THE FIRST SECTION , WHEREin is contained a plaine and sensible declaration of the circles of the Sphere , and the termes vsed in the doctrine de primo mobili , after another Methode than is yet in any other language .

THE circles of the Sphere haue more than once alreadie bin written of in English : notwithstanding I think it wil not be accounted labour lost , though it were only for the better vnderstanding of the conclusions following , here to handle them againe as principles in the beginning of this treatise . Aristotle and Ptolomey for proofe of some matters here propounded , haue vsed many exquisite arguments , which I meane not to prosecute , but hoping from the testimonie of sense in such manner to deduce the positions , that any meane capacitie may haue so reasonable a conceit of them , that with probabilitie they may easily be admitted , I will referre their exact and more subtile demonstration , with the reproofe of such as impugne them , to some others handling , or to some other place . Therefore requiring first the reader not to cast vntimely doubts , nor hastily to iudge of any part by it selfe , before he hath considered , and in some manner vnderstood the whole discourse , I will according to Hippocrates his counsell begin with the notablest and easiest things . Whosoeuer doth but cast vp his eyes vnto heauen , presently perceiueth that it compasseth him round about in manner of halfe a globe or an Hemisphere : and if he stand vpon some high place , or be at Sea farre from land , where nothing can be séene but water and the Skie , his eye , if he turne himselfe about , will represent vnto him at the lowest bounds or limits , which he seeth , the fashion of a circle , vpon whose plaine , as vpon a base , this visible Hemisphere seemeth to be placed : therefore that Circle was first in Gréeke , and is now commonly in English called the Horizon , that is to say , bounding or limiting , vz. the compasse of your sight . The largenes of this Circle , euen as it falleth vnder view , is of so great a compasse , as you neede not restraine the center thereof , according to the precise Mathematicall definition , to one determinate , exquisite , indiuisible , and very poynt , or pricke , but without sensible error , as your eye will plainly testifie , any one at pleasure may bee taken in the place where you stand . From a center so taken , if there be , or be imagined , a plumbe line or line perpendicular to the plaine of the Horizon extended vnto the heauen , the place , which there it toucheth , is commonly called by an Arabian name the Zenith , being in truth the pole of the Horizon , and the line it selfe his Axis . By this Axis , and any lines crossing it , if plainnes be euery way extended reaching vnto heauen , they marke out their circumferences , or semicircles , cutting one another in the Zenith : but in the Horizon their sections are right lines , cutting one another in his center . Those circles are named Azimutes , and are imagined by Astronomers to be cut by other circles parallel to the Horizon , which they terme Alinicantars and circles of Altitude , because the portion of the Azimute , which is betwéene the Horizon and the Parallel , sheweth how his aboue the Horizon that poynt of the Parallel is , by which the Azimute passeth . Furthermore , in a cléere night beholding the bright shining Starres , you shall euidently perceiue how they change their places continually , some to rise and shew themselues , other to goe downe vnder the Horizon , and to be hidden from your sight , onely if you place your selfe so , that your right hand be towards their rising , and your left hand toward their going downe , looking right foorth , and somewhat vpward , you shall behold certen Starres , which are all times of the night to bée seene , and neuer

depiction of constallations

Charles Wayne .

pole star .

