the stone untill it be held perpendicular , for that shall be one of the Poles of the stone which you may marke out ; in like manner finde out the other Pole : Now to finde out which of those Poles is North or South , place a needle being touched with one of the Poles upon a smooth convex body , ( as the nayle of ones finger or such like , ) and marke which way the end of the needle that was touched turneth : if to the South , then the point that touched it was the South Pole , &c. and it is most certaine and according to reason and experience : that if it be suspended in aequilibrio in the aire , or supported upon the water , it will turne contrary to the needle that toucheth it ; for then the Pole that was marked for the South shall turne to the North , &c.

PROBLEM . LXVIII . Of the properties of Aeolipiles or bowles to blow the fire .

THese are concave vessels of brasse or copper , or other materiall which may indure the fire : having a small hole very narrow by which it is filled with water , then placing it to the fire , before it bee hot there is no effect seene ; but assoone as the heate doth penitrate it , the water begins to rarifie and issueth forth with a hideous and marvellous force ; it is pleasure to see how it blowes the fire with great noyse .

diagram

Now touching the forme of these vessels , they are not made of one like fashion : some makes them like a bowle , some like a head painted representing the winde , some makes them like a peare : as though one would put it to rost at the fire , when one would have it to blow , for the tale of it is hollow , in forme of a funnell , having at the toppe a very little hole no greater than the head of a pinne .

Some doe accustome to put within the Aeolipile a crooked funnell of many foldings , to the end that the winde that impetuously rowles to and fro within , may imitate the noyse of thunder .

Others content themselves with a simple funnell placed right upward , somewhat wider at the toppe than else where like a Cone , whose basis is the mouth of the funnell : and there may be placed a bowle of iron or brasse , which by the vapoures that are cast out will cause it to leape up , and dance over the mouth of the Aeolipile .

Lastly , some apply neare to hole small wind-mills , or such like , which easily turne by reason of the vapours ; or by help of two or more bowed funnells , a bowle may be made to turne : these Aelopililes are of excellent use for the melting of mettalls and such like .

Now it is cunning and subtiltie to fill one of these Aeolipiles with water at so little a hole , and therefore requires the knowledge of a Philosopher to finde it out : and the way is thus .

Heate the Aeolipiles being empty , and the aire which is within it will become extreamely rarified ; then being thus hot throw it into water , and the aire will begin to bee condensed : by which meanes it will occupie lesse roome , therefore the water will immediately enter in at the hole to avoide vacuitie : thus you have some practicall speculation upon the Aeolipile .

PROBLEM . LXIX . Of the Thermometer : or an instrument to measure the degrees of heat and cold in the aire .

THis Instrument is like a Cylindricall pipe of Glasse , which hath a little ball or bowle at the toppe : the small end of which is placed into a vessell of water below , as by the figure may be seene .

Then put some coloured liquor into the Cylindricall glasse , as blew , red , yealow , greene , or such like : such as is not thicke . This being done the use may he thus .

diagram

These that will determine this change by numbers and degrees , may draw a line upon the Cylinder of the Thermometer ; and divide it into 4 degrees , according to the ancient Philosophers , or into 4 degrees according to the Physitians , dividing each of these 8 into 8 others to have in all 64 divisions , and by this way they may not onely distinguish upon what degree the water ascendeth in the morning , at midday , and at any other houre : but also one may know how much one day is hotter or colder than another : by marking how many degrees the water ascendeth or descendeth , one may compare the hottest and coldest dayes in a whole yeare together with these of another yeare : againe one may know how much hotter one roome is than another , by which also one might keepe a chamber , a furnis , a stove , &c. alwayes in an equalitie of heate , by making the water of the Thermometer rest alwayes upon one and the same degree : in briefe , one may judge in some measure the burning of fevers , and neare unto what extension the aire can bee rarified by the greatest heate .

Many make use of these glasses to judge of the weather , for it is observed that if the water fall in 3 or 4 houres a degree or thereabout , that raine insueth ; and the water will stand at that stay , untill the weather change : marke the water at your going to bed , for if in the morning it hath descended raine followeth , but if it bee mounted higher , it argueth faire-weather : so in very cold weather , if it fall suddainly , it is snow or some sleekey weather that will insue .

PROBLEM . LXX . Of the proportion of humaine bodies of statues , of Colossus or huge images , and of monstrous Giants .

PYthagoras had reason to say that man is the measure of all things .

First , because he is the most perfect amongst all bodily creatures , and according to the Maxime of Philosophers , that which is most perfect , and the first in ranke , measureth all the rest .

Secondly , because in effect the ordinary measure of a foote , the intch , the cubit , the pace , have taken their names and greatnesse from humaine bodies .

Thirdly , because the simmetrie and concordancie of the parts is so admirable , that all workes which are well proportionable , as namely the building of Temples , of Shippes , of Pillars , and such like peeces of Architecture , are in some measure fashioned and composed after his proportion . And we know that the Arke of Noah built by the commandement of God , was in length 300 cubits , in bredth 50 cubits , in height or depth 30 cubits , so that the length containes the bredth 6 times , and 10 times the depth : now a man being measured you will finde him to have the same proportion in length , breadth , and depth .

Vilalpandus treating of the Temple of Salomon , that chiefetaine of workes was modulated all of good Architecture , and curiously to be observed in many peeces to keepe the same proportion as the body to his parts : so that by the greatnesse of the worke and proportionable symmetrie , some dare assure themselves that by knowledge of one onely part of that building , one might know all the measures of that goodly structure .

Some Architects say that the foundation of houses , and basis of columnes , are as the foote ; the tôp , and roofe as the head ; the rest as the body : those which have beene somewhat more curious , have noted that as in humaine bodies , the parts are uniforme as the nose , the mouth , &c. these which are double are put on one side or other , with a perfect equallitie in the same Architecture .

In like manner , some have beene yet more curious than solid ; comparing all the ornaments of a Corinth to the parts of the face , as the brow , the eyes , the nose , the mouth ; the rounding of pillars , to the writhing of haire , the chanells of columnes , to the fouldings of womens robes , &c.

Now building being a worke of the best Artist , there is much reason why man ought to make his imitation from the chiefe worke of nature ; which is man .

Hence it is that Vitruvious in his third book , and all the best Architectures , treateth of the proportion of man ; and amongst others Albert Dureus hath made a whole booke of the measures of mans body , from the foot to the head ; let them reade it who will , they may have a perfect knowledge therof : but I will content my selfe , and it may satisfie some with that which followeth .

First , the length of a man well made , which commonly is called height , is equall to the distance from one end of his finger to the other : when the armes are extended as wide as they may be .

Secondly , if a man have his feet and hands extended or stretched in forme of S. Andrewes Crosse , placing one foote of a paire of Compasses upon his navill , one may describe a circle which will passe by the ends of his hands and feet , and drawing lines by the termes of the hands and feet , you have a square within a circle .

Thirdly , the breadth of man , or the space which is from one side to another ; the breast , the head , and the necke , makes the 6 part of all the body taken in length or height .

Fourthly , the length of the face is equall to the length of the hand , taken from the small of the arme , unto the extremity of the longest finger .

Fiftly , the thickenesse of the body taken from the belly to the backe ; the one or the other is the tenth part of the whole body , or as some will have , it the ninth part , little lesse .

Sixtly , the height of the brow , the length of the nose , the space betweene the nose and the chinne , the length of the eares , the greatnesse of the thumbe , are perfectly equall one to the other .

What would you say to make an admirable report of the other parts , if I should reckon them in their least ; but in that I desire to be excused , and will rather extract some conclusion upon that which is delivered .

In the first place knowing the proportion of a man , it is easie to Painters , image-makers , &c. perfectly to proportionate their worke ; and by the same is made most evident , that which is related of the images and statues of Greece , that upon a day diverse workemen having enterprised to make the face of a man , being severed one from another in sundry places , all the parts being made and put together , the face was found in a most lively and true proportion .

Secondly , it is a thing most cleare that by the helpe of proportion , the body of Hercules was measured by the knowledge of his foote onely ; a Lyon by his claw , the Gyant by his thumbe , and a Man by any parte of his body . For so it was that Pythagoras having measured the length of Hercules foote , by the steps which was left upon the ground , found out all his height : and so it was that Phydias having onely the claw of a Lyon , did figure and draw out all the beast according to his true type or forme ; so the exquisite Painter Timantus , having painted a Pigmey or Dwarfe , which he measured with a fadome made with the intch of a Gyant ; it was sufficient to know the greatnesse of that Gyant .

To be short , we may by like methode come easily to the knowledge of many fine antiquities touching Statues , Colosses , and monstrous Gyants , onely supposing one had found but one only part of them , as the head , the hand , the foote , or some bone mentioned in ancient Histories .

Of Statues , of Colossus , or huge images .

VItruvius relates in his second booke that the Architect Dinocrates was desirous to put out to the world some notable thing , went to Alexander the great , and proposed unto him a high and speciall peece of worke which he had projected : as to figure out the mount Athos in forme of a great Statue , which should hold in his right hand a Towne capable to receive ten thousand men : and in his left hand a vessell to receive all the water that floweth from the mountaine , which with an ingine should cast into the Sea . This is a pretty project , said Alexander , but because there was not field roome thereabout to nourish and retaine the Citizens of that place , Alexander was wise not to entertaine the designe .

Now let it bee required of what greatnesse this Statue might have beene , the Towne in his right hand , and the receiver of water in his left hand if it had beene made .

For the Statue , it could not bee higher than the mountaine it selfe , and the mountaine was about a mile in height plume or perpendicular ; therefore the hand of this Statue ought to bee the 10th part of his height , which would bee 500 foote , and so the bredth of his hand would be 250 foote ; the length now multiplyed by the bredth , makes an hundred twenty five thousand square feete ; for the quantitie of his hand to make the towne in , to lodge the said 10 thousand men , allowing to each man neere about 12 foote of square ground : now judge the capacitie of the other parts of this Colossus by that which is already delivered .

Secondly , Plinie in his 34 booke of his naturall History , speakes of the famous Colossus that was at Rhodes , betweene whose legges a Shippe might passe with his sailes open or displayed , the Statue being of 70 cubits high : and other Histories reports that the Sarazins having broken it , did load 900 Camells with the mettle of it , now what might be the greatnes and weight of this Statue .

For answere it is usually allowed for a Cammells burthen 1200 pound weight , therefore all the Colossus did weigh 1080000 pound weight , which is ten hundred and forescore thousand pound weight .

Now according to the former rules , the head being the tenth part of the body , this Statues head should bee of 7 cubits , that is to say , 10 foote and a halfe ; and seeing that the nose , the brow , and the thumbe , are the third part of the face ; his nose was 3 foote and a halfe long , and so much also was his thumbe in length : now the thicknesse being alwayes the third part of the length , it should seeme that his thumbe was a foote thicke at the least .

Thirdly , the said Plinie in the same place reports that Nero did cause to come out of France into Itally , a brave and bold Statue-maker called Zenodocus , to erect him a Colossus of brasse , which was made of 120 foot in height , which Nero caused to bee painted in the same height . Now would you know the greatnesse of the members of this Colossus , the breadth would be 20 foote , his face 12 foote , his thumbe and his nose 4 foote , according to the proportion before delivered .

Thus I have a faire field or subject to extend my selfe upon , but it is upon another occasion that it was undertaken ; let us speake therefore a word touching the Gyants , and then passe away to the matter .

Of monstrous Gyants .

YOu will hardly beleeve all that which I say touching this , neither will I beleeve all that which Authors say upon this subject : notwithstanding you nor I cannot deny but that long agoe there hath beene men of a most prodigious greatnesse ; for the holy writings witnesse this themselves in Deut. Chap. 3. that there was a certaine Gyant called Ogge , of the Towne of Rabath , who had a bed of iron , the length thereof was 9 cubits , and in bredth 4 cubits .

So in the first of Kings Chap. 17. there is mention made of Goliah , whose height was a palme and 6 cubits , that is more then 9 foote , he was armed from the head to the foote , and his Curiat onely with the iron of his lance , weighed five thousand and sixe hundred sicles , which in our common weight , is more than 233 pound , of 12 ounces to the pound . Now it is certaine that the rest of his armes taking his Target , Helmet , Braselets , and other Armour together , did weigh at the least 5 hundred pound , a thing prodigious ; seeing that the strongest man that now is , can hardly beare 200 pound , yet this Gyant carries this as a vesture without paine .

Solinus reporteth in his 5 Chap. of his Historie , that during the Grecians warre after a great overflowing of the rivers , there was found upon the sands the carkasse of a man , whose length was 33 cubits , ( that is 49 foote and a halfe ) therefore according to the proportion delivered , his face should bee 5 foote in length , a thing prodigious and monstrous .

Plinie in his 7. booke and 16. Chap. saith , that in the I le of Crete or Candie , a mountaine being cleaven by an earthquake , there was a body standing upright , which had 46 cubits of height : some beleeves that it was the body of Orion or Othus , ( but I thinke rather it was some Ghost or some delusion , ) whose hand should have beene 7 foote , and his nose two foot and a half long . But that which Plutarch in the life of Sertorius reports of is more strange , 〈◊〉 saith that in Timgy a Morative Towne ; where it is thought that the Gyant Antheus was buried , Sertorius could not beleeve that which was reported of his prodigious greatnesse , caused his sepulcher to bee opened , and found that his body did containe 60 cubits in length , then by proportion hee should bee 10 cubits or 15 foote in bredth ; 9 foote for the length of his face , 3 foote for his thumbe , which is neare the capacitie of the Colossus at Rhodes .

But behold here a fine fable of Symphoris Campesius , in his booke intituled Hortus Gallicus , who sayes that in the Kingdome of Sicile , at the foote of a mountaine neare Trepane , in opening the foundation of a house , they found a Cave in which was laid a Gyant , which held in stead of a staffe a great post like the mast of a Shippe : and going to handle it , it mouldered all into ashes except the bones which remained of an exceeding great measure , that in his head there might be easily placed 5 quarters of corne , and by proportion it should seeme that his length was 200 cubits , or 300 foote : if he had said that hee had beene 300 cubits in length , then he might have made us beleeve that Noahs Arke was but great enough for his sepulcher .

Who can beleeve that any man ever had 20 cubits , or 30 foote in length for his face , and a nose of 10 foote long ? but it is very certaine that there hath been men of very great stature , as the holy Scriptures before witnesseth , and many Authours worthy of beliefe relateth : Iosephus Acosta in his first booke of the Indian History , Chap. 19. a late writer , reporteth that at Peru was found the bones of a Gyant , which was 3 times greater than these of ours are , that is , 18 foote : for it is usually attributed to the tallest ordinary man in these our times but 6 foote of length ; and Histories are full of the description of other Gyants of 9 , 10 , and 12 foote of height , and it hath beene seene in our times some which have had such heights as these .

PROBLEM . LXXI . Of the game at the Palme , at Trappe , at Bowles , Paile-maile and others .

THe Mathematickes often findeth place in sundry Games to aide and assist the Gamesters , though not unknowne unto them : hence by Mathematicall principles , the games at Tennis may be assisted ; for all the moving in it is by right lines and reflections . From whence comes it , that from the appearances of flat or convex Glasses , the production and reflection of the species are explained , is it not by right lines ? in the same proportion one might sufficiently deliver the motion of a balle or bowle by Geometricall lines and Angles .

diagram

And the first maxime is thus : When a Bowle toucheth another Bowle , or when a trapsticke striketh the Balle , the moving of the Balle is made in a right line , which is drawn from the Center of the Bowle by the point of contingencie .

Secondly , in all kinde of such motion ; when a Balle or Bowle rebounds , be it either against wood , a wall , upon a Drumme , a pavement , or upon a Racket ; the incident Angle is alwayes equall to the Angle of reflection .

Now following these maximes it is easie to conclude , first in what part of the wood or wall , one may make the Bowle or Balle goe to reflect or rebound , to such a place as one would : Secondly , how one may cast a Bowle upon another , in such sort that the first or the second shall goe and meete with the third , keeping the reflection or Angle of incidence equall . Thirdly , how one may touch a Bowle to send it to what part one pleaseth : such and many other practices may bee done . At the exercises at Keyles there must be taken heed that the motion , slacke or diminisheth by little and little , and may bee noted that the Maximes of reflections cannot be exactly observed by locall motion , as in the beames of light and of other quallities , whereof it is necessary to supply it by industry or by strength , otherwise one may be frustrated in that respect .

PROBLEM . LXXII . Of the Game of square formes .

NVmbers have an admirable secrecie , diversly applyed , as before in part is shewed , and here I will say some thing by way of transmutation of numbers .

diagram

It s answered thus , in the first forme the men were as the figure A , then each of these 4 Souldiers placed themselves at each Gate , and removing one man from each Angle to each Gate , then would they be also 9 in each side according to the figure B. Lastly , these 4 Souldiers at the Gates take away each one his Cum●rade , and placing two of these men which are at each Gate to each Angle , there will bee still 9 for each side of the square , according to the figure C. In like manner if there were 12 men , how might they be placed about a square that the first side shall have 3 every way , then disordered , so that they might be 4 every way ; and lastly being transported might make 5 every way , and this is according to the figures , F. G. H.

PROBLEM . LXXIII . How to make the string of a Viole sencibly shake , without any one touching it .

THis is a miracle in musicke , yet easie to bee experimented ; take a Viole or other Instrument , and choose two strings , so that there bee one betweene them ; make these two strings agree in one and the same tune : then move the Viole bow upon the greater string , and you shall see a wonder : for in the same time that that shakes which you play upon , the other will likewise sencibly shake without any one touching it ; and it is more admirable that the string which is betweene them will not shake at all : and if you put the first string to another tune or note , and loosing the pin of the string , or stopping it with your finger in any fret , the other string will not shake : and the same will happen if you take two Violes , and strike upon a string of the one , the string of the other will sencibly shake .

Now it may bee demanded how comes this shaking , is it in the ●●●ult sympathie , or is it in the strings being wound up to like notes o● tunes , that so ea●y the other may receive the impression of the 〈◊〉 , which is agitated or moved by the shaking or the trembling of the other : and whence is it that the Viole bow moved upon the first string , doth instantly in the same time move the third string and not the second ; if the cause be not either in the first or second : I leave to others to discant on .

EXAMINATION .

IN this Examination we have something else to imagine , than the bare sympathie of the Cords one to another : for first there ought to be considered the different effect that it produceth by extension upon one and the same Cord in capacitie : then what might be produced upon different Cords of length and bignesse to make them accord in a n●ison or octavo , or some consort intermediate : this being naturally examined , it will be facill to lay open a way to the knowledge of the true and immediate cause of this noble and admirable Phenomeny . Now this will sencibly appeare when the Cords are of equall length and greatnesse , and set to an unison ; but when the Cords differ from their equalitie , it will be lesse sencible : hence in one and the same Instrument , Cords at a unison shall excite or shake more than that which is at an octavo , and more than those which are of an intermediate proportionall consort : as for the other consorts they are not exempted , though the effect be not so sencible , yet more in one than in another : and the experiment will seeme more admirable in taking two Lutes , Violes &c. and in seting them to one tune : for then in touching the Cord of the one , it will give a sencible motion to the Cord of the other : and not onely so but also a harmony .

PROBLEM . LXXIIII . Of a vessell which containes three severall kindes of liquor , all put in at one bung-hole , and drawne out at one tappe severally without mixture .

THe vessell is thus made , it must be divided into three sells for to containe the three liquors , which admit to be Sacke , Clarret , and Whitewine : Now in the bung-hole there is an Ingine with three pipes , each extending to his proper sell , into which there is put a broach or funnell piersed in three places , in such sort that placing one of the holes right against the pipe which answereth unto him , the other two pipes are stopped ; then when it is full , turne the funnell , and then the former hole will be stopped and another open , to cast in other wine without mixing it with the other .

Now to draw out also without mixture , at the bottome of the vessell there must be placed a pipe or broach which may have three pipes , and a cocke piersed with three holes so artificially done , that turning the cocke , the hole which answereth to such of the pipes that is placed at the bottome , may issue forth such wine as belongeth to that pipe , and turning the Cocke to another pipe , the former hole will bee stopped : and so there will issue

diagram forth another kinde of wine without any mixtures ; but the Cocke may bee so ordered that there may come out by it two wines together , or all three kindes at once : but it seemes best when that in one vessell and at one Cocke , a man may draw severall kindes of wine , and which he pleaseth to drinke .

PROBLEM . LXXV . Of Burning-glasses .

IN this insuing discourse I will shew the invention of Prometheus how to steale fire from Heaven , and bring it downe to the Earth ; this is done by a little round Glasse , or made of steele , by which one may light a Candle and make it flame , kindle Fire-brans to make them burne , melt Lead , Tinne , Gould , and Silver , in little time : with as great ease as though it had beene put into a Cruzet over a great fire .

diagram

But this is nothing to the burning of those Glasses which are hollow , namely these which are of steele well polished , according to a parabolicall or ovall section : A sphaericall Glasse , or that which is according to the segment of a Sphaere , burnes very effectually about the fourth part of the Diamitor ; notwithstanding the Parabolie and Eclipticke sections have a great effect : by which Glasses there is also diverse figures represented forth to the eye .

The cause of this burning is the uniting of the beames of the Sunne , which heates mightily in the point of concourse or inflammation , which is either by transmission or reflection : Now it is pleasant to behold when one breatheth in the point of concourse , or throweth small dust there , or sprinkles vapours of hot water in that place ; by which the pyramidall point , or point of inflammation is knowne . Now some Authors promiseth to make Glasses which shall burne a great distance off , but yet not seene vulgarly produced , of which if they were made , the Parabolie makes the greatest effect , and is generally held to bee the invention of Archimedes or Proclus .

Maginus in the 5. Chap. of his Treatise of sphericall Glasses , shewes how one may serve himselfe with a concave Glasse , to light fire in the shaddow , or neare such a place where the Sunne shines not , which is by helpe of a flat Glasse , by which may be made a percussion of the beames of the Sunne into the concave Glasse , adding unto it that it serves to good use to put fire to a Mine , provided that the combustible matter bee well applyed before the concave Glasse ; in which hee sayes true : but because all the effect of the practice depends upon the placing of the Glasse and the Powder which he speakes not of : I will deliver here a rule more generall .

How one may place a Burning-glasse with his combustible matter in such sort , that at a convenient houre of the day , the Sunne shining , it shall take fire and burne : Now it is certaine that the point of inflammation or burning , is changed as the Sunne changeth place , and no more nor lesse , then the shaddow turnes about the stile of a Dyall ; therefore have regard to the Suns motion , and his height and place : a Bowle of Crystall in the same place that the toppe of the stile is , and the Powder or other combustible matter under the meridian , or houre of 12 , 1 , 2 , 3 , &c. or any other houre , and under the Sunnes arch for that day : now the Sunne comming to the houre of 12 , to 1 , 2 , 3 , &c. the Sunne casting his beames through the Crystall Bowle , will fire the materiall or combustible thing , which meets in the point of burning : the like may be observed of other Burning-glasses .

EXAMINATION .

IT is certaine in the first part of this Probleme that Conicall concave and sphericall Glasses , of what matter soever , being placed to receive the beames of the Sunne will excite heate , and that heate is so much the greater , by how much it is neere the point of concurse or inflamation . But that Archimedes or Proclus did fire or burne Shippes with such Glasses , the ancient Histories are silent , yea themselves say nothing ; besides the great difficultie that doth oppose it in remotenesse , and the matter that the effect is to worke upon : Now by a common Glasse wee fire things neere at hand , from which it seemes very facill to such which are lesse read , to doe it at a farre greater distances , and so by relation some deliver to the world by supposition that which never was done in action : this we say the rather , not to take away the most excellent and admirable effect whith are in Burning-glasses , but to shew the variety of antiquity , and truth of History : and as touching to burne at a great distance as is said of some , it is absolutely impossible ; and that the Parabolicall and Ovall Glasses were of Archimedes and Proclus invention , is much uncertaine : for besides the construction of such Glasses , they are more difficult than the obtuse concave ones are , and further , they cast not a great heate but neere at hand ; for if it bee cast farre off , the effect is little , and the heate weake : or otherwise such Glasses must be greatly extended to contract many beames to amasse a sufficient quantity of beames in Parabolicall and Conicall Glasses , the point of inflammation ought to concurre in a point , which is very difficult to bee done in a due proportion : Moreover if the place be farre remote as is supposed before , such a Glasse cannot be used but at a great inclination of the Sunne , by which the effect of burning is diminished , by reason of the weakenesse of the Sunne-beames .

And here may be noted in the last part of this Probleme , that by reason of obstacles if one plain Glasse be not sufficient ; a second Glasse may bee applyed to help it : that so if by one simple reflection it cannot be done , yet by a double reflexion the Sun-beames may be cast into the said Caverne or Mine ; and though the reflected beames in this case be weake , yet upon a fit cumbustible matter it will not faile to doe the effect .

PROBLEM . LXXVI . Containing many pleasant Questions by way of Arithmeticke .

I Will not insert in this Probleme that which is drawne from the Greeke Epigrams , but proposing the Question immediatly will give the answere also , without staying to shew the manner how they are answered ; in this I will not be tyed to the Greeke tearmes , which I account not proper to this place , neither to my purpose ; let these reade that will Diophanta Scheubelius upon Euclide and others , and they may be satisfied .

Of the Asse and the Mule.

IT happened that the Mule and the Asse upon a day making a voyage , each of them carryed a Barrell full of wine : now the lasie Asse felt her selfe over loaden , complained and bowed under her burthen ; which the Mule seeing , said unto her being angry , ( for it was in the time when beasts spake ) thou great Asse , wherefore complainest thou ? if I had but onely one measure of that which thou carriest , I should be loaden twice as much as thou art , and if I should give a measure of my loading to thee , yet my burthen would be as much as thine .

Now how many measures did each of them carry ? Answere , the Mule did carry 7 measures , and the Asse 5 measures : for if the Mule had one of the measures of the Asses loading , then the Mule would have 8 measures , which is double to 4 : and giving one to the Asse , each of them would have equall burthens : to wit , 6 measures a peece .

Of the number of Souldiers that fought before old Troy.

HOmer being asked by Hesiodus how many Grecian Souldiers came against Troy , who answered him thus ; the Grecians , said Homer , made 7 fires or had 7 Kitchins , and before every fire , or in every Kitchin there was 50 broaches turning to rost a great quantitie of flesh , and each broach had meate enough to satisfie 900 men : now judge how many men there might be . Answere , 315000. that is , three hundred and fifteene thousand men , which is cleare by multiplying 7 by 50 , and the product by 900 makes the said 315000.

Of the number of Crownes that two men had .

IOhn and Peter had certain number of crownes , Iohn said to Peter , if you give me 10 of your crownes , I shall have three times as much as you have : but Peter said to Iohn if you give me 10 of your crownes I shall have 5 times as much as you have : how much had each of them ? Answere , Iohn had 15 crownes and 5 sevenths of a crowne , and Peter had 18 crownes , and 4 sevenths of a crowne . For if you adde 10 of Peters crownes to these of Iohns , then should Iohn have 25 crownes and 5 sevenths of a crowne , which is triple to that of Peters , viz. 8 , and 4 seventhes : and Iohn giving 10 to Peter , Peter should have then 28 crownes , and 4 seventhes of a crowne , which is Quintupla , or 5 times as much as Iohn had left , viz. 5 crownes aad 5 seventhes .

In like manner two Gamesters playing together , A. and B : after play A. said to B , give me 2 crownes of thy money , and I shall have twice as much as thou hast : and B. said to A. give me 2 crownes of thy money , and I shall have 4 times as much as thou hast : now how much had each ? Answere , A. had 3 and 5 seventhes , and B. had 4 and 6 seventhes .

About the houre of the day .

SOme one asked a Mathematician what a clocke it was , who answered that the rest of the day is foure thirds of that which is past : now judge what a clocke it is . Answere , if the day were according to the Iewes and ancient Romans , which made it alwayes to bee 12. houres , it was then the 5. houre , and one seventh of an houre , so there remained of the whole day 6 6/7 that is , 6 houres , and 6 seventhes of an houre . Now if you take the ⅓ of 5 1/7 it is 12/7 or 1 and 5/7 which multiplyed by 4 makes 6 and 6/7 which is the remainder of the day as before : but if the day had beene 24 houres , then the houre had beene 10 of the clocke , and two seventhes of an houre , which is found out by dividing 12 , or 24 by 7/3.

There might have beene added many curious propositions in this kinde , but they would bee too difficult for the most part of people : therefore I have omitted them .

Of Pythagoras Schollers .

PYthagoras being asked what number of Schollers hee had , answered , that halfe of them studied Mathematickes , the fourth part Physicke , the seventh part Rethoricke , and besides he had 3 women : now judge you saith he , how many Schollers I have . Answere , he had in all 28 ; the halfe of which is 14 , the quarter of which is 7 , and the seventh part of which is 4 : which 14 , 7 , and 4 , makes 25 , and the other 3 to make up the 28 , were the 3 women .

Of the number of Apples given amongst the Graces and the Muses .

THe three Graces carrying Apples upon a day , the one as many as the other , meet with the 9 Muses , who asked of them some of their apples ; so each of the Graces gave to each of the Muses alike , and the distribution being made , they found that the Graces and the Muses had one as many as the other : The question is how many apples each Grace had , and how many they gave to each Muse . To answere the question , joyne the number of Graces and Muses together which makes 12 , and so many apples had each Grace : Now may you take the double , triple , &c. of 12. that is 24 , 36 , &c. conditionally , that if each Grace had but 12 , then may there be allotted to each Muse but one onely ; if 24 , then to each 2 apples ; if 36 , then to each Muse 3 apples ; and so the distribution being made , they have a like number , that is , one as many as the other .

Of the Testament or last Will of a dying Father .

A Dying Father left a thousand crownes amongst his two children ; the one being legittimate , and the other a Bastard , conditionally that the fifth part which his legittimate Sonne should have , should exceed by 10 , the fourth part of that which the Bastard should have : what was each ones part ? Answere , the legittimate Sonne had 577 crownes , and 7/9 and the Bastard 422 crownes and 2/9 : now the fift part of 577 and 7 ninthes is 115 , and 5/9 and the fourth part of 422 and 2/9 is 105 and 5/9 which is lesse then 115 5/9 by 10 , according to the Will of the Testator .

Of the Cuppes of Craesus .

CRaesus gave to the Temple of the Gods sixe Cups of Gould , which weighed together 600 Drammes , but each Cup was heavier one than another by one Dramme : how much did each of them therefore weigh ? Answere , the first weighed 102 Drammes and a halfe ; the second 101 Drammes and a halfe ; the third 100 Drammes and ½ ; the fourth 99 and a halfe ; the fift 98 and a halfe ; and the sixt Cup weighed 79 Drammes and a halfe : which together makes 600 Drammes as before .

Of Cupids Apples .

CVpid complained to his mother that the Muses had taken away his apples , Clio , said he , tooke from me the fift part , Euterpe the twelfth part , Thalia the eight part , Melpomene the twentieth part , Erates the seventh part , Terpomene the fourth part : Polyhymnia tooke away 30 , Vrania 120 , and Calliope 300 : so there were left me but 5. Apples ; how many had he in all at the first , I answer 3360.

There are an infinite of such like questions amongst the Greeke Epigrammes : but it would be unpleasant to expresse them all : I will onely adde one more , and shew a generall rule for all the rest .

Of a Mans Age.

A Man was said to passe the halfe part of his life in childhood , the fourth part in his youth , the third part in Manhood , and 18. yeares besides in olde age : what might his Age be ? the answer is , 72. yeares : which and all others is thus resolved : multiplie ⅙ . ¼ . and ⅓ . together , that is , 6. by 4. makes 24. and that againe by 3. makes 72. then take the third part of 72. which is 24. the fourth part of it , which is 18 , and the sixth part of it which is 12. these added together make 54. which taken from 72. rests 18. this divided by 18. ( spoken in the Question ) gives 1 , which multiplyed by the summe of the parts , viz. 72. makes 72. the Answer as before .

Of the Lion of Bronze placed upon a Fountaine with his Epigramme .

OVt of my right eye if I let water passe , I can fill the Cisterne in 2. dayes : if I let it passe out of the left eye , it wil be filled in 3. dayes , if it passe out of my feete the Cisterne will bee 4. dayes a filling ; but if I let the water passe out of my mouth , I can fill the Cisterne then in 6. houres : in what time should I fill it , if I powre forth the water at all the passages at once .

The Greekes ( the greatest talkers in the world ) variously applie this question to divers statues , and pipes of Fountaines : and the solution is by the Rule of 3. by a generall Rule , or by Algeber .

They have also in their Anthologie many other questions , but because they are more proper to exercise , than to recreate the spirit , I passe them over as before with silence .

PROBLEM . LXXVII . Divers excellent and admirable experiments upon Glasses .

THere is nothing in the world so beautifull as light : and nothing more recreative to the sight , than Glasses which reflect : therefore I will now produce some experiments upon them , not that I will dive into their depth ( that were to lay open a misterious thing ) but that which may delight and recreate the spirits : Let us suppose therefore these principles , upon which is built the demonstration of the apparances which is made in all sort of Glasses .

First , that the rayes or beames , which reflecteth upon a Glasse , maketh the Angle of Incident equall to the Angle of Reflection , by the first Theo. of the Catoptick of Euc.

Secondly , that in all plaine Glasses , the Images are seene in the perpendicular line to the Glasse as farre within the Glasse as it is without it .

Thirdly , in Concave , or Convex Glasses , the Images are seene in the right line which passeth from the object and through the Center in the Glasse Theo. 17. and 18.

And here you are to understand that there is not meant onely these which are simple Glasses or Glasses of steele , but all other bodies , which may represent the visible Image of things by reason of their reflection , as water , marble , muttle , or such like . Now take a Glasse in your hand and make experiment upon that which followeth .

Experiment upon flat and plaine Glasses .

FIrst , a man cannot see any thing in these Glasses , if he be not directly and in a perpendicular line before it , neither can bee see an object in these Glasses , if it be not in such a place , that makes the Angle of incidence equall to the Angle of reflexion : therefore when a Glasse stands upright , that is , perpendicular to the Horizon , you cannot see that which is above , ex - the Glasse be placed downe flat : and to see that on the right hand , you must bee on the left hand , &c.

Secondly , an Image cannot bee seene in a Glasse , if it be not raised above the surface of it ; or place a Glasse upon a wall , you shall see nothing which is upon the plaine of the wall ; and place it upon a Table or Horizontall Plaine , you shall see nothing of that which is upon the Table .

Thirdly , in a plaine Glasse all that is seene appeares or seemes to sinke behinde the Glasse , as much as the Image is before the Glasse : as before is said .

Fourthly , as in water a Glasse lying downe flat , or Horizontall , Towers , Trees , Men , or any height doth appeare , inversed or upside downe ; and a Glasse placed upright , the right hand of the Image seemes to bee the left , and the left seemes to be the right .

Fiftly , will you see in a Chamber that which ● done in the street , without being seene : then a Glasse must bee disposed , that the line upon which the Images come on the Glasse , make the Angle of incidence equall to that Angle of reflexion .

diagram

Seventhly , present a Candle upon a plaine Glasse , and looke flauntingly upon it , so that the Candle and the Glasse bee neere in a right line , you shall see 3. 4 5. &c Images ; from one and the same Candle .

Eightly , take two plaine Glasses , and hold them one against the other , you shall alternately see them often times one within the other , yea within themselves , againe and againe .

Ninthly , if you hold a plaine Glasse behind your head , & another before your face , you may see the hinder part of your head , in that Glasse which you hould before your face .

Tenthly , you may have a fine experiment if you place two Glasses togeather , that they make an acute angle , and so the lesser the angle is , the more apparances you shall see , the one direct , the other inversed , the one approaching , and the other retyring .

Eleventhly , it is wonder and astonishment to some , to see within a Glasse an Image without knowing from whence it came , and it may be done many wayes : as place a Glasse higher than the eye of the behoulder , and right against it is some Image ; so it resteth not upon the beho●der , but doth cast the Image upwards . Then place another object , so that it reflect , or cast the Image downeward to the eye of the spectator , without perceiving it being hid behind something , for then the Glasse will represent a quite contrary thing , either than that which is before the Glasse , or that which is about it .

Twelthly , if there bee ingraved behind the backside of a Glasse , or drawne any Image upon it , it will appeare before as an Image , without any appearance : or portrature to be perceived .

EXAMINATION .

THis 12. Article of ingraving an Image behind the Glasse , will be of no great consequence , because the linaments will seeme so obscure , but if there were painted some Image , and then that covered according to the usuall covering of Glasses behind , and so made up like an ordinary looking Glasse having an Image in the middle , in this respect it would be sufficient pleasant : and that which would admire the Ignorant , and able to exercise the most subtillest , and that principally if the Glasse bee in an obscure place , and the light which is given to it be somewhat farre off .

PLace a Glasse neare the floare of a Chamber , and make a hole through the place under the Glasse , so that these which are below may not perceive it , and dispose a bright Image under the hole so that it may cast his species upon the Glasse , and it will cause admiration to those which are below that know not the cause ; The same may be done by placing the Image in a Chamber adjoyning , and so make it to be seene upon the side of the wall .

In these Chanell Images which shew one side a deaths head , and another side a faire face : and right before some other thing : it is a thing evident , that setting a plaine Glasse sidewise to this Image you shall see in it a contrary thing , then that which was presented before sidewise .

Lastly , it is a fine secret to present unto a plaine Glasse writing with such industrey , that one may reade it in the Glasse , & yet out of the Glasse there is nothing to be knowne , which will thus happen , if the writing be writ backward : But that which is more strange , to shew a kind of writing to a plaine Glasse , it shall appeare another kind of writing both against sence and forme , as if there were presented to the Glasse WEL. it would shew it ΜΕΓ if it were written thus MIV , and presented to the Glasse , it would appeare thus VIM ; for in the first , if the Glasse ly flat then the things are inversed that are perpendicular to the Glasse , if the Glasse and the object be upright , then that on the right hand , is turned to the left , at in the latter .

And here I cease to speake further of these plaine Glasses , eyther of the Admirable multiplications , or appearances , which is made in a great number of them ; for to content the sight in this particular , one must have recourse to the Cabinets of great Personages who inrich themselves with most beautifull ones .

Experiments upon Gibbous , or convex Sphaericall Glasses .

IF they be in the forme of a Bowle , or part of a great Globe of Glasse , there is singular contentment to contemplate on them .

First , because they present the objects lesse and more gracious , and by how more the Images are separated from the Glasse , by so much the more they deminish in Magnitude .

Secondly , they that shew the Images playting , or foulding , which is very pleasant , especially when the Glasse is placed downe , and behold in it some Blanching , seeling , &c. The upper part of a Gallerie , the porch of a Hall , &c. for they will be represented as a great vessell having more belly in the middle then at the two ends , and Fosts , and Ioists of Timber will seeme as Circles .

Thirdly , that which ravisheth the spirits , by the eye , and which shames the best perspective Painting that a Painter can make , is the beautifull contraction of the Images , that appeare within the sphericitie of these small Glasses , for present the Glasse to the lower end of a Gallarie , or at the Corner of a great Court full of People ; or towards a great street , Church , fortification , an Army of men , to a whole Cittie ; all the faire Architecture , and apparances will be seene contracted within the circuit of the Glasse with such varietie of Colours , and distinctions in the lesser parts , that I know not in the world what is more agreeable to the sight and pleasant to behold , in which you will not have an exact proportion but it will be variable , according to the distance of the Object from the Glasse .

Experimenss upon hollow , or Concave Sphaericall Glasses .

I Have heretofore spoken how they may burne , being made of Glasse , or Mettle , it remaines now that I deliver some pleasant uses of them , which they represent unto our sight , and so much the more notable it will be , by how much the greater the Glasse is , and the Globe from whence it is extracted .

EXAMINATION .

IN this we may observe that a section of 2. 3. or 4. Inches in diamiter , may be segments of spheares of 2. 3. or 4. foote , nay of so many fadome , for it is certaine that amongst these which comprehend a great portion of a lesser spheare , and these which comprehend a little segment of a great spheare whether they be equall or not in section , there will happen an evident difference in one and the same experiment , in the number , situation , quantitie , and figure of the Images of one or many different objects .

MAginus , in a little Tractat that he had upon these Glasses , witnesseth of himselfe that he hath caused many to bee polished for sundry great Lords of Italy , and Germanie , which were segments of Globes of 2. 3. and 4. foot diamiter ; and I wish you had some such like to see the experiments of that which followeth ; it is not difficult to have such made , or bought here in Towne , the contentment herein , would beare with the cost .

EXAMINATION .

TOuching Maginus hee hath nothing ayded us to the knowledge of the truth by his extract out of Vitelius , but left it : expecting it from others , rather than to be plunged in the search of it himselfe , affecting rather the forging of the matter , and composition of the Glasses , than Geometrically to establish their effects .

FIrst therefore in Concave Glasses , the Images are seene sometimes upon the surface of the Glasses , sometimes as though they were within it and behind it , deepely sunke into it , sometimes they are seene before , and without the Glasse , sometimes betweene the object and the Glasse ; sometimes in the place of the eye , sometimes farther from the Glasse then the object is : which comes to passe by reason of the divers concourse of the beames , and change of the place of the Images in the line of flection .

EXAMINATION .

THe relation of these apparances passe currant amongst most men , but because the curious may not receive prejudice in their experiments , some thing ought to bee said thereof to give it a more lively touch , in the true causes of these apparances ; in the first place it is impossible that the Image can be upon the surface of the Glasse , and it is a principall point to declare truly in which place the Image is seene in the Glasse : these that are more learned in Opticall knowledge affirme the contrary , and nature it selfe gives it a certaine place according to its position ; being alwayes seene in the line of reflection , which Alhazen , Vicellious , and others full of great knowledge , have confirmed by their writings : but in their particular they were two much occupied by the authority of the Ancients , who were not sufficiently circumspect in experience , upon which the principles of this subject ought to be built , and searched not fully , into the true cause of these apparances , seeing they leave unto posterities many falcities in their writings , and these that followed them for the most part fell into the like errors .

As for the Images to bide in the eye , it cannot be but is impertinent and absurd ; but it followeth that , by how much neerer the object approacheth to the Glasse , by so much the more the appearances seemes to come to the eye : and if the eye be without the point of concourse , and the object also ; as long as the object approacheth thereto , the representation of the Image cometh neere the eye , but passing the point of concourse it goes backe agains : these appearances thus approaching doth not a little astonish these which are ignorant of the cause : they are inversed , if the eye be without the point of concourse untill the object bee within , but contrarily if the eye be betweene the point of concourse and the Glasse , then the Images are direct : and if the eye or the object be in the point of concourse , the Glasse will be enlightened , and the Images confused ; and if there were but a sparke of fire in the said point of concourse , all the Glasse would seeme a burning firebrand , and we dare say it would occurre without chance , and in the night be the most certaine and subtilest light that can be , if a Candle were placed there . And whosoever shall enter into the serch of the truth of new experiments in this subject , without doubt hee will confirme what wee here speake of : and will finde new lights with a conveniable position to the Glasse , he will have reflexion of quantities , of truth , and fine secrets in nature , yet not knowne , which he may easily comprehend if he have but an indifferent sight , and may assure himselfe that the Images cannot exceed the fight , nor trouble it ; a thing too much absurd to nature .

And it is an absolute verity in this science , that the eye being once placed in the line of reflexion of any object , and moved in the same line : the object is seene in one and the same place immutable ; or if the Image and the eye move in their owne lines , the representation in the Glasse seemes to invest it selfe continually with a different figure .

NOw the Image comming thus to the eye , these which know not the secret drawes their sword when he sees an Image thus to issue out of the Glasse , or a Pistoll which some one holds behinde : and some Glasses will shew a sword wholly drawne out , separated from the Glasse , as though it were in the aire : and it is dayly exercised , that a man may touch the Image of his hand or his face out of the Glasse , which comes out the farther , by how much the Glasse is great and the Center remote .

EXAMINATION .

NOw that a Pistolle being presented to a Glasse behinde a man , and should come out of the Glasse and make him afraid , that stands before seeming to shoote at him : this cannot bee , for no object whatsoever presented to a concave Glasse , if it be not neerer to the Glasse then the eye is , it comes not out to the sight of the party ; therefore he needes not feare that which is said to be behinde his backe , and comes out of the Glasse , for if it doth come out , it must then necessarily be before his face : so in a concave Glasse , whose Center is farre remote ; if a sword , sticke , or such like be presented to the Glasse , it shall totally be seene to come forth of the Glasse , and all the hand that holds it . And here generally note , that if an Image bee seene to issue out of the Glasse to come towards the face of any one that stands by , the object shall be likewise seene to thrust towards that face in the Glasse , and may easily be knowne to all the standers by : so many persons standing before a Glasse , if one of the company take a sword and would make it issue forth towards any other that stands there : let him chuse his image in the glasse , and carry the sword right towards it , and the effect will follow . In like manner ones hand being presented to the Glasse ; as it is thrust towards the Center , so the representation of it comes towards it : and so the hands will seeme to be united , or to touch one another .

FRom which may bee concluded , if such a Glasse be placed at the seeling or planching of a Hall , so that the face bee Horizontall and looke downeward ; one may see under it as it were a man hanging by the feete ; and if there were many placed so , one could not enter into that place without great feare or scarcing : for one should see many men in the aire as if they were hanging by the feete .

EXAMINATION .

TOuching a Glasse tyed at a seeling or planching , that one may see a man hang by the feete in the aire , and so many Glasses , many men may be seene : without caution this is very absurd , for if the Glasse or Glasses bee not so great that the Center of the spheare upon which it was made , extend not neere to the head of him that is under it , it will not pleasantly appeare ; and though the Glasse should be of that capacitie that the Center did extend so farre , yet will not the Images bee seene to them which are from the Glasse , but onely to these which are under it , or neere unto it : and to them it will notably appeare , and it would be most admirable to have a Gallerie vated over with such Glasses , which would wonderfully astonish any one that enters into it : for all the things in the Gallery would be seene to hang in the aire , and you could not walke without incountering ayrie apparitions .

SEcondly , in flat or plaine Glasses the Image is seene equall to his object , and to represent a whole man , there ought to be a Glasse as great as the Image is : In convex Glasses the Images are seene alwaies lesse , in concave Glasses they may be seene greater or lesser , but not truly proportionable , by reason the diverse reflexions which contracts or inlargeth the Species : when ●he eye is betweene the Center and the surface of the Glasse , the Image appeares sometimes ●very great and deformed , and those which have but the appearance of the beginning of a beard on their chinne , may cheare up themselves to see they have a great beard ; these that seeme to be faire will thrust away the Glasse with despight , because it will transforme their beautie : these that put their hand to the Glasse will seeme to have the hand of a Gyant , and if one puts his finger to the Glasse it will be seene as a great Py●amide of flesh , inversed against his finger .

Thirdly , it is a thing admirable that the eye being approached to the point of concourse of the Glasse , there will bee seene nothing but an intermixture or confusion : but retyring backe a little from that point , ( because the rayes doth there meete , ) he shall see his Image inversed , having his head below and his feet above .

Fourthly , the diverse appearances caused by the motion of objects , either retiring or approaching : whether they turne to the right hand or to the left hand , whether the Glasse be hung against a wall , or whether it bee placed upon a Pavement , as also what may be represented by the mutuall aspect of concave Glasses , with plaine and convex Glasses : but I will with silence passe them over , onely say some thing of two rare experiments more as followeth .

The first is to represent by helpe of the Sun , such letters as one would upon the front of a house : so that one may reade them ; Magin●● do●h deliver the way thus . Write the letters saith he sufficiently bigge , but inversed upon the surface of the Glasse with some kinde of colour , or these letters may bee written with wax ; ( the easier to bee taken out againe : ) for then placing the Glasse to the Sunne , the letters which are written there will bee reverberated , or reflected upon the wall : hence it was perhaps that Pythagoras did promise with this invention to write upon the Moone .

In the second place , how a man may sundry wayes helpe himselfe with such a Glasse , with a lighted Torch or Candle , placed in the point of concourse or inflammation , which is neare the fourth part of the Diamiter : for by this meanes the light of the Candle will be reverberated into the Glasse , and will be cast backe againe very farre by parrallell lines , making so great a light that one may cleerely see that which is done farre off , yea in the campe of an Enimie : and those which shall see the Glasse a farre off , will thinke they see a Silver Basin inlightened , or a fire more resplendant then the Torch . It is this way that there are made certaine Lanthornes which dazell the eyes of those which comes against them ; yet it serves singular well to enlighten those which carry them , accommodating a Candle with a little hollow Glasse , so that it may sucessively bee applyed to the point of inflammation .

In like manner by this reflected light , one may reade farre off , provided that the letters be indifferent great , as an Epitaph placed high , or in a place obscure ; or the letter of a friend which dares not approach without perill or suspition .

EXAMINATION .

THis will not bee scarce sencible upon a wall remote from the Glasse , and but indifferently seene upon a wall which is neare the Glasse , and withall it must be in obscuritie or shadowed : or else it will not be seen . To cast light in the night to a place remote , with a Candle placed in the point of concourse or inflammation , is one of the most notablest properties which can be shewne in a concave Glasse : for if in the point of inflammation of a parabolicall section , a Candle bee placed , the light will bee reflected by parallell lines , as a columne or Cylinder ; but in the sphericall section it is defective in part , the beames being not united in one point , but somewhat scattering : notwithstanding it casteth a very great beautifull light .

LAstly , these which feare to hurt their sight by the approach of Lampes or Candles , may by this artifice place at some corner of a Chamber , a Lampe with a hollow Glasse behinde it , which will commodiously reflect the light upon a Table , or to a place assigned : so that the Glasse bee somewhat raised to make the light to streeke upon the Table with sharpe Angles , as the Sunne doth when it is but a little elevated above the Horizon : for this light shall exceed the light of many Candles placed in the Roome , and bee more pleasant to the sight of him that useth it .

Of other Glasses of pleasure .

FIrst , the Columnary and Pyramidall Glasses that are contained under right lines , doth represent the Images as plaine Glasses doe ; and if they bee bowing , then they represent the Image , as the concave and convex Glasses doe .

Secondly , those Glasses which are plaine , but have ascents of Angles in the middle , will shew one to have foure eyes , two mouthes , two noses , &c.

EXAMINATION .

THese experiments will be found different according to the diverse meeting of the Glasses , which commonly are made scuing wise at the end , by which there will be two diverse superficies i● the Glasse , making the exteriour Angle somewhat raised , at the interiour onely one superficies , which may bee covered according to ordinary Glasses to cause a reflexion , and so it will be but one Glasse , which by refraction according to the different thickenesse of the Glasse , and different Angles of the scuing forme , doe differently present the Images to the eye , as foure eyes , two mouthes , two noses ; sometimes three eyes , one mouth , and one nose , the one large and the other long , sometimes two eyes onely ; with the mouth and the nose deformed , which the Glasse ( impenitrable ) will not shew . And if there be an interiour solid Angle , according to the difference of it , ( as if it be more sharpe ) there will be represented two distinct double Images , that is , two entire visages , and as the Angle is open , by so much the more the double Images will reunite and enter one within another , which will present sometimes a whole visage extended at large , to have foure eyes , two noses , and two mouthes ; and by moving the Glasse the Angle will vanish , and so the two superficies will be turned into one , and the duplicitie of Images will also vanish and appeare but one onely : and this is easily experimented with two little Glasse of steell , or such like so united , that they make diverse Angles and inclinations .

THirdly , there are Glasses which make men seeme pale , red , and coloured in diverse manners , which is caused by the dye of the Glasse , or the diverse refraction of the Species : and these which are made of Silver , Latine , Steele , &c. doth give the Images a diverse colour also . In which one may see that the appearances by some are made faire , younger or older than they are ; and contrarily others will make them foule and deformed : and give them a contrary visage , for if a Glasse bee cut as it may be , or if many peeces of Glasse bee placed together to make a conveniable reflexion : there might be made of a Mole ( as it were ) a mountaine , of one Haire a Tree , a Fly to be as an Elephant : but I should be too long if I should say all that which might be said upon the property of Glasses . I will therefore conclude this discourse of the properties of these Glasses with these foure recreative Pr●blemes following .

PROBLEM : LXXVIII . 1. How to shew to one that is suspitious , what is done in another Chamber or Roome : notwithstanding the interposition of the wall .

FOr the performance of this , there must bee placed three Glasses in the two Chambers , of which one of them shall bee tyed to the planching or seeling , that it may be common to communicate the Species to each Glasse by reflexion , there being left some hole at the top of the wall against the Glasse to this end : the two other Glasses must be placed against the two walls at right Angles , as the figure here sheweth at B. and C.

Then the sight at E. by the line of incidence F E , shall fall upon the Glasse B A , and reflect upon the superficies of the Glasse B C , in the point G ; so that if the

diagram eye be at G , it should see E , and E , would reflect upon the third Glasse in the point H , and the eye that is at L , will see the Image that is at E. in the point of the Catheti : which Image shall come to the eye of the suspicious , viz. at L. by helpe of the third Glasse , upon which is made the second reflexion , and so brings unto the eye the object , though a wall be betweene it .

Corolaire . 1.

BY this invention of reflexions the assiegents of a Towne may be seene upon the Rampart : notwithstanding the Parapet ; which the asseiged may doe by placing a Glasse in the hollow of the Ditch , and placing another upon the toppe of the wall , so that the line of incidence comming to the bottome of the Ditch , make an Angle equall to the Angle of reflexion , then by this scituation and reflexion , the Image of the asseigment will bee seene to him that is upon the Rampart .

Corolaire . 2.

BY which also may bee inferred , that the same reflexions may bee seene in a Regular Polygon , and placing as may Glasses as there are sides , counting two for one ; for then the object being set to one of the Glasses , and the eye in the other , the Image will be seene easily .

Corolaire . 3.

FArther , notwithstanding the interposition of many Walls , Chambers , or Cabinets , one may see that which passeth through the most remotest of them , by placing of many Glasses as there are openings in the walls , making them to receive the incident Angles equall : that is , placing them in such sort by some Geometricall assistant , that the incident points may meete in the middle of the Glasses : but here all the defect will be , that the Images passing by so many reflexions , will be very weake and scarce observable .

PROBLEM . LXXIX . How with a Musket to strike a marke , not looking towards it , as exact as one aymed at it .

AS let the eye be at O , and the marke C ; place a plaine Glasse perpendicular as A B : so the marke C shall hee seene in Catheti C A , viz. in D , and the line

diagram of reflexion is D : now let the Musket F E , upon a rest , bee moved to and fro untill it be seene in the line O D , which admit to be H G : so giving fire to the Musket , it shall undoubtedly strike the marke .

Corolaires . From which may be gathered , that one may exactly shoote out of a Musket to a place which is not seene , being hindered by some obstacle , or other interposition .

AS let the eye be at M , the marke C , and the wall which keepes it from being seene , admit to be Q R : then

diagram set up a plaine Glasse as A B , and let the Musket be G H , placed upon his rest P O. Now because the marke C is seene at D , move the Musket to and fro untill it doth agree with the line of reflexion MB , which suppose at L I , so shall it be truly placed , and giving fire to the Musket , it shall not faile to strike the said marke at C.

PROBLEM . LXXX . How to make an Image to be seene hanging in the aire , having his head downeward .

TAke two Glasses , and place them at right Angles one unto the other , as admit A B , and C B , of which admit C B Horizontall , & let the eye be at H , & the object or image to be D E ; so D will bee reflected

diagram at F , so to N , so to H , E : then at G , so to M and then to H ; and by a double reflexion ED will seeme in Q R , the highest point D in R , and the point E in Q inversed as was said , taking D for the head , and E for the feete ; so it will be a man inversed , which will seeme to be flying in the aire : if the Image had wings unto it , and had secretly some motion : and if the Glasse were bigge enough to receive many reflexions , it would deceive the sight the more by admiring the changing of colours that would be seene by that motion .

PROBLEM . LXXXI . How to make a company of representative Souldiers seeme to be a Regiment , or how few in number may bee multiplyed to seeme to be many in number .

TO make the experiment upon men , there must be prepared two great Glasses ; but in stead of it we will suppose two lesser , as G H. and F I , one placed right against another perpendicular to the Horizon ,

diagram upon a plaine levell Table : between which Glasses let there bee ranged in Battalion-wife upon the same Table an number of small men , according to the square G , H , I , F , or in any other forme or posture : then may you evidently see how the said battle will bee multiplyed and seene farre bigger in the appearance than it is in effect .

Corolaire .

BY this invention you may make a little Cabinet of foure foote long , and two foote large , ( more or lesse ) which being filled with Rockes or such like things , or there being put into it Silver , Gould , stones of luster , Iewels , &c. and the walls of the said Cabinet being all covered or hung with plaine Glasse ; these visibles will appeare manifoldly increased , by reason of the multiplicitie of reflexions , and at the opening of the said Cabinet , having set something which might hide them from being seene , those that looke into it will be astonished to see so few in number which before seemed to be so many .

PROBLEM . LXXXII . Of fine and pleasant Dyalls .

COuld you choose a more ridiculous one than the naturall Dyall written amongst the Greeke Epigrams , upon which some sound Poet made verses ; shewing that a man carryeth about him alwaies a Dyall in his face by meanes of the nose and teeth : and is not this a jolly Dyall , for he neede not but open the mouth , the lines shall bee all the teeth , and the nose shall serve for the stile .

Of a Dyall of hearbes .

CAn you have a finer thing in a Garden , or in the middle of a Compartement , than to see the lines and the number of houres represented with little bushie hearbes , as of Hyssope or such which is proper to be cut in the borders ; and at the top of the stile to have a fanne to shew which way the winde bloweth : this is very pleasant and usefull .

Of the Dyall upon the fingers and the hand .

IS it not a commoditie very agreeable , when one is in the field or in some village without any other Dyall , to see onely by the hand what of the clocke it is , which gives it very neare ; and may bee practised by the left hand in this manner .

Take a straw or like thing of the length of the Index , or the second finger , hold this straw very right betweene the thumbe and the right finger , then stretch forth the hand and turne your backe and the palme of your hand towards the Sunne ; so that the shaddow of the muscle which is under the thumbe touch the line of life , which is betweene the middle of the two other great lines , which is seene in the palme of the hand ; this done , the end of the shaddow will shew what of the clocke it is : for at the end of the great finger it is 7 in the morning or 5 in the evening ; at the end of the Ring finger it is 8 in the morning , or 4 in the evening ; at the end of the little finger or first joynt , it is 9 in the morning , or 3 in the afternoone ; 10 and 2 at the second joynt , 11 and 1 at the third joynt , and midday in the line following , which comes from the end of the Index .

Of a Dyall which was about an Obeliske at Rome .

WAs not this a pretty fetch upon a pavement , to choose an Obeliske for a Dyall , having 106 foote in height , without removing the Basis of it ? Plinie assures us in his 26 booke and 8 Chap. that the Emperour Augustus having accommodated in the field of Mars an Obeliske of this height , he made about it a pavement , and by

diagram the industry of Manilius the Mathematitian , there was enchaced markes of Copper upon the Pavement , and placed also an apple of Gould upon the toppe of the said Obeliske , to know the houre and the course of the Sunne , with the increase and decrease of dayes by the same shadow : and in the same manner doe some by the shaddow of their head or other stile , make the like experiments in Astronomie .

Of Dyalls with Glasses .

PTolomie writes , as Cardanus reports ; that long agoe there were Glasses which served for Dyalls , and presented the face of the behoulder as many times as the houre ought to be , twice if it were 2 of the clocke ; 9 if it were 9 , &c. But this was thought to be done by the helpe of water , and not by Glasses ; which did leake by little and little out of the vessell , discovering anon one Glasse , then anon two Glasses , then 3 , 4 , 5 Glasses , &c. to shew so many faces as there were houres , which was onely by leaking of water .

Of a Dyall which hath a Glasse in the place of the Still .

WHat will you say of the invention of Mathematicians , which finde out dayly so many fine and curious novelties ? they have now a way to make Dyalls upon the wainscore or seeling of a Chamber , and there where the Sunne can never shine , or the beames of the Sunne cannot directly strike : and this is done in placing of a little Glasse in the place of the stile which reflecteth the light , with the same condition that the shaddow of the stile sheweth the houre : and it is easie to make experiment upon a common Dyall , changing onely the disposition of the Dyall , and tying to the end of the stile a peece of plaine Glasse . The Almaines use it much , who by this way have no greater trouble , but to put their noses out of their beds and see what a clocke it is ; which is reflected by a little hole in the window upon the wall or seeling of the Chamber .

EXAMINATION .

IN this there is two experiments considerable , the first is with a very little Glasse placed so that it may be open to the beames of the Sunne ; the other hath respect to a spacious or great Glasse placed to a very little hole , so that the Sun may shine on it , for then the shaddow which is cast upon the Dyall is converted into beames of the Sunne , and will reflect and bee cast upon a plaine opposite : and in the other it is a hole in the window or such like , by which may passe the beames of the Sunne which representeth the extreamity of the stile , and the Glasse representeth the plaine of the Dyall , upon which the beames being cast in manner of shaddowes reflecteth upon a plaine opposite : and it is needfull that in this second way the Glasse may be spatious as before to receive the delineaments of the Dyall .

Otherwise you may draw the lineaments of a Dyall upon any plaine looking-glasse which reflecteth the Sunne-beames , for the applying a stile or a pearle at the extreamitie of it : and placed to the Sunne , the reflexion will be answerable to the delineaments on the Glasse : but here note that the Glasse ought to be great , and so the delineaments thereon .

But that which is most noble is to draw houre lines upon the outside of the Glasse of a window , and placing a stile thereto upon the outside , the shaddow of the stile will be seene within , and so you have the houre more certaine without any difficultie .

Of Dyalls with water .

SVch kinde of Dyalls were made in ancient times , and also these of sand : before they had skill to make Sun-dyalls or Dyalls with wheeles ; for they used to fill a vessell with water , and having experience by tryall that it would runne out all in a day , they did marke within the vessell the houres noted by the running of the water ; and some did set a peece of light board in the vessell to swimme upon the top of the water , carrying a little statue , which with a small sticke did point out the houre upon a columne or wall , figured with houre notes as the vessell was figured within .

diagram

Now it seemes a safer way that the water passe out by drop and drop , and drop into a Cylindricall Glasse by helpe of a Pipe : for having marked the exterior part of the Cylinder in the houre notes , the water it selfe which falls within it , will shew what of the clocke it is , farre better than the running of sand ; for by this may you have the parts of the houres most accurate , which commonly by sand is not had : and to which may be added the houres of other Countreyes with greater ease . And here note that as soone as the water is out of one of the Glasses you may turne it over into the same againe out of the other , and so let it runne an new .

PROBLEM . LXXXIII . Of Cannons or great Artillery . Souldiers , and others would willingly see this Probleme , which containes three or foure subtile questions : The first is how to charge a Cannon without Powder .

THis may be done with aire and water only , having throwne cold water into the Cannon , which might be squirted forceably in by the closure of the mouth of the Peece , that so by this pressure the aire might more condence ; then having a round peeee of wood very just , and oyled well for the better to slide , and thrust the Bullet when it shall be time : This peece of wood may bee held fast with some Pole , for feare it be not thrust out before his time : then let fire bee made about the Trunion or hinder part of the Peece to heate the aire and water , and then when one would shoote it , let the pole be quickly loosened : for then the aire searching a greater place , and having way now offered , will thrust out the wood and the bullet very quicke : the experimence which wee have in long trunkes shooting out pellats with aire only , sheweth the verity of this Probleme .

2. In the second question it may be demanded , how much time doth the Bullet of Cannon spend in the aire before it falls to the ground .

THe resolution of this Question depends upon the goodnesse of the Peece and charge thereof , seeing in each there is great difference . It is reported that Ticho Brahe , and the Landsgrave did make an experiment

diagram upon a Cannon in Germany , which being charged and shot off ; the Bullet spent two minutes of time in the aire before it fell : and the distance was a German mile , which distance proportionated to an houres time , makes 120. Italian miles .

3. In the third question it may be asked , how it comes to passe , that a Cannon shooting upwards , the Bullet flies with more violence than being shot point-blanke , or shooting downeward .

IF we regard the effect of a Cannon when it is to batter a wall , the Question is false , seeing it is most evident that the blowes which fall perpendicular upon a wall , are more violent than these which strikes byas-wise or glaunsingly .

But considering the strength of the blow only , the Question is most true , and often experimented to be found true : a Peece mounted at the best of the Randon , which is neare halfe of the right , conveyes her Bullet with a farre greater violence than that which is shot at , Point blanke or mounted paralell to the Horizon .

The common reason is , that shooting high , the fire carries the bowle a longer time in the aire , and the aire moves more facill upwards , than downewards , because that the ayrie circles that the motion of the bullet makes are soonest broken . Howsoever this be the generall tenet , it is curious to find out the inequallity of moving of the aire ; whether the Bullet fly upward , downeward , or right forward , to produce a sencible difference of motion : and some thinke that the Cannon being mounted , the Bullet pressing the Powder maketh a greatar resistance , and so causeth all the Powder to be inflamed before the Bullet is throwne out , which makes it to be more violent than otherwise it would be . When the Cannon is otherwise disposed , the contrary arives , the fire leaves the Bullet , and and the Bullet rouling from the Powder resists lesse : and it is usually seene , that shooting out of a Musket charged onely with Powder ; to shoote to a marke of Paper placed Point blanke , that there are seene many small holes in the paper , which cannot be other than the graines of Powder which did not take fire : but this latter accident may happen from the overcharging of the Peece , or the length of it , or windy , or dampenesse of the Powder .

From which some may thinke , that a Cannon pointed right to the Zenith , should shoote with greater violence , than in any other mount or forme whatsoever : and by some it hath beene imagined , that a Bullet shot in this fashion hath beene consumed , melt , and lost in the aire , by reason of the violence of the blow , and the activitie of the fire ; and that sundry experiments hath beene made in this nature , and the Bullet never found . But it is hard to beleeve this assertion : it may rather be supposed that the Bullet falling farre from the Peece cannot be discerned where it falls : and so comes to be lost .

4. In the fourth place it may be asked , whether the discharge of a Cannon be so much the greater , by how much it is longer .

IT seemeth at the first to bee most true , that the longer the Peece is , the more violent it shootes : and to speake generally , that which is direction by a Trunke , Pipe , or other concavitie , is conveyed so much the more violent , or better , by how much it is longer ; either in respect of the sight , hearing , water , fire , &c. and the reason seemes to hold in Cannons , because in these that are long , the fire is retained a longer time in the concavitie of the Peece , and so throwes out the Bullet with more violence ; and experience lets us see that taking Cannons of the same boare , but of diversitie of length from 8 foote to 12 ; that the Cannon of 9 foote long hath more force than that of 8 foot long , and 10 more than that of 9 , and so unto 12 foote of length . Now the usuall Cannon carries 600 Paces , some more , some lesse ; yea , some but 200 Paces from the Peece , and may shoote into soft earth 15 or 17 foote , into sand or earth which is loose , 22 or 24 foote ; and in firme ground , about 10 or 12 foot , &c.

It hath beene seene lately in Germany , where there was made Peeces from 8 foote long to 17 foote of like boare , that shooting out of any Peece which was longer than 12 foote ; the force was diminished , and the more in length the Peece increaseth , the lesse his force was ; therefore the length ought to bee in a meane measure ; and it is often seene , the greater the Cannon is , by so much the service is greater : but to have it too long or too short , is not convenient , but a meane proportion of length to bee taken ; otherwise the flame of the fire will bee overpressed with aire : which hinders the motion in respect of substance , and distance of getting out ,

diagram

PROBLEM . LXXXIIII . Of prodigious progression and multiplication , of Creatures , Plants , Fruites , Numbers , Gold , Silver , &c. when they are alwayes augmented by certaine proportion .

HEre we shall shew things no lesse admirable , as recreative , and yet so certaine and easie to be demonstrated , that there needes not but Multiplication only , to try each particular : and first ,

Of graines of Mustard-seed .

FIrst , therefore it is certaine that the increase of one graine of Mustard-seed for 20 yeares space , cannot bee contained within the visible world , nay if it were a hundred times greater than it is : and holding nothing besides from the Center of the earth even unto the firmament , but onely small graines of Mustard-seed . Now because this seemes but words , it must be proved by Art ; as may bee done in this wise , as suppose one Mustard-seed sowne to bring forth a tree or branch , in each extendure of which might be a thousand graines : but we will suppose onely a thousand in the whole tree , and let us proceed to 20 yeares , every seed to bring forth yearely a thousand graines ; now multiplying alwayes by a thousand , in lesse then 17 years you shall have so many graines which will surpasse the sands , which are able to fill the whole firmament : for following the supposition of Archimedes , and the most probable opinion of the greatnesse of the firmament which Tico Brahe hath left us ; the number of graines of sand will be sufficiently expressed with 49 Ciphers , but the number of graines of Mustard-seed at the end of 17 yeares will have 52 Ciphers : and moreover graines of Mustard-seed , are farre greater than these of the sands : it is therefore evident that at the seventeenth yeare , all the graines of Mustard-seed , which shall successively spring from one graine onely , cannot be contained within the limits of the whole firmament ; what should it be then , if it should bee multiplyed againe by a thousand for the 18 yeare : and that againe by a thousand for every yeares increase untill you came to the 20 yeare ? its a thing as cleare as the day , that such a heap of Mustard-seed would be a hundred thousand times greater than the earth : and being onely but the increase of one graine in 20 yeares .

Of Pigges .

SEcondly , is it not a strange proposition , to say that the great Turke with all his Revenues , is not able to maintaine for one yeares time , all the Pigges that a Sow may pigge with all her race , that is , the increase with the increase unto 12 yeares : this seemes impossible , yet it s most true ; for let us suppose and put the case that a Sow bring forth but 6 , two males , and 4 females , and that each female shall bring forth as many every yeare , during the space of 12 yeares , at the end of the time there will be found above 33 millions of Pigges : now allowing a crowne for the maintenance of each Pigge for a yeare , ( which is as little as may be , being but neare a halfe of a farthing allowance for each day ; ) there must bee at the least so many crownes to maintaine them , one a yeare , viz. 33 millions , which exceedes the Turkes revenue by much .

Of graines of Corne.

THirdly , it will make one astonished to thinke that a graine of Corne , with his increase successively for the space of 12 yeares will produce in grains 244140625000000000000 , which is able to load almost all the creatures in the world .

To open which , let it be supposed that the first yeare one graine being sowed brings forth 50 , ( but sometimes there is seen 70 , sometimes 100 fold ) which graines sowen the next yeare , every one to produce 50 , and so consequently the whole and increase to be sowen every yeare , untill 12 yeares bee expired , there will bee of increase the aforesaid prodigious summe of grains , viz. 244140625000000000000 , which will make a cubicall heape of 6258522 graines every way , which is more than a cubicall body of 31 miles every way : for allowing 40 graines in length to each foote , the Cube would bee 156463 foot every way : from which it is evident that if there were two hundred thousand Citties as great as London , allowing to each 3 miles square every way , and 100 foot in height , there would not bee sufficient roome to containe the aforesaid quantitie of Corne : and suppose a bushell of Corne were equall unto two Cubicke feete , which might containe twenty hundred thousand graines , then would there be 122070462500000 bushells , and allowing 30 bushells to a Tunne , it would bee able to loade 8138030833 vessells , which is more than eight thousand one hundred and thirty eigh millions , shippe loadings of 500 Tunne to each shippe : a quantitie so great that the Sea is scarce able to beare , or the universall world able to finde vessells to carry it : And if this Corne should bee valued at halfe a crowne the bushell , it would amount unto 15258807812500 pounds sterling , which I thinke exceedes all the Treasures of all the Princes , and of other particular men in the whole world : and is not this good husbandry to sowe one graine of Corne , and to continue it in sowing , the increase onely for 12 yeares to have so great a profit .

Of the increase of Sheepe .

FOurthly , those that have great flockes of Sheepe may bee quickly rich if they would preserve their Sheepe without killing or selling of them : so that every Sheepe produce one each yeare , for at the end of 16 yeares , 100 Sheepe will multiply and increase unto 61689●00 , which is above 60 millions , and 16 hundred thousand Sheepe : now supposing them worth but a crowne a peece , it would amount unto 15422400 pounds sterling , which is above 15 millions , and foure hundred and twenty thousand pounds , a faire increase of one Sheepe : and a large portion for a Childe if it should bee allotted .

Of the increase of Cod-fish , Carpes , &c.

FIftly , if there be any creatures in the world that doth abound with increase or fertilitie , it may be rightly attributed to fish ; for they in their kindes produce such a great multitude of egges , and brings forth so many little ones , that if a great part were not destroyed continually , within a little while they would fill all the Sea , Ponds , and Rivers in the world ; and it is easie to shew how it would come so to passe , onely by supposing them to increase without taking or destroying them for the space of 10 or 12 yeares : having regard to the soliditie of the waters which are allotted for to lodge and containe these creatures , as their bounds and place of rest to live in .

Of the increase and multiplication of men .

SIxtly , there are some that cannot conceive how it can be that from eight persons ( which was saved after the deluge or Noahs flood ) should spring such a world of people to begin a Monarchie under Nimrod , being but 200 yeares after the flood , and that amongst them should be raised an army of two hundred thousand fighting Men : But it is easily proved if we take but one of the Children of Noah , and suppose that a new generation of people begun at every 30 yeares , and that it be continued to the seventh generation which is 200 yeares ; for then of one onely family there would bee produced one hundred and eleven thousand soules , three hundred and five to begin the world : though in that time men lived longer , and were more capable of multiplication and increase : which number springing onely from a simple production of one yearely , would be farre greater , if one man should have many wives , which in ancient times they had : from which it is also that the Children of Israel , who came into Egypt but onely 70 soules , yet after 210 yeares captivitie , they came forth with their hostes ; that there was told sixe hundred thousand fighting men , besides old people , women and children ; and he that shall separate but one of the families of Ioseph , it would bee sufficient to make up that number : how much more should it bee then if wee should adjoyne many families together ?

Of the increase of numbers .

SEventhly , what summe of money shall the Citie of London bee worth , if it should bee sold , and the mony be paid in a yeare after this manner : the first weeke to pay a pinne , the second weeke 2 pinnes , the third weeke 4 pinnes , the fourth weeke 8 pinnes , the fift weeke 16 pinnes : and so doubling untill the 52 weekes , or the yeare be expired .

Here one would thinke that the value of the pinnes would amount but to a small matter , in comparison of the Treasures , or riches of the whole Citie : yet it is most probable that the number of pinnes would amount unto the sum of 4519599628681215 , and if we should allow unto a quarter a hundred thousand pinnes , the whole would containe nintie eight millions , foure hundred thousand Tunne : which is able to loade 45930 Shippes of a thousand Tunne a peece : and if wee should allow a thousand pinnes for a penny , the summe of money would amount unto above eighteene thousand , eight hundred and thirty millions of pounds sterling , an high price to sell a Citie at : yet certaine , according to that first proposed . So if 40 Townes were sold upon condition to give for the first a penny , for the second 2 pence , for the third 4 pence , &c. by doubling all the rest unto the last , it would amount unto this number of pence , 1099511627775 , which in pounds is 4581298444 , that is foure thousand five hundred and fourescore millions of pounds and more .

Of a man that gathered up Apples , Stones , or such like upon a condition .

EIghtly , admit there were an hundred Apples , Stones , or such like things that were placed in a straight line or right forme , a pace one from another , and a basket being placed a pace from the first : how many paces would there be made to put all these Stones into the basket , by fetching one by one : this would require neare halfe a day to doe it , for there would be made tenne thousand and a hundred paces before he should gather them all up .

Of Changes in Bells , in musicall Instruments , transmutation of places , in numbers , letters , men or such like .

NInthly , is it not an admirable thing to consider how the skill of numbers doth easily furnish us with the knowledge of mysterious and hidden things , which simply looked into by others that are not versed in Arithmeticke , doe present unto them a world of confusion and difficultie .

As in the first place , it is often debated amongst our common Ringers , what number of Changes there might be made in 5 , 6 , 7 , 8 , or more Bells : who spend much time to answere their owne doubts , entering often into a Labyrinth in the serch thereof : or if there were 10 voyces , how many severall notes might there be ? These are propositions of such facillitie , that a child which can but multiply one number by another , may easily resolve it , which is but only to multiply every number from the unitie successively in each others product , unto the terme assigned : so the 6. number that is against 6. in the Table , is 720 , and so many Changes may be made upon 6 Bells , upon 5 there are 120 , &c.

In like manner against 10 in the Table is 3628800 , that is , three millions , sixe hundred twenty eight thousand , eight hundred & fourescore : which shewes that 10 voyces may have so many consorts , each man keeping his owne note , but onely altering his place ; and so of stringed Instruments : & the Gamauth may be varied according to which , answerable to the number against X , viz. 1124001075070399680000 notes , from which may be drawne this , or the like proposition .

diagram

Hence from this mutabilitie of transmutation , it is no marvell that by 24 letters there ariseth and is made such variety of languages in the world , and such infinite number of words in each language ; seeing the diversitie of syllables produceth that effect ; and also by the interchangeing and placing of letters amongst the vowels , and amongst themselves maketh these syllables : which alphabet of 24 letters may be varied so many times , vi . 620448593438860623360000 which is sixe hundred twenty thousand , foure hundred forty eight millions , five hundred ninety three thousand , foure hundred thirty eight millions of millions , and more .

Now allowing that a man may reade or speake one hundred thousand words in an houre , which is twice more words than there are contained in the Psalmes of David , ( a taske too great for any man to doe in so short a time ) and if there were foure thousand sixe hundred and fifty thousand millions of men , they could not speake these words ; ( according to the hourely proportion aforesaid in threescore and ten thousand yeares ; which variation and transmutation of letters , if they should bee written in bookes , allowing to each leafe 28000 words , ( which is as many as possibly could bee inserted , ) and to each booke a reame or 20 quire of the largest and thinnest printing paper ; so that each book being about 15 inches long , 12 broad , and 6 thicke : the bookes that would be made of the transmutation of the 24 letters aforesaid , would bee at least 38778037089928788 : and if a Library of a mile square every way , of 50 foot high , were made to containe 250 Galleries of 20 foote broad a peece , it would containe foure hundred millions of the said bookes : so there must be to containe the rest no lesse than 96945092 such Libraries ; and if the bookes were extended over the surface of the Globe of the earth , it would a decuple covering unto it : a thing seeming most incredible that 24 letters in their transmutation should produce such a prodigious number ; yet most certaine and infallible in computation .

Of a Servant hired upon certaine conditions .

A Servant said unto his master , that hee would dwell with him all his life time , if he would but onely lend him land to sowe one graine of Corne with all his increase for 8 yeares time ; how thinke you of this bargaine : for if he had but a quarter of an intch of ground for each graine , and each graine to bring forth yearely of increase 40 graines ; the whole sum would amount unto , at the terme aforesaid , 6553600000000 graines : and seeing that three thousand and sixe hundred millions of intches doe but make one mile square in the superficies , it shall bee able to receive fourteene thousand and foure hundred millions of graines , which is 14400000000 : thus dividing the aforesaid 6553600000000 , the Quotient will bee 455 , and so many square miles of land must there be to sow the increase of one graine of Corne for 8 yeares , which makes at the least foure hundred and twenty thousand Acres of land , which rated but at five shillings the Acre per Annum , amounts unto one hundred thousand pound ; which is twelve thousand and five hundred pound a yeare , to bee continued for 8 yeares ; a pretty pay for Master Servants 8 yeares service .

PROBLEM . LXXXV . Of Fountaines , Hydriatiques , Machinecke , and other experiments upon water , or other liquor .

1. First how to make water at the foote of a mountaine to ascend to the top of it , and so to descend on the other side .

TO doe this there must bee a Pipe of lead , which may come from the Fountaine A , to the top of the Mountaine B ; and so to descend on the other side a little lower than the Fountaine , as at C : then make a hole in the Pipe at the toppe of the

diagram Mountaine , as at B , and stop the end of the Pipe at A and C ; and fill this Pipe at B with water : and close it very carefully againe at B , that no aire get in : then unstop the end at A , and at C ; then will the water perpetually runne up the hill , and descend on the other side , which is an invention of great consequence to furnish Villages that want water .

2. Secondly , how to know what wine or other liquor there is in a vessell without opening the bung-hole , and without making any other hole , than that by which it runs out at the toppe .

IN this Probleme there is nothing but to take a bowed pipe of Glasse , and put it into the faucets hole , and stopping it close about : for then you shall see the wine or liquor to ascend in this Pipe , untill it bee just even with the liquor in the vessell ; by which a man may fill the vessell , or put more into it : and so if need were , one may empty one vessell into another without opening the bung-hole .

3. Thirdly , how is it that it is said that a vessell holds more water being placed at the foote of a Mountaine , than standing upon the toppe of it .

THis is a thing most certaine , because that water and all other liquor disposeth it selfe spherically about the Center of the earth ; and by how much the vessell is nearer the Center , by so much the more the surface of the water makes a lesser spheare , and therefore every part more gibbous or swelling , than the like part in a greater spheare : and therefore when the same vessell is farther from the Center of the earth , the surface of the water makes a greater spheare , and therefore lesse gibbous , or swelling over the vessell : from whence it is evident that a vessell neare the Center of the earth holds more water than that which is farther remote from it ; and so consequently a vessell placed at the bottome of the Mountaine holds more water , than being placed on the top of the Mountaine : First , therefore one may conclude , that one and the same vessell will alwayes

diagram hold more : by how much it is nearer the center of the earth . Secondly , if a vessell be very neare the Center of the earth , there will bee more water above the brims of it , than there is within the vessell . Thirdly , a vessell full of water comming to the Center will spherically increase , and by little and little leave the vessell ; and passing the Center , the vessell will be all emptied . Fourthly , one cannot carry a Paile of water from a low place to a higher , but it will more and more run out and over , because that in ascending it lies more levell , but descending it swelles and becomes more gibbous .

4. Fourthly , to conduct water from the toppe of one Mountaine , to the top of another .

AS admit on the top of a Mountaine there is a spring , and at the toppe of the other Mountaine there are inhabitants which wants water : now to make a bridge from one Mountaine to another , were difficult and too great a charge ; by way of Pipes it is easie and of no great price : for if at the spring on the toppe of the Mountaine be placed a Pipe , to descend into the valley , and ascend to the other Mountaine , the water will runne naturally , and continually , provided that the spring be somewhat higher than the passage of the water at the inhabitants .

5. Fiftly , of a fine Fountaine which spouts water very high , and with great violence by turning of a Cocke .

LEt there be a vessell as A B , made close in all his parts , in the middle of which let C D be a Pipe open at D neare the bottome , and then with a Squirt squirt in the water at C , stopped above by the cocke or faucet C , with as great violence as

diagram possible you can ; and turne the Cocke immediately . Now there being an indifferent quantitie of water & aire in the vessell , the water keepes it selfe in the bottome , and the aire which was greatly pressed , seekes for more place , that turning the cocke the water issueth forth at the Pipe , and flyes very high ; and that especially if the vessell bee a little heated : some make use of this for an Ewer to wash hands withall , and therefore putting a moveable Pipe above C , such as the figure sheweth : which the water will cause to turne very quicke , pleasurable to behold .

6. Sixtly , of Archimedes screw , which makes water ascend by descending .

THis is nothing else but a Cylinder , about the which is a Pipe in forme of a screw , and when one turnes it , the water descends alwaies in respect of the Pipe : for it passeth from one part which is higher to that which is lower , and at the end of the engine the water is found higher than it was at the spring . This great enginer admirable in all Mathematicall Arts invented this Instrument to wash King Hieroies great vessells ,

diagram as some Authors sayes , also to water the fields of Egypt , as Diodorus witnesseth : and Carda●●● reporteth that a Citizen of Milan having made the like engine , thinking himselfe to bee the first inventer , conceived such exceeding joy , that he became foll . 2.

Againe a thing may ascend by descending , if a spirall line bee made having many circulations or revolutions ; the last being alwayes lesser than the first , yet higher than the Plaine supposed : it is most certaine that then putting a ball into it , and turning the spirall line so , that the first circulation may bee perpendicular , or touch alwayes the supposed Plaine : the ball shall in descending continually ascend , untill at last it come to the highest part of the spirall line , & so fall out . And here especially may be noted , that a moving body as water , or a Bullet , or such like , will never ascend if the helicall revolution of the screw be not inclining to the Horizon : so that according to this inclination the ball or liquor , may descend alwayes by a continuall motion and revolution . And this experiment may be more usefull , naturally made with a threed of iron ; or latine turned or bowed helically about a Cylinder , with some distinction of distances betweene the Helices ; for then having drawne out the Cylinder , or having hung or tied some weight at it in such sort , that the water may easily drop if one lift up the said thred : these helices or revolutions , notwithstanding will remaine inclining to the Horizon , and then turning it about forward , the said weight will ascend , but backward it will descend . Now if the revolutions bee alike , and of equallitie amongst themselves ; and the whirling or turning motion be quicke , the sight will be so deceived , that producing the action it will seeme to the ignorant no lesse than a miracle .

7. Seventhly , of another fine Fountaine of pleasure .

THis is an engine that hath two wheeles with cogges , or teeth as A B , which are placed within an Ovall C D , in such sort , that the teeth of the one , may enter into the notches of the other ; but so just that neither aire nor water may enter into the Ovall coffer , either by the middle or by the sides , for the wheele must joyne so neare to the sides of the coffer , that there be no vacuitie : to this there is an axeltree with a handle to each

diagram wheele , so that they may be turned , and A being turned , that turneth the other wheele that is opposite : by which motion the aire that is in E , and the water that is carried by the hollow of the wheeles of each side , by continuall motion , is constrained to mount and flie out by the funnell F : now to make the water runne what way one would have it , there may be applyed upon the toppe of the Pipe F , two other moveable Pipés inserted one within another ; as the figure sheweth . But here note that there may accrue some inconveniency in this machanicke , seeing that by quicke turning the cogges or teeth of the wheeles running one against another , may neare breake them , and so give way to the aire to enter in , which being violently inclosed will escape to occupie the place of the water , whose weight makes it so quicke : howsoever , if this Machine be curiously made as an able workeman may easily doe , it is a most soveraigne engine , to cast water high and farre off for to quench fires . And to have it to raine to a place assigned , accommodate a socket having a Pipe at the middle , which may point towards the place being set at the top thereof , and so having great discretion in turning the Axis of the wheele , it may worke exceeding well , and continue long .

8. Eightly , of a fine watering potte for gardens .

THis may be made in forme of a Bottle according to the last figure or such like , having at the bottome many small holes , & at the necke of it another hole somewhat greater than these at the bottome , which hole at the toppe you must unstop when you would fill this watering pot , for then it is nothing but putting the lower end into a paile of water , for so it will fill it selfe by degrees : and being full , put your thumbe on the hole at the necke to stop it , for then may you carry it from place to place , and it will not sensibly runne out , yet something will if it were so close stopped , and all in time contrary to to the ancient tenet in Philosophy , that aire will not penetrate .

9. Ninthly , how easily to take wine out of a vessell at the bung-hole , without piercing of a hole in the vessell .

IN this there is no need but to have a Cane or Pipe of Glasse or such like , one of the ends of which may be closed up almost , leaving some small hole at the end ; for then if that end be set into the vessell at the bung-hole , the whole Cane or Pipe will bee

diagram filled by little and little , and once being still , stoppe the other and which is without ▪ and then pull out the Cane or Pipe , so will it bee full of wine ; then opening a little the toppe above , you may fill a Glasse or other Potte with it , for as the wine issueth out , the aire commeth into the Cane or Pipe to supply vacuity .

10. Tenthly , how to measure irregular bodies by helpe of water .

SOme throw in the body or magnitude into a vessell , and keepe that which floweth out over , saying it is alwayes equall to the thing cast into the water : but it is more neater this way to powre into a vessell such a quantity of water , which may be thought sufficient to cover the body or magnitude , and make a marke how high the water is in the vessell , then powre out all this water into another vessell , and let the body or magnitude be placed into the first vessell ; then powre in water from the second vessell , untill it ascend unto the former marke made in the first vessell ; so the water which remaines in the second vessell , is equall to the body or magnitude put into the water : but here note that this is not exact or free from error , yet nearer the truth than any Geometrician can otherwise possibly measure , and these bodyes that are not so full of powers are more truly measured this way , than others are .

11. To finde the weight of water .

SEeing that 574/1000 part of an ounce weight , makes a cubicall inch of water : and every pound weight Haverdepoise makes 27 cubicall intches , and 9/10 fere , and that 7 Gallons and a halfe wine measure makes a foote cubicall , it is easie by inversion , that knowing the quantitie of a vessell in Gallons , to finde his content in cubicall feete or weight : and that late famous Geometrician Master Brigs found a cubicall foote of water to weigh neare 62 pound weight Haverdepoize . But the late learned Simon Stevin found a cubicall foote of water to weight 65 pound , which difference may arise from the inequallitie of water ; for some waters are more ponderous than others , and some difference may be from the weight of a pound , and the measure of a foote : thus the weight and quantitie of a solid foote settled , it is easie for Arithmetitians to give the contents of vessells or bodies which containe liquids .

12. To finde the charge that a vessell may carry , as Shippes , Boates , or such like .

THis is generally conceived , that a vessell may carry as much weight as that water weigheth , which is equall unto the vessell in bignesse , in abating onely the weight of the vessell : we see that a barrell of wine or water cast into the water , will not sinke to the bottome but swimme easily , and if a Shippe had not iron and other ponderosities in it , it might swimme full of water without sinking : in the same manner if the vessell were loaden with lead , so much should the water weigh : hence it is that Marriners calls Shippes of 50 thousand Tunnes , because they may containe one or two thousand Tunne , and so consequently carry as much .

13. How comes it that a Shippe having safely sayled in the vaste Ocean , and being come into the Port or harbour , without any tempest will sinke downe right .

THe cause of this is that a vessell may carry more upon some kinde of water than upon other ; now the water of the Sea is thicker and heavier than that of Rivers , Wells , or Fountains ; therefore the loading of a vessell which is accounted sufficient in the Sea , becomes too great in the harbour or sweet water . Now some thinke that it is the depth of the water that makes vessells more easie to swimme , but it is an abuse ; for if the loading of a Shippe bee no heavier than the water that would occupie that place , the Ship should as easily swim upon that water , as if it did swim upon a thousand fathom deepe of water ; and if the water be no thicker than a leafe of paper , and weigheth but an ounce under a heavy body , it will support it , as well as if the water under it weighed ten thousand pound weight : hence it is if there be a vessell capable of a little more than a thousand pound weight of water , you may put into this vessell a peece of wood , which shall weigh a thousand pound weight ; ( but lighter in his kinde than the like of magnitude of water : ) for then powring in but a quarte of water or a very little quantitie of water , the wood will swimme on the top of it , ( provided that the wood touch not the sides of the vessell : ) which is a fine experiment , and seemes admirable in the performance .

14. How a grosse body of mettle may swimme upon the water .

THis is done by extending the mettle into a thinne Plate , to make it hollow in forme of a vessell ; so that the greatnesse of the vessell which the aire with it containeth , be equall to the magnitude of the water , which weighes as much as it ; for all bodies may swimme without sinking , if they occupie the place of water equall in weight unto them , as if it weighed 12 pound , it must have the place of 12 pound of water : hence it is that wee see floating upon the water great vessells of Copper or Brasse , when they are hollow in forme of a Chaldron . And how can it be otherwise conceived of Ilands in the Sea that swimme and floate ? is it not that they are hollow and some part like unto a Boate , or that their earth is very light and spongeous , or having many concavities in the body of it , or much wood within it .

And it would bee a pretty proposition to shew how much every kinde of mettle should bee inlarged , to make it swimme upon the water : which doth depend upon the proportions that is betweene the weight of the water and each mettle . Now the proportion that is betweene mettles and water of equall magnitude , according to some Authors is as followeth .

A magnitude of 10 pound weight of water will require for the like magnitude of Gould . 187 ½ Lead . 116 ½ Silver . 104 Copper . 91 Iron . 81 Tinne . 75

From which is inferred , that to make a peece of Copper of 10 pound weight to swimme , it must bee so made hollow , that it may hold 9 times that weight of water and somewhat more , that is to say , 91 pound : seeing that Copper and water of like magnitudes in their ponderosities , are as before , as 10 to 91.

15. How to weigh the lightnesse of the aire .

PLace a Ballance of wood turned upside downe into the water , that so it may swim , then let water be inclosed within some body , as within a Bladder or such like ; and suppose that such a quantitie of aire should weigh one pound , place it under one of the Ballances , and place under the other as much weight of lightnesse as may counter-ballance and keepe the other Ballance that it rise not out of the water : by which you shall see how much the lightnesse is .

But without any Ballance doe this ; take a Cubicall hollow vessell , or that which is Cylindricall , which may swimme on the water , and as it sinketh by placing of weights upon it , marke how much ; for then if you would examine the weight of any body , you have nothing to doe but to put it into this vessell , and marke how deepe it sinkes ; for so many pound it weighes as the weights put in doth make it so to sinke .

diagram

16. Being given a body , to marke it about , and shew how much of it will sinke in the water , or swimme above the water .

THis is done by knowing the weight of the body which is given , and the quantitie of water , which weighes as much as that body ; for then certainely it will sinke so deepe , untill it occupieth the place of that quantitie of water .

17. To finde how much severall mettle or other bodies doe weigh lesse in the water than in the aire .

TAke a Ballance and weigh ( as for example ) 9 pound of Gould , Silver , Lead , or Stone in the aire , so it hang in aequilibrio ; then comming to the water , take the same quantitie of Gould , Silver , Lead , or Stone , and let it softly downe into it , and you shall see that you shall neede a lesse counterpoise in the other Ballance to counter-ballance it : wherefore all solids or bodyes weigh lesse in the water than in the aire , and so much the lesse it will be , by how much the water is grosse and thicke , because the weight findes a greater resistance , and therefore the water supports more than aire : and further , because the water by the ponderositie is displeased , and so strives to be there againe , pressing to it , by reason of the other waters that are about it , according to the proportion of his weight . Archimedes demonstrateth , that all bodies weigh lesse in the water ( or in like liquor ) by how much they occupie place : and if the water weigh a pound weight , the magnitude in the water shall weigh a pound lesse than in the aire .

Now by knowing the proportion of water and mettles , it is found that Gould loseth in the water the 19 part of his waight : Copper the 9 part , Quickesilver the 15 part , Lead the 12 part , Silver the 10 part , Iron the 8 part , Tinne the 7 part and a little more : wherefore in materiall and absolute weight , Gould in respect of the water that it occupieth weigheth 18 , and ¾ times heavier than the like quantitie of water , that is , as 18 ¾ to the Quickesilver 15 times : Lead 11 and ⅗ , Silver 10 and ⅖ , Copper 9 and 1/●0 , Iron 8 and ½ , and Tinne 8 and ½ . Contrarily in respect of greatnesse , if the water be as heavy as the Gould , then is the water almost 19 times greater than the magnitude of the Gould , and so may you judge of the rest .

18. How is it that a ballance having like weight in each scale , and hanging in aequilibrio in the aire : being placed in another place , ( without removing any weight ) it shall cease to hang in aequilibrio sencibly : yea by a great difference of weight .

THis is easie to be resolved by considering different mettles , which though they weigh equall in the aire , yet in the water there will bee an apparant difference ; as suppose so that in the scale of each Ballance be placed 18 pound weight of severall mettles , the one Gould and the other Copper , which being in aequilibrio in the aire , placed in the water , will not hang so , because that the Gould loseth neare the 18 part of his weight , which is about 1 pound , and the Copper loseth but his 9 part , which is 2 pound : wherefore the Gold in the water weigheth but 17 pound , and the Copper 16 pound , which is a difference most sencible to confirme that point .

19. To shew what waters are heavier one than another , and how much .

PHysitians have an especiall respect unto this , judging that water which is lightest is most healthfull and medicinall for the body ; and Sea-men know that the heaviest waters doe beare most , and it is knowne which water is heaviest thus . Take a peece of waxe and fasten lead unto it , or some such like thing that it may but precisely swimme , for then it is equall to the like magnitude of water ; then put it into another vessell which hath contrary water , and if it sinke , then is that water lighter than the other : but if it sinke not so deepe , then it argueth the water to be heavier or more grosser than the first water ; or one may take a peece of wood , and marke the quantitie of sinking of it into severall waters , by which you may judge which is lightest or heaviest , for in that which it sinkes most , that is infallibly the lightest ; and so contrarily .

20. How to make a Pound of water weigh as much as 10 , 20 , 30 , or a hundred pound of Lead ; nay as much as a thousand , or ten thousand pound weight .

THis proposition seemes very impossible , yet water inclosed in a vessell , being constrained to dilate it selfe , doth weigh so much as though there were in the concavitie of it a sollid body of water .

There are many wayes to experiment this proposition , but to verifie it , it may be sufficient to produce two excellent ones onely : which had they not beene really acted , little credit might have beene given unto it .

The first way is thus : Take a Magnitude which takes up as much place as a hundred or a thousand pound of water , & suppose that it were tied to some thing that it may hang in the aire ; then make a Ballance that one of the scales may inviron it , yet so that it touch not the sides of it : but leave space enough for one pound of water : then having placed 100 pound weight in the other scale , throw in the water about the Magnitude , so that one pound of water shall weigh downe the hundred pound in the other Ballance .

diagram

PROBLEM . LXXXVI . Of sundry Questions of Arithmeticke , and first of the number of sands .

IT may be said incontinent , that to undertake this were impossible , either to number the sands of Libya , or the sands of the Sea ; and it was this that the Poets sung , and that which the vulgar beleeves ; nay , that which long agoe certaine Philosophers to Gelon King of Sicily reported , that the graines of sand were innumerable : But I answere with Archimedes , that not onely one may number these which are at the border and about the Sea ; but these which are able to fill the whole world : if there were nothing else but sand , and the graines of sands admitted to bee so small , that 10 may make but one graine of Poppy : for at the end of the account there neede not to expresse them , but this number 30840979456 , and 35 Ciphers at the end of it . Clavius and Archimedes makes it somewhat more ; because they make a greater firmament than Ticho Brahe doth ; and if they augment the Vniverse , it is easie for us to augment the number , and declare assuredly how many graines of sand there is requisite to fill another world , in comparison that our visible world were but as one graine of sand , an atome or a point ; for there is nothing to doe but to multiply the number by it selfe , which will amount to ninety places , whereof twenty are these , 95143798134910955936 , and 70 Ciphers at the end of it : which amounts to a most prodigious number , and is easily supputated : for supposing that a graine of Poppy doth containe 10 graines of sand , there is nothing but to compare that little bowle of a graine of Poppy , with a bowle of an inch or of a foote , and that to be compared with that of the earth , and then that of the earth with that of the firmament ; and so of the rest .

2. Divers mettles being melted together in one body , to finde the mixture of them .

THis was a notable invention of Archimedes , related by Vtrivious in his Architecture , where he reporteth that the Gould-smith which King Hiero imployed for the making of the Goulden Crowne , which was to be dedicated to the gods , had stolen part of it and mixed Silver in the place of it : the King suspicious of the worke proposed it to Archimedes , if by Art he could discover without breaking of the Crowne , if there had beene made mixture of any other mettle with the Gould . The way which he found out was by bathing himselfe , for as hee entred into the vessell of water , ( in which he bathed himselfe ) so the water ascended or flew out over it , and as hee pulled out his body the water descended : from which he gathered that if a Bowle of pure Gould , Silver , or other mettle were cast into a vessell of water , the water proportionally according to the thing cast in would ascend ; and so by way of Arithmeticke the question lay open to bee resolved : who being so intensively taken with the invention , leapes out of the Bath all naked , crying as a man transported , I have found , I have found , and so discovered it .

Now some say that he tooke two Masses , the one of pure Gould , and the other of pure Silver , each equall to the weight of the Crowne , and therefore unequall in magnitude or greatnesse ; and then knowing the severall quantities of water which was answerable to the Crowne , and the severall Masses , he subtilly collected , that if the Crowne occupied more place within the water than the Masse of Gould did : it appeared that there was Silver or other mettle melt with it . Now by the rule of position , suppose that each of the three Masses weighed 18 pound a peece , and that the Masse of Gould did occupie the place of one pound of water , that of Silver a pound and a halfe , and the Crowne one pound and a quarter only : then thus he might operate : the Masse of Silver which weighed 18 pounds , cast into the water , did cast out halfe a pound of water more than the Masse of Gould , which weighed 18 pound ; and the Crowne which weighed also 18 pound , being put into a vessell full of water , threw out more water than the Masse of Gold by a quarter of a pound , ( because of mixt mettle which was in it : ) therefore by the rule of proportion , if halfe a pound of water ( the excesse ) be answerable to 18 pound of Silver , one quarter of a pound of excesse shall be answerable to 9 pound of Silver , and so much was mixed in the Crowne .

Some judge the way to bee more facill by weighing the Crowne first in the aire , then in the water ; in the aire it weighed 18 pound , and if it were pure Gould , in the water it would weigh but 17 pound ; if it were Copper it would weigh but 16 pound ; but because wee will suppose that Gould and Copper is mixed together , it will weigh lesse then 17 pound , yet more than 16 pound , and that according to the proportion mixed : let it then be supposed that it weighed in the water 16 pound and 3 quarters , then might one say by proportion , if the difference of one pound of losse , ( which is betweene 16 and 17 ) bee answerable to 18 pound , to what shall one quarter of difference be answerable to , which is betweene 17 and 16¾ , and it will be 4 pound and a halfe ; and so much Copper was mixed with the Gould .

Many men have delivered sundry wayes to resolve this proposition since Archimedes invention , and it were tedious to relate the diversities .

Baptista Benedictus amongst his Arithmeticall Theoremes , delivers his way thus : if a Masse of Gold , of equall bignesse to the Crowne did weigh 20 pound , and another of Silver at a capacitie or bignesse at pleasure , as suppose did weigh 12 pound , the Crowne or the mixt body would weigh more than the Silver , and lesser than the Gould ; suppose it weighed 16 pound which is 4 pound lesse than the Gould by 8 pound , then may one say , if 8 pound of difference come from 12 pound of Silver , from whence comes 4 pound which will be 6 pound , and so much Silver was mixed in it , &c.

3. Three men bought a quantitie of wine , each paid alike , and each was to have alike ; it happened at the last partition that there was 21 Barrells , of which 7 were full , 7 halfe full , and 7 empty , how must they share the wine and vessells , that each have as many vessells one as another , & as much wine one as another .

THis may be answered two wayes as followeth , and these numbers 2 , 2 , 3 ; or 3 , 3 , 1 , may serve for direction , and signifies that the first person ought to have 3 Barrells full , & as many empty ones , and one which is halfe full ; so hee shall have 7 vessells and 3 Barrels , and a halfe of liquor : and one of the other shall in like manner have as much , so there will remaine for the third man 1 Barrell full , 5 which are halfe full , and 1 empty , and so every one shall have alike both in vessells and wine . And generally to answere such questions , divide the number of vessells by the number of persons , and if the Quotient be not an intire number , the question is impossible ; but when it is an intire number , there must be made as many parts as there are 3 persons , seeing that each part is lesse than the halfe of the said Quotient : as dividing 21 by 3 there comes 7 for the Quotient , which may be parted in these thre parts , 2 , 2 , 3 , or 3 , 3 , 1 , each of which being lesse than halfe of 7.

4. There is a Ladder which stands upright against a wall of 10 foote high ; the foot of it is pulled out 6 foote from the wall upon the pavement : how much hath the top of the Ladder descended .

THe answere is , 2 foot ; for by Pythagoras rule the square of D B , the Hypotenusae is equall to the square of

diagram D A 6 , and A B 10. Now if D A bee 6 foot , and A B 10 foot , the squares are 36 and 100 , which 36 taken from 100 rests 64 , whose Roote-quadrat is 8 ; so the foot of the Ladder being now at D , the toppe will bee at C , 2 foote lower than it was when it was at B.

PROBLEM . LXXXVII . Witty suits or debates betweene Caius and Sempronius , upon the forme of figures ; which Geometricians call Isoperimeter , or equall in circuit or compasse .

MArvell not at it if I make the Mathematickes take place at the Barre , and if I set forth here Bartoleus , who witnesseth of himselfe , that being then an ancient Doctor in the Law , he himselfe tooke upon him to learne the elements and principles of Geometry , by which he might set forth certaine Lawes touching the divisions of Fields , Waters , Ilands , and other incident places : now

diagram this shall be to shew in passing by , that these sciences are profitable and behovefull for Iudges , Counsellors , or such , to explaine many things which falles out in Lawes , to avoid ambiguities , contentions , and suits often .

1. Incident .

CAius had a field which was directly square , having 24 measures in Circuit , that was 6 on each side : Sempronius desiring to fit himselfe , prayed Caius to change with him for a field which should bee equivalent unto his ; and the bargaine being concluded , he gave him for counterchange a peece of ground which had just as much in circuit as his had ; but it was not square , yet Quadrangular and Rectangled having 9 measures in length for each of the two longest sides , and 3 in bredth for each shorter side : Now Caius which was not the most subtillest nor wisest in the world excepted his bargaine at the first , but afterwards having conferred with a Land measurer and Mathematitian , found that he was overreached in his bargaine , and that his field contained 36 square measures , and the other field ha●● but 27 measures , ( a thing easie to be knowne by multiplying the length by the bredth : ) Sempronius contested with him in suite of Law , and argued that figures which have equall Perimeter or circuit , are equall amongst themselves : my field , saith he , hath equall circuit with yours , therefore it is equall unto it in quantitie . Now this was sufficient to delude a Iudge which was ignorant in Geometricall proportions , but a Mathematician will easily declare the deceit , being assured that figures which are Isoperimeter , or equall in circuit , have not alwayes equall capacitie or quantitie : seeing that with the same circuit , there may bee infinite figures made which shall be more and more capable , by how much they have more Angles , equall sides , and approach nearer unto a circle , ( which is the most capablest figure of all , ) because that all his parts are extended one from another , and from the middle or Center as much as may be : so we see by an infallible rule of experience , that a square is more capable of quantitie than a Triangle of the same circuit , and a Pentagone more than a square , and so of others , so that they be regular figures that have their sides equall , otherwise there might be that a regular Triangle , having 24 measures in circuit might have more capacitie than a rectangled Parallelogram which had also 24 measures of circuit , as if it were 11 in length and 1 in breadth , the cercuit is still 24 ; yet the quantitie is but 11 : and if it had 6 every way , it gives the same Perimeter , viz. 24. but a quantitie of 36 as before .

2. Incident .

SEmpronius having borrowed of Caius a sacke of Corne , which was 6 foot high and 2 foote broad , and when there was question made to repay it , Sempronius gave Caius backe two sackes full of Corne , which had each of them 6 foot high and 1 foot broad : who beleeved that if the sackes were full hee was repaid , and it seemes to have an appearance of truth barely looked on . But it is most evident in demonstration , that the two sackes of Corne paid by Sempronius to Caius , is but halfe of that one sacke which he lent him : for a Cylinder or sacke having one foot of diameter , and 6 foot of length , is but the 4 part of another Cylinder , whose length is 6 foot , and his diameter is 2 foot : therefore two of the lesser Cylinders or sackes is but halfe of the greater ; and so Caius was deceived in halfe his Corne.

3. Incident .

SOme one from a common Fountaine of a Citie hath a Pipe of water of an inch diameter ; to have it more commodious , he hath leave to take as much more water , whereupon hee gives order that a Pipe be made of two inches diameter . Now you will say presently that it is reason to bee so bigge , to have just twice as much water as he had before : but if the Magistrate of the Citie

diagram understood Geometricall proportions , hee would soone cause it to bee amended , and shew that hee hath not onely taken twice as much water as hee had before , but foure times asmuch ; for a Circular hole which is two inches diameter is foure times greater than that of one inch ; and therefore will cast out foure times asmuch water as that of one inch , and so the deceit is double also in this .

Moreover if there were a heape of Corne of 20 foot every way , which was borrowed to be paid next yeare : the party having his Corne in heapes of 12 foote every way , and of 10 foote every way , proffers him 4 heapes of the greater , or 7 heapes of the lesser , for his owne heape of 20 every way , which was lent : here it seemes that the proffer is faire , nay with advantage , yet the losse would be neare 1000 foot . Infinite of such causes doe arise from Geometricall figures , which are able to deceive a Iudge or Magistrate , which is not somewhat seene in Mathematicall Documents .

PROBLEM . LXXXVIII . Containing sundry Questions in matter of Cosmography .

FIrst , it may be demanded , where is the middle of the world ; I speake not here Mathematically , but as the vulgar people who aske where is the middle of the world : in this sence to speake absolutely there is no point which may be said to be the middle of the surface ; for the middle of a Globe is every where : notwithstanding the Holy Scriptures speaketh respectively , and makes mention of the middle of the earth , and the interpreters apply it to the Citie of Ierusalem placed in the middle of Palestina , and the habitable world ; that in effect taking a mappe of the world , and placing one foot of the Compasses upon Ierusalem , and extending the other foot to the extremity of Europe , Asia , and Africa ; you shall see that the Citie of Ierusalem is as a Center to that Circle .

2. Secondly , how much is the depth of the earth , the height of the heavens , and the compasse of the world .

FFom the surface of the earth unto the Center according to ancient traditions , is 3436 miles , so the whole thickenesse is 6872 miles , of which the whole compasse or circuit of the earth is 21600 miles .

From the Center of the earth to the Moone there is neare 56 Semidiameters of the earth , which is about 192416 miles : unto the Sunne there is 1142 Semidiameters of the earth , that is in miles 3924912 ; from the starry firmament to the Center of the earth there is 14000 Semidiameters , that is , 48184000 miles , according to the opinion and observation of that learned Ticho Brahe .

From these measures one may collect by Arithmeticall supputations , many pleasant propositions in this manner .

First , if you imagine there were a hole through the earth , and that a milstone should bee let fall downe into this hole , and to move a mile in each minute of time , it would be more than two dayes and a halfe before it would come to the Center , and being there it would hang in the aire .

Secondly , if a man should goe every day 20 miles , it would bee three yeares wanting but a fortnight , before he could goe once about the earth ; and if a Bird should fly round about it in two dayes , then must the motion be 450 miles in an houre .

Thirdly , the Moone runnes a greater compasse each houre , than if in the same time shee should runne twice the Circumference of the whole earth .

Fourthly , admit it bee supposed that one should goe 20 miles in ascending upwards the heavens every day , hee should bee above 15 yeares before hee could attaine to the Orbe of the Moone .

Fifthly , the Sunne makes a greater way in one day than the Moone doth in 20 dayes , because that the Orbe of the Sunnes circumference is at the least 20 times greater than the Orbe of the Moone .

Sixthly , if a milstone should descend from the place of the Sunne a thousand miles every houre , ( which is above 15 miles in a minute , farre beyond the proportion of motion ) it would be above 163 dayes before it would fall downe to the earth .

Seventhly , the Sunne in his proper spheare moves more than seven thousand five hundred and seventy miles in one minute of time : now there is no Bullet of a Cannon , Arrow , Thunderbolt , or tempest of winde that moves with such quickenesse .

Eighthly , it is of a farre higher nature to consider the exceeding and unmoveable quicknesse of the starry firmament , for a starre being in the Equator , ( which is just betweene the Poles of the world ) makes 12598666 miles in one houre , which is two hundred , nine thousand nine hundred and ninety foure miles in one minute of time : & if a Horseman should ride every day 40 miles , hee could not ride such a compasse in a thousand yeares as the starry firmament moves in one houre , which is more than if one should move about the earth a thousand times in one houre , and quicker than possible thought can be imagined : and if a starre should fly in the aire about the earth with such a prodigious quickenesse , it would burne and consume all the world here below . Behold therefore how time passeth and death hasteth on : this made Copernicus , not unadvisedly to attribute this motion of Primum mobile to the earth , and not to the starry firmament : for it is beyond humaine sence to apprehend or conceive the rapture and violence of that motion being quicker than thought ; and the word of God testifieth that the Lord made all things in number , measure , weight , and time .

PROBLEM . LXXXXII . To finde the Bissextile yeare , the Dominicall letter , and the letters of the moneth .

LEt 123 , or 124 , or 125 , or 26 , or 27 , ( which is the remainder of 1500 , or 1600 ) be divided by 4 , which is the number of the Leape-yeare , and that which remaines of the division shewes the Leape yeare ; as if one remaine , it shewes that it is the first yeare since the Bissextile or Leape yeare : if two , it is the second yeare , &c. and if nothing remaine , then it is the Bissextile or Leape yeare , and the Quotient shewes you how many Bissextiles or Leape yeares there are contained in so many yeares .

To finde the Circle of the Sun by the fingers .

LEt 123 , 24 , 25 , 26 , or 27 , bee divided by 28 , ( which is the Circle of the Sunne , or whole revolution of the Dominicall letters ) and that which remaines is the number of joynts , which is to bee accounted upon the fingers by Filius esto Dei , coelum bonus accipe gratis : and where the number ends , that finger it sheweth the yeare which is present , and the words of the verse shewes the Dominicall letter .

Example .

DIvide 123 by 28 for the yeare , ( and so of other yeares ) and the Quotient is 4 , and there remaineth 11 , for which you must account 11 words ; Filius esto Dei , &c. upon the joynts beginning from the first joynt of the Index , and you shall have the answere .

For the present to know the Dominicall letter for each moneth , account from Ianuary unto the moneth required , including Ianuary ; and if there bee 8 , 9 , 7 , or 5 , you must begin upon the end of the finger from the thumbe and account , Adam degebat , &c. as many words as there are moneths , for then one shall have the letter which begins the moneth ; then to know what day of the moneth it is , see how many times 7 is comprehended in the number of dayes , and take the rest : suppose 4. account upon the first finger within and without by the joynts unto the number of 4 , which ends at the end of the finger : from whence it may bee inferred that the day required was Wednesday , Sunday being attributed to the first joynt of the first finger or Index : and so you have the present yeare , the Dominicall letter , the letter which begins the Moneth , and all the dayes of the Moneth .

PROBLEM . LXXXXIII . To finde the New and Full Moone in each Moneth .

ADde to the Epact for the yeare , the Moneth from March ; then subtract that surplus from 30 , and the rest is the day of the Moneth that it will bee New Moone , and adding unto it 14 , you shall have that Full Moone .

Note .

THat the Epact is made alwayes by adding 11 unto 30 , and if it passe 30 , subtract 30 , and adde 11 to the remainder : and so ad infinitum : as if the Epact were 12 , adde 11 to it makes 23 for the Epact next yeare , to which adde 11 makes 34 , subtract 30 , rests 41 the Epact for the yeare after , and 15 for the yeare following that , and for the next , and 7 for the next , &c.

PROBLEM . LXXXXIIII . To finde the Latitude of a Countrey .

THese that dwell betweene the North Pole and the Tropicke of Cancer , have their spring and summer betweene the 10. of March , and the 1● . of September : and therefore in any day betweene that time , get the sunnes distance by instrumentall observation from the zeni●h at noone , and adde the declination of the sunne for that day to it : so the Aggragate , or such is the Latitude , or Poles height of that Countrey . Now the declination of the sunne for any day is found out by Tables calculated to that end : or Mechanically by the Globe , or by Instrument it may be indifferently had : and here note that if the day be betweene the 13. of September and the 10. of March , then the sunnes declination , for that day must be taken out of the distance of the sunne from the zenith at noone : so shall you have the Latitude , as before .

PROBLEM . LXXXXV . Of the Climats of countries , and to finde in what Climate any countrey is under .

Climats as they are taken Geographically signifie nothing else but when the length of the longest day of any place , is halfe an houre longer , or shorter than it is in another place ( and so of the shortest day ) and this account to begin from the Equinoctiall Circle , seeing all Countries under it have the shortest and longest day that can bee but 12. houres ; But all other Countries that are from the Equinoctiall Circle either towards the North or South of it unto the Poles themselves , are sayd to bee in some one Climate or other , from the Equinoctiall to either of the poles Circles , ( which are in the Latitude of 66. gr. 30. m. ) betweene each of which poler Circles and the Equinoctiall Circle there is accounted 24 Climats , which differ one from another by halfe an hours time : then from each Poler Circle , to each Pole there are reckoned 6. other Climats which differ one from another by a months time : so the whole earth is divided into 60. Climats , 30 being allotted to the Northerne Hemispheare , and 30. to the Southerne Hemispheare . And here note that though these Climats which are betweene the Equinoctiall & the poller Circles are equall one unto the other in respect of time , to wit , by halfe an houre , yet the Latitude , breadth , or internall , contained betweene Climate and Climite , is not equall : & by how much any Climate is farther from the Equinoctiall than another Climate , by so much the lesser is the internall betweene that Climate and the next : so these that are nearest the Equinoctial are largest ; and these which are farthest off most contracted & to find what Climate any Countrey is under : subtract the length of an Equinoctiall day to wit , 12 , houres from the length of the longest day of that Countrey ; the remainder being doubled shewes the Climate : So at London the longest day is neare 16. houres and a halfe ; 12. taken from it there remaines 4. houres and a halfe which doubled makes 9. halfe houres , that is , 9. Climats ; so London is in the 9. Climate .

PROBLEM . LXXXXVI . Of Longitude and Latitude of the Earth and of the Starres .

LOngitude of a Countrey , or place , is an arcke of the Aequator contained betweene the Meridian of the Azoros , and the Meridian of the place ; and the greatest Longitude that can be is 360 degrees .

Note .

That the first Meridian may be taken at pleasure upon the Terrestriall Globe or Mappe , for that some of the ancient Astonomers would have it at Hercules Pillars , which is at the straights at Gibralter : Ptolomy placed it at the Canary Iland , but now in these lattter times it is held to bee neare the Azores . But why it was first placed by Ptolomy at the Canary Ilands , was because that in his time these Ilands were the farthest westerne parts of the world that was then discovered : And why it retaines his place now at Saint Michels neare the Azores , is that because of many accurate observations made of late by many expert Navigators and Mathematicians , they have found the Needle there to have no variation , but to point North and South : that , is to each Pole of the world : and why the Longitude from thence is accounted Eastwards , is from the motion of the Sunne Eastward ; or that Ptolomy and others did hould it more convenient to begin from the westerne part of the world and so account the Longitude Eastward from Countrey to Countrey that was then knowne ; till they came to the Easterne part of Asia , rather than to make a beginning upon that which was unknowne : and having made up their account of reckoning the Longitude from the Westerne part to the Easterne part of the world knowne , they supposed the rest to be all sea ; which since their deaths hath beene found almost to be another habitable world .

To finde the Longitude of a Countrey .

IF it be upon the Globe , bring the Countrey to the Brasen Meridian , and whatsoever degree that Meridian cuts in the Equinoctiall , that degree is the Longitude of that Place : if it be in a Mappe , then marke what Meridian passeth over it ; so have you the Longitude thereof : if no Meridian passe over it , then take a paire of Compasses , and measure the distance betweene the Place and the next Meridian , and apply it to the divided parallel or Aequator ; so have you the Longitude required .

Of the Latitude of Countries .

LAtitude of a Countrey is the distance of a Countrey from the Equinoctiall , or it is an Arke of the Meridian contained betweene the Zenith of the place and the Aequator ; which is twofold , viz. either North Latitude or South Latitude , eyther of which extendeth from the Equinoctiall to eyther Pole ; so the greatest Latitude that can be is but 90. degrees : If any Northerne Countrey have the Articke Circle verticall , which is in the Latitude of 66. gr. 30. m. the sunne will touch the Horizon in the North part thereof , and the longest day will be there then 24. houres : if the Countrey have lesse Latitude than 66. degrees 30. m. the sunne will rise and set ; but if it have more Latitude than 66. gr. 30 , m. it will bee visible for many dayes : and if the Countrey bee under the Pole , the sunne will make a Circular motion above the Earth and be visible for a halfe yeare : so under the Pole there will be but one day , and one night in the whole yeare .

diagram

To finde the Latitude of Countries .

IF it be upon a Globe ,

diagram bring the place to the Brasen Meridian , and the number of degrees which it meeteth therewith , is the Latitude of the place . Or with a paire of Compasses take the distance betweene the Countrey and the Equinoctiall ; which applyed unto the Equinoctiall will shew the Latitude of that Countrey ; which is equall to the Poles height ; if it be upon a Mappe . Then marke what parallel passeth over the Countrey and where it crosseth the Meridian , that shall be the Latitude : but if no parallel passeth over it , then take the distance betweene the place and the next parallell , which applyed to the divided Meridian from that parallell will shew the Latitude of that place .

To finde the distance of Places .

IF it be upon a Globe : then with a paire of Compasses take the distance betweene the two places , and apply it to the divided Meridian or Aequator , and the number of degrees shall shew the distance ; each degree beeing 60. miles . If it be in a Mappe ( according to Wrights projection ) take the distance with a paire of Compasses betweene the two places , and apply this distance to the divided Meridian on the Mappe right against the two places ; so as many degrees as is contained betweene the feete of the Compasses , so much is the distance betweene the two places . If the distance of two places be required in a particular Mappe then with the Compasses take the distance betweene the two places , and apply it to the scale of Miles , so have you the distance : if the scale bee too short , take the scale betweene the Compasses , and apply that to the two Places as often as you can , so have you the distance required .

Of the Longitude , Latitude , Declination , and distance of the Starres .

THe Declination of a starre is the nearest distance of a starre from the Aequator ; the Latitude of a starre is the nearest distance of a starre from the Eclipticke : the Longitude of a starre is an Arke of the Eclipticke contained betweene the beginning of Aries , and the Circle of the starres Latitude , which is a Circle drawne from the Pole of the Ecliptick unto the starre , and so to the Eclipticke . The distance betweene two starres in heaven is taken by a Crosse staffe or other Instrument , and upon a Globe it is done by taking betweene the feet of the Compasses the two starres , and applying it to the Aequator , so have you the distance betweene those two starres .

How it is that two Horses or other creatures being foled or brought forth into the world at one and the same time , that after certaine dayes travell the one lived longer than the other , notwithstanding they dyed together in one and the same moment also .

THis is easie to be answered : let one of them travell towarde the West and the other towards the East : then that which goes towards the West followeth the Sunne : shall have the day somewhat longer than if there had beene no travell made : and that which goes East by going against the Sunne , shall have the day shorter : and so respect of travell though they dye at one and the selfe same houre and moment of time , the one shall be older than the other .

From which consideration may be inferred that a Christian , a Iew , and a Zarazen , may have their Sabbaths all upon one and the same day , though notwithstanding the Zarazen houlds his Sabath upon the Friday , the Iew upon the Saturday , and the Christian upon the Sonday : For being all three resident in one place , if the Zarazen and the Christian begin their travell upon the Saturday , the Christian going West : and the Zarazen Eastwards , shall compasse the Globe of the earth , the Christian at the conclusion shall gaine a day and the Zarazen shall lose a day , and so meete with the Iew every one upon his owne Sabbath .

Certaine fine Observations .

VNder the Equinoctiall the Needle hangs in aequilibrio , but in these parts it inclines under the Horizon , and being under the Pole it is thought it will hang verticall .

In these Countries which are without the Tropicall Circles , the Sunne comes East and West every day for a halfe yeare ; but being under the Equinoctiall the Sunne is never East , nor West but twice in the yeare , to wit , the 10. of March and the 13. of September .

If a shippe be in the Latitude of 23. gr. 30. m. that is , if it have eyther of the Tropickes verticall : then at what time the Sunnes Altitude is equall to his distance from any of the Equinoctiall points , then the Sunne is due East or West .

If a shippe be betweene the Equinoctiall and eyther of the Tropicks , the Sunne will come twice to one point of the Compasse in the forenoone , that is , in one and the same position .

Vnder the Equinoctiall neare Guinea there is but two sorts of winds all the yeare , 6. months a Northerly winde , and 6. months a Southerly winde , and the flux of the Sea is accordingly .

If two ships under the Equinoctiall be 100. leagues asunder , and should sayle Northerly untill they were come under the Articke Circle , they should then be but 50. leagues asunder .

These which have the Articke Circle verticall : when the Sunne is in the Tropicke of Cancer : the Sunne setteth not but toucheth the westerne part of the Horizon .

If the complement of the Sunnes height at noone be found equall to the Suns Declination for that day , then the Equinoctiall is verticall : or a shippe making such an observation , the Equinoctiall is in the Zenith or direct over them : by which Navigators know when they crosse the line , in their travels to the Indies , or other parts .

The Sunne being in the Equinoctiall , the extremity of the still in any Sunne dyall upon a plaine ; maketh a right line , otherwise it is Elipticall , Hyperbolicall , &c.

When the shadow of a man , or other thing upon a Horizontall plaine is equall unto it in length , then is the Sunne in the middle point betweene the Horizon and the Zenith , that is , 45. degrees high .

PROBLEME LXXXXVII . To make a Triangle that shall have three right Angles .

OPen the Compasses at pleasure : and upon A , describe an Arke B C. then at the same opening , place one of the feet in B , and describe the Arke A C.

diagram Lastly , place one of the feet of the Compasses in C. and describe the Arke A B. so shall you have the sphericall Aequilaterall Triangle A B C. right angled at A , at B , and at C. that is , each angle comprehended 90. degrees : which can never be in any plaine Triangle , whether it be Equilaterall , Isocelle , scaleve , Orthogonall , or Opigonall .

PROBLEM . LXXXXVIII . To divide a line in as many equall parts as one will , without compasses , or without seeing of it .

THis Proposition hath a fallacie in it , and cannot be practised but upon a Maincordion : for the Mathematicall line which proceedes from the flux of a point , cannot be divided in that wise : One may have therefore an Instrument which is called Maincordion , because there is but one cord : and if you desire to divide your line into 3. parts , run your finger upon the frets untill you sound a third in musicke : if you would have the fourth part of the line , then finde the fourth sound , a fift , &c. so shall you have the answer .

PROBLEM . LXXXXVIIII . To draw a line which shall incline to another line , yet never meete : against the Axiome of Parallels .

THis is done by helpe of a Conoyde line , produced by a right line upon one and the same plaine , held in great account amongst the Ancients , and it is drawne after this manner .

Draw a right line infinitely , and upon some end of it , as at I , draw

diagram a perpendicular line IA. augment it to H. then from A. draw lines at pleasure to intersect the line I. M. in each of which lines from the right line , I. M. transferre I H. viz. K B. L C. O D. P E. Q F. M G. then from those points draw the line H. B. C. D. E. F. G. which will not meet with the line I M. and yet incline nearer and nearer unto it .

PROBLEM . C. To observe the variation of the compasses , or needle in any places .

FIrst describe a Circle upon a plaine , so that the Sunne may shine on it both before noone and afternoone : in the center of which Circle place a Gnomon or wire prependicular as A B. and an houre before noone marke the extremitie of the shaddow of A B. which suppose it be at C. describe a Circle at that semidiameter C D F. then after noone marke when the top of the shadow of A B. toucheth the Circle , which admit in D ; devide the distance C D , into two equall parts which suppose at E. draw the line E A F. which is the Meridian line , or line of North & South : now

diagram if the Arke of the Circle C D. bee devided into degrees : place a Needle G H , upon a plaine set up in the Center , & marke how many degrees the point of the Needle G , is from E. so much doth the Needle vary from the North in that place .

PROBLEM . CI. How to finde at any time which way the wind is in ones Chamber , without going abroad .

Won the Planching or floore of a Chamber , Parlor , or Hall , that you intend to have this devise , let there come downe from the top of the house a hollow post , in which place an Iron rod that it ascend above the house 10 , or 6. foote with a vane or

diagram a scouchen at it to shew the winds without : and at the lower end of this rod of Iron , place a Dart which may by the mooving of the vane with the winde without , turne this Dart which is within : a-about which upon the plaister must be described a Circle divided into the 32. points of the Mariners Compasse pointed and distinguished to that end : then may it be marked by placing a Compasse by it ; for having noted the North point , the East , &c. it is easie to note all the rest of the points : and so at any time comming into this Roome , you have nothing to doe but to looke up to the Dart , which will point you out what way the winde bloweth at that instant .

PROBLEM . CII . How to draw a parallell sphericall line with great ease .

FIrst draw an obscure line G F. in the middle of it make two points A B , ( which serves for Centers ) then place one foote of the Compasses in B , and extend the other foote to A , and describe the semicircle A C : then place one foot of the Compasses in A , and extend the other foote to C , and describe the semicircle C D. Now place the Compasses in B , and extend the other foote unto D , and describe the semicircle D E , and so ad infinitum ,

diagram which being done neatly , that there bee no right line seene nor where the Compasses were placed , will seeme very strange how possibly it could bee drawne with such exactnes , to such which are ignorant of that way .

PROBLEM . CIII . To measure an inaccessible distance : as the bredth of a River with the helpe of ones hat onely .

THe way of this is easie , for having ones hat upon his head , come neare to the banke of the River , and houlding your head upright ( which may bee by puttting a small sticke to some one of your buttons to prop up the chin ) plucke downe the brim or edge of your hat untill you may but see the other side of the water ; then turne about the body in the same posture that it was before , towards some plaine , and marke where the sight by the brimme of the hat glaunceth on the ground ; for the distance from that place to your standing , is the bredth of the River required .

PROBLEM . CIIII. How to measure a height with two strawes or two small stickes .

TAke two strawes or two stickes which are one as long as another , and place them at right Angles one to the other , as A B. and A C. then houlding A B. parallel to the ground , place the end A. to the eye at A. and looking to the other top B C. at C. by going backward or forward untill you may

diagram see the top of the Tower or Tree , which suppose at E. So the distance from your standing to the Tower or Tree , is equall to the height thereof above the levell of the eye : to which if you adde your owne height you have the whole height .

Otherwise .

TAke an ordinary

diagram square which Carpenters or other workemen use , as H K L. and placing H. to the eye so that H K. be levell , goe backe or come nearer untill that by it you may see the top M. for then the distance from you to the height is equall to the height .

PROBLEM . CV . How to make statues , letters , bowles , or other things which are placed in the side of a high building , to be seene below of an equall bignesse .

LEt B C. be a Pillar 27. yards high , and let it be required that three yards above the levell of the eye A , viz. at B. bee placed a Globe and 9 yards above B. be placed another , and 22. yards above that be placed another Globe : how much shall the Diamiter

diagram of these Globes be , that at the eye , at A , they may all appeare to be of one and the same Magnitude : It is thus done , first draw a line as A K. & upon K. erect a prependicular K X. divide this line into 27. parts , and according to A K. describe an Arke K Y. then from K. in the perpendicular K X , account 3. parts . viz. at L , which shall represent the former three yardes , and draw the line L A : from L , in the sayd perpendicular reckon the diamiter of the lesser Globe of what Magnitude it is intended to be : suppose S L. and draw the line S A. cutting the Arke V K. in N. then from K. in the perpendicular account 9. yards , which admit at T. draw T A. cutting Y K. in O. transferre the Arke M N. from A to P. and draw A P. which will cut the perpendicular in V. so a line drawne from the middle of V F. unto the visuall lines A T , and A V , shall be the diamiter of the next Globe : Lastly , account from K. in the perpendicular X K. 22 parts , and draw the line W A. cutting Y K , in Q. then take the Arke M N , and transferre it from Q , to R. and draw A R. which will cut the perpendicular in X. so the line which passeth by the middle of X W. perpendicular to the visuall line A W , and A X. be the Diamiter of the third Globe , to wit 5 , 6. which measures transferred in the Pillar B C. which sheweth the true Magnitude of the Globes 1 , 2 , 3. from this an Architecter doth proportion his Images , and the foulding of the Robes which are most deformed at the eye below in the making , yet most perfect when it is set in his true height above the eye .

PROBLEM . CVI. How to disguise or disfigure an Image , as a head , an arme , a whole body , &c. so that it hath no proportion , the eares to become long : the nose as that of a swan , the mouth as a coaches entrance , &c. yet the eye placed at a certaine point will be seene in a direct and exact proportion .

I Will not strive to set a Geometricall figure here for feare it may seeme too difficult to understand , but I will indeavour by discourse how Mechanically with a Candle you may perceive it sencible : first there must be made a figure upon Paper such as you please , according to his just proportion , and paint it as a Picture ( which painters know well enough to doe ) afterwards put a Candle upon the Table , and interpose this figure obliquely , betweene the said Candle and the Bookes of Paper , where you desire to have the figure disguised in such sort that the height passe athwart the hole of the Picture : then will it carry all the forme of the Picture upon the Paper , but with deformity ; follow these tracts and marks out the light with a Coles blacke head or Inke : and you have your desire .

To finde now the point where the eye must see it in his naturall forme : it is accustomed according to the order of Perspective , to place this point in the line drawne in height , equall to the largenesse of the narrowest side of the deformed square , and it is by this way that it is performed .

PROBLEM . CVII . How a Canon after that it hath shot , may be covered from the battery of the enemy .

LEt the mouth of a Canon be I. the Canon M. his charge N O. the wheele L. the axle● tree P B. upon which the Canon is placed , at which end towards B , is placed a pillar A E. supported with props D C. E , F , G. about which the Axeltree

diagram turneth : now the Cannon being to shoot , it retires to H. which cannot be directly because of the Axeltree , but it make a segment of a Circle , & hides himselfe behind the wall Q R , and so preserves it selfe from the Enimies battery , by which meanes one may avoyd many inconveniences which might arise : and moreover one man may more easily replace it againe for another shot by helpe of poles tyed to the wall , or other helpes which may multiply the strength .

PROBLEM . CVIII . How to make a Lever by which one man may alone place a Cannon upon his carriage , or raise what other weight he would .

FIrst place two thicke boards upright , as the figure sheweth , pierced with holes , alike opposite one unto another as C D , and E F : and let L , and M , be the two barrs of Iron which passeth through the holes G H , and F , K ; the two supports , or

diagram props , A B. the Cannon , O P , the Lever R S , the two notches in the Lever , and Q , the hooke where the burthen or Cannon is tyed to . The rest of the operation is facill , that the youngest schollers or learners cannot faile to performe it : to teach Minerva were in vaine , and it were to Mathematicians injury in the succeeding Ages .

PROBLEM . CIX . How to make a Clocke with one onely wheele .

MAke the body

diagram of an ordinary Dyall , and divide the houre in the Circle into 12. parts : make a great wheele in height above the Axeltree , to the which you shall place the cord of your counterpoise , so that it may descend , that in 12 houres of time your Index or Needle may make one revolution , which may bee knowne by a watch which you may have by you : then put a balence which may stop the course of the wheele , and give it a regular motion , and you shall see an effect as just from this as from a Clocke with many wheeles .

PROBLEM . CX . How by helpe of two wheeles to make a Child to draw up alone a hogshead of water at a time : and being drawne up shall cast out it selfe into another vessell as one would have it .

LEt R be the Pit from whence water is to be drawne ; P , the hooke to throw out the water when it is brought up ( this hooke must be moveable ) let A B , bee the Axis of the wheele S F , which wheele hath divers forkes of Iron made at G , equally fastened at the wheele ; let I , be a Card , which is drawne by K , to make the wheele S , to turne , which wheele S , beares proportion to the wheele T , as 8 to 2 : let N be a Chaine of Iron to which is tyed the vessell O : and the other which is in the Pit : E F is a peece of wood which hath a mortes in 1 , and 2 , by which the Cord I , passeth , tyed at the wall , as K H. and the other peece of Timber of the little wheele as M , mortised in likewise for the chaine to passe through :

diagram draw the Cord I , by K , and the wheele will turne , and so consequently the wheele T , which will cause the vessell O , to raise : which being empty , draw the Cord againe by Y , and the other vessell which is in the pit will come out by the same reason . This is an invention which wil save labour if practised ; but here is to be noted that the pit must be large enough , to the end that it containe two great vessels to passe up and downe one by another .

PROBLEM . CXI . To make a Ladder of Cords which may be carryed in ones pocket : by which one may easily mount up a Wall , or Tree alone .

TAke two Pullies A , and D , unto that of A , let there be fastned a Crampe of Iron as B ; and at D , let there be fastned a staffe of a foote & a halfe long as F , then the Pully A : place a hand of Iron , as E , to which tie a Cord of an halfe inch thicke ( which may be of silke because it is for the pocket : ) then strive to make fast the Pully A , by the helpe of the Crampe of Iron B , to the place that you intend to scale ; and the staffe F , being tyed at

diagram the Fully D , put it betweene your legges as though you would sit upon it : then houlding the Cord C , in your hand , you may guide your selfe to the place required : which may be made more facill by the multiplying of Pullies . This secret is most excellent in Warre , and for lovers , its supportablenesse avoyds suspition .

PROBLEM . CXII . How to make a Pumpe whose strength is maruelous by reason of the great weight of water that it is able to bring up at once , and so by continuance .

LEt 〈◊〉〈◊〉〈◊〉〈◊〉〈◊〉 , be the height of the Case about two or three foote high , and broader according to discretion : the rest of the Case or concavity let be O : let the sucker of the Pumpe which is made , be just for the Case or Pumpes head 〈◊〉〈◊〉〈◊〉〈◊〉〈◊〉 , & may be made of wood or brasse of 4. inches thick , having a hole at E , which descending raiseth up the

diagram cover P , by which issueth forth the water and ascending or raising up it shuts it or makes it close : R S , is the handle of the sucker tyed to the handle T X , which works in the post V Z. Let A , B , C , D , be a peece of Brasse , G the peece which enters into the hole to F , to keepe out the Ayre . H , I , K , L , the peece tyed at the funnell or pipe : in which playes the Iron rod or axis G , so that it passe through the other peece MN , which is tyed with the end of the pipe of Brasse .

Note , that the lower end of the Cisterne ought to bee rested upon a Grediron or Iron Grate , which may be tyed in the pit ; by which meane lifting up and putting downe the handle , you may draw ten times more water than otherwise you could .

PROBLEM . CXIII . How by meanes of a Cisterne , to make water of a Pit continually to ascend without strength , or the assistance of any other Pumpe .

LEt I L , be the Pit where one would cause water to ascend continually to each office of a house or the places which are separated from it : let there be made a receiver as A , well closed up with lead or other matter that ayre enter not in , to which fasten a pipe of lead as at E , which may have vent at pleasure : then let there bee made a Cisterne as B , which may bee communicative to A ,

diagram by helpe of the pipe G , from which Cisterne B , may issue the water of pipe D , which may descend to H , which is a little below the levell of the water of the pit as much as is G H : to the end of which shall be soudred close a Cocke which shall cast out the water by K H. Now to make use of it , let B be filled ful of water , & when you would have it run turne the Cocke , for then the water in B , will descend by K : and for feare that there should be vacuity , nature which abhors it , will labour to furnish and supply that emptinesse out of the spring F , and that the Pit dry not , the Pipe ought to bee small of an indifferent capacitie according to the greatnesse or smalnesse of the spring .

PROBLEM . CXIIII . How out of a fountaine to cast the water very high : different from a Probleme formerly delivered .

LEt the fountaine be B D , of a round forme ( seeing it is the most capable and most perfect figure ) place into it two pipes conjoyned as E A , and H C , so that no Ayre may enter in at the place of joyning : let each of the Pipes have a Cocke G , and L :

diagram the Cocke at G , being closed , open that at I , and so with a squirt force the water through the hole at H , then close the Cocke at A , and draw out the squirt , and open the Cocke at G : the Aire being before rarified will extend his dimensions and force the water with such violence , that it will amount above the height of one or two Pikes : and so much the more by how much the Machine is great : this violence will last but a little while if the Pipe have too great an opening , for as the Ayre approacheth to his naturall place , so the force will diminish .

PROBLEME CXV . How to empty the water of a Cisterne by a Pipe which shall have a motion of it selfe .

LEt A B , be the vessell ; C D E , the Pipe : H G , a little vessell under the greater , in which one end of the Pipe is , viz. C , and let the other end of the Pipe E , passe through the bottome of the vessell at F , then as

diagram the vessell filleth so will the Pipe , & when the vessell shall be full as farre as P O , the Pipe will begin to runne at E , of his owne accord , and never cease untill the vessell bee wholly empty .

PROBLEM . CXVI . How to squirt or spout out a great height , so that one pot of water shall last a long time .

LEt there be prepared two vessels of Brasse , lead , or of other matter of equall substance , as are the two vessels A B , and B D , & let them be joyned together by the two Pillars M N , and E F : then let there be a pipe H G. which may passe through the cover of the vessell C D , and passe through A B , into G , making a little bunch or rising in the cover of the vessell A B , so that the pipe touch it not at the bottome : then let there be sodered fast another Pipe I L , which may be separated from the bottome of the vessell , and may have his bunchie swelling as the former without touching the bottome : as is represented in L , and passing through the bottome of A B , may be continued unto I , that is to say , to make an opening

diagram to the cover of the vessell A B , & let it have a little mouth as a Trumpet : to that end to receive the water . Then there must further be added a very small Pipe which may passe through the bottome of the vessell A B , as let it be O F , and let there be a bunch , or swelling over it as at P , so that it touch not also the bottome : let there be further made to this lesser vessell an edge in forme of a Basen to receive the water , which being done powre water into the Pipe I L , untill the vessell C D , be full : then turne the whole machine upside downe that the vessell C D , may be uppermost , and A B , undermost : so by helpe of the Pipe G H , the water of the vessell C D , will runne into the vessell A B , to have passage by the Pipe P O. This motion is pleasant at a feast in filling the said vessell with wine , which will spout it out as though it were from a boyling fountaine , in the forme of a thred very pleasant to behould .

PROBLEM . CXVII . How to practise excellently the reanimation of simples , in case the plants may not be transported to be replanted by reason of distance of places .

TAke what simple you please , burne it and take the ashes of it , and let it bee calcinated two houres betweene two Creusets well luted , and extract the salt : that is , to put water into it in moving of it ; then let it settle , and doe it two or three times , afterwards evaporate it , that is , let the water be boyled in some vessell , untill it bee all consumed : then there will remaine a salt at the bottome , which you shall afterwards sowe in good Ground well prepared : such as the Theater of husbandry sheweth , and you shall have your desire .

PROBLEM . CXVIII . How to make an infalliable perpetuall motion .

MIxe 5. or 6. ounces of ☿ with his equall weight of ♃ , grinde it together with 10. or 12. ounces of sublimate dissolved in a celler upon a Marble the space of 4. dayes , and it will become like Oyle Olive , which destill with fire of chaffe or driving fire , and it will sublime dry substance , then put water upon the earth ( in forme of Lye ) which will be at the bottome of the Limbecke , and dissolve that which you ; can filter it , then distill it , and there will bee produced very subtill Antomes , which put into a bottle close stopped , and keepe it dry , and you shall have your desire , with astonishment to all the world , and especially to these which have travelled herein without fruit .

PROBLEM . CXIX . Of the admirable invention of making the Philosophers Tree , which one may see with his eye to grow by little and little .

TAke two ounces of Aquafortis and dissolve in it halfe an ounce of fine silver refined in a Cappell : then take an ounce of Aqua-fortis and two drams of Quicke silver : which put in it , and mixe these two dissolved things together ; then cast it into a Viole of halfe a pound of water , which may be well stopped ; for then every day you may see it grow both in the Tree and in the branch . This liquid serves to blacke haire which is red , or white , without fading untill they fall : but here is to be noted that great care ought to bee had in annointing the haire , for feare of touching the flesh : for this composition is very Corrosive or searching , that as soone as it toucheth the flesh it raiseth blisters , and bladders very painefull .

PROBLEM . CXX . How to make the representation of the great world .

DRaw salt niter out of salt Earth which is found along the Rivers side , and at the foote of Mountaines , where especially are Minerals of Gould and silver : mixe that Niter well clensed with ♃ , then calcinate it hermetically ; then put it in a Limbecke and let the receiver be of Glasse , well luted and alwayes in which let there be placed leaves of Gould at the bottome , then put

diagram fire under the Limbecke untill vapours arise which will cleve unto the Gould ; augment your fire untill there ascend no more , then take away your receiver and close it hermetically , & make a Lampe fire under it untill you may see presented in it that which nature affords us : as Flowers , Trees , Fruits , Fountaines , Sunne , Moone , Starres , &c. Behould here the forme of the Limbecke , and the receiver : A represents the Limbecke , B stands for the receiver .

PROBLEM CXXI . How to make a Cone , or a Pyramidall body move upon a Table without springs or other Artificiall meanes : so that it shall move by the edge of the Table without falling .

THis proposition is not so thornie and subtile as it seemes to be , for putting under a Cone of paper a Beetle or such like creature , you shall have pleasure

diagram with astonishment & admiration to these which are ignorant in the cause : for this animall will strive alwayes to free herselfe from the captivity in which shee is in by the imprisonment of the Cone : for comming neere the edge of the Table shee will returne to the other side for feare of falling .

PROBLEM . CXXII . To cleave an Anvill with the blow of a Pistoll .

THis is proper to a warrier , and to performe it , let the Anvill be heated red hot as one can possible , in such sort that all the solidity of the body bee softned by the fire : then charge the Pistoll with a bullet of silver , and so have you infallibly the experiment .

PROBLEM . CXXIII . How to rost a Capon carried in a Budget at a Saddle bow , in the space of riding 5. or 6. miles .

HAving made it ready and larded it , stuffe it with Butter ; then heate a peece of steele which may be formed round according to the length of the Capon , and big enough to fill the Belly of it , and then stop it with Butter ; then wrap it up well and inclose it in a Box in the Budget , and you shall have your desire : it is said that Count Mansfield served himselfe with no others , but such as were made ready in this kind , for that it loseth none of its substance , and it is dressed very equally .

PROBLEM . CXXIIII . How to make a Candle burne and continue three times as long as otherwise it would .

VNto the end of a Candle halfe burned sticke a farthing lesse or more , to make it hang perpendicular in a vessell of water , so that it swimme above the water ; then light it , and it will sustaine it selfe &

diagram floate in this manner ; and being placed into a fountaine , pond , or lake that runs slowly , where many people assemble , it will cause an extreame feare to these which come therein in the night , knowing not what it is .

PROBLEM . CXXV . How out of a quantitie of wine to extract that which is most windy , and evill , that it hurt not a sicke Person .

TAke two viols in

diagram such sort that they bee of like greatnesse both in the belly and the necke ; fill one of them of wine , and the other of water : let the mouth of that which hath the water be placed into the mouth of that which hath the wine , so the water shall be uppermost : now because the water is heavier than the wine , it will descend into the other violl , and the wine which is highest will ascend above to supply the place of the water , and so there will be a mutuall interchange of liquids : and by this penitration the wine will lose her vapors .

PROBLEM . CXXVI . How to make two Marmouzets one of which shall light a Candle , and the other put it out .

Won the side of a wall make the figure of a Marmouzet or other animall or forme , and right against it on the other wall make another ; in the mouth of each put a pipe or quill so Artificially that it be not perceived : in one of which place salt peeter very fine , and dry and puluerised : and at the end set a little match of Paper : in the other place sulphur beaten small : then houlding a Candle lighted in your hand , say to one of these Images by way of commaund , blow out the Condle : then lighting the Paper with the Candle , the salt peeter will blow out the Candle immediatly : and going to the other Image ( before the match of the Candle be out ) touch the sulphur with it and say , light the Candle , and it will immediatly be lighted , which will cause an admiration to these which see the action : if it be done with a secret dexterity .

PROBLEM . CXXVII . How to keepe wine fresh as if it were in a celler though it were in the heate of Summer , and without Ice or snow , yea though it were carried at a saddles bow , and exposed to the Sunne all the day .

SEt your wine in a violl of Glasse ; and place it in a Box made of wood , leather , or such like : about which violl place salt peeter , and it will preserve it and keepe it very fresh : this experiment is not a little commodious for these which are not neare fresh waters , and whose dwellings are much exposed to the Sunne .

PROBLEM . CXXVIII . To make a Cement which indureth or lasteth as marble , which resisteth ayre and water without ever disjoyning or uncemiting

TAke a quantitie of strong and gluing Morter well beaten , mixe with this as much new s●eaked Lime , and upon it cast Oyle of Olive , or Linseede Oyle , and it will become hard as Marble being applyed in time .

PROBLEM . CXXIX . How to melt mettle very quicke , yea in a shell upon little fire .

MAke a bed upon a bed of mettle with powder of Sulphur , of Salt peeter , and sawdust alike ; then put fire to the sayd powder with a burning Charcole , and you shall see that the mettle will dissolve incontinent and bee in a Masse . This secret is most excellent and hath beene practised by the reverend father Mercenne of the order of the Minims .

PROBLEM . CXXX . How to make Iron or Steele exceeding hard .

QVench your Blade or other Instrument seven times in the blood of a male Hog , mixt with Goose grease , and at each time dry it at the fire before you wet it : and it will become exceeding hard , and not brittle , which is not ordinary according to other temperings and quenchings of Iron : an experiment of small cost , often proved , and of great consequence for Armorie in warlike negotiations .

PROBLEM . CXXXI . To preserve fire as long as you will , imitating the inextinguable fire of Vostales .

AFter that you have extracted the burning spirit of the salt of ♃ , by the degrees of fire , as is required according to the Art of Chimistrie , the fire being kindled of it selfe , breake the Limbecke , and the Irons which are found at the bottome will flame and appeare as burning Coles as soone as they feele the ayre ; which if you promtly inclose in a violl of Glasse , and that you stop it exactly with some good lute : or to be more assured it may be closed up with Hermes wax for feare that the Ayre get not in . Then will it keepe more than a thousand yeares ( as a man may say ) yea at the bottome of the Sea ; and opening it at the end of the time , as soone as it feeles the Ayre it takes fire with which you may light a Match . This secret merits to be travailed ofter and put in practise , for that it is not common , and full of astonishment , seeing that all kind of fire lasteth but as long as his matter lasteth , and that there is no matter to be found that will so long indure .