Little Beare

go down ; amongst some of which placed after this fashion , there is one commonly called the Pole star , which being the last in the tayle of the constellation called the little Beare , lyeth in manner directly as it were in a right line , with those two in the hindermost whéeles of Charles his wayne . This Starre seemeth little or nothing to remoue out of his place , and indeede not farre from it there is a poynt , or pricke , which remaineth in one and the same place alwaies immoueable . The Azimute passing by the Horizons Axis , and a right line drawne from this immoueable point , or the pole starre , is properly called the Meridian circle ; the common section of it and the Horizon , being a right line , is the Meridian line , or the line of North and South ; the right line , which crosseth this Meridian line at right angles in the center of the Horizon , is called the line of true East , and true West , or simply the line of East and West , which poynts the ends thereof extended directly fall vpon . The Arimute standing vpon this line , Ioannes de Roias , & others , specially such as write of Dyalling , as it were for dignitie and preheminence , doe call the Verticall circle : which name being common to all Azimutes , because they passe by the Zenith , in Latin called Vertex . or punctum eregione verticis : for a distinction Gemma Frosius hath named it the Circle of the East . The other Azimutes haue no proper names , but are measured or determined in the Horizons circumference . That , and so likewise all other Circles , Astronomers doe imagine to be diuided into 360. equall parts , which they name degrées , that is to say , euerie quarter or quadrant into 90. degrees : euery degrée they further diuide into 60. minutes , euery minute into 60. seconds , euery second into 60. thirds , and so continue sometimes vnto tenths , and may goe further if they will . By these degrees , minutes , &c. which are betwéene that point , where any Azimute cutteth the Horizon , and the Meridian line , or the line of East and West , the Azimute is determined , assigned , or said to be giuen . Vpon the points where the Verticall circle cutteth the Horizon , which poynts are the true poles of the Meridian , and the precise East and West , if by often and diligent viewing you shall see two Starres , the one in the East , and the other at the same time right against it in the West , in winter time euen in one night , you may behold that which is in the East first ascending , and then againe descending at length to come into the West , and that which was in the West being till that time hidden from your sight , then to appeare againe rising in the East : all this while continually the like shape of an Hemisphere being still represented to your eye , without any chaunge or alteration , whereby you may gather the heauen to bee a perfect Globe , or Sphere , hauing that part vnder the Horizon equall and like to that which you sée aboue it , and that the place where you stand is the very center thereof . A line drawne from the pole Starre , or rather from the poynt immoueable before mentioned , called the Articke , or North pole , a line ( I say ) drawne , or imagined to be drawne from that poynt to the place of your standing , is called the Aris of the world , and extended to the other side of the celestiall Sphere , which is vnder vs , falleth there vpon the South or Antarcticke pole , which in these our countries neuer appeareth . These things , being but a little héedily considered , be so manifest and apparant , that neither example nor figure is greatly requisite for the perfect vnderstanding of them : yet in this beginning to remoue all difficultie , and to make euery thing as plaine as may be , doe thus much : In some plaine ground , or rather vpon a poste , or stone , or some such like thing made exactly smooth , and lying very flat , without any manner of leaning or declining , which you must warily and diligently trie by your leuel , and your plumbe line , take the center A , vpon which describe a circle B C D E , representing the Horizon , whose circumference you may diuide , or imagine onely to be diuided into degrées , and from A , the center thereof , erect a Stéele or wier , standing plumbe vpright , or perpendicular to the flat of the circle A B C D , by triall of your plumbe rule : then take a boord made precise square , hauing the side somewhat longer than the semidiameter of the circle B C D E , and set one corner thereof in the center A , so that one of the sides containing it , may agrée iust with the Stéele or wier , and the other with the circles plaine : then looking along the vpper edge , or through two sights set vpon the edge , and continually lifting it vp without swaruing , till the side that lay vpon the flat of the circle agrée with the Stéele : the line of your sight , or the line drawne from the center ( for in respect of the heauens mightie distance , the difference betwéene them is not sensible ) shall , howsoeuer the square be placed , describe

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an Azimute . And if staying the edge of the square at one height , the corner be continually kept in the center without slipping , by turning it round about the Stéele , you shall describe an Almicantar , parallel to the Horizon . In this manner , carying the square about , & lifting it vp & downe , till you see the Pole starre , or if you can aime at it , the often spoken of immoueable poynt , staying it fast in that situation , either of the edges without sensible error may bee taken for the Axis of the world , which extended falleth on both the Poles , that which is seene being the Arctick Pole , and the Antarctick that which is vnder the Horizon . In lifting it vp and downe , you shall in the heauen poynt out the Meridian circle , and bringing it iust to the flat of the circle B C D E , the edge will there shew the right line B D , which is the Meridian line . The line C E , in A crossing the line B D , is the line of right East , and right West : the Azimute standing vpon C E , is the Vertical circle , or the circle of the East : the Azimute standing vpon G F , is sometime said to be of so many degrees , as are betwéene B the North poynt of the Horizon , and G , where the Azimute standing vpon G F cutteth the Horizon , vz. the circumference B G , denominateth the Azimute standing vpon G F , and sometime that circumference G E , which containeth the number of the degrées betweéene the same poynt , and the line of East and West E C , which bée the very poles of the Meridian . Working by the Pole starre , these things will somewhat varie from exactnes , which some helpe by awayting the time , when the starre next the whéeles of Charles wayne , commonly called the filler or hill horse , is directly ouer or vnder the Pole star , so that the square , being lifted vp and downe close by the Stéele , passeth by them both . But howsoeuer , this may suffice for some conceit of these termes , hereafter shall be taught other most precise waies , to discribe and take them most exactly . To returne againe therefore to our principall purpose , in beholding of the Starres , how they continually rising in the East side of the Horizon , ascend vnto the Meridian , and so from thence descend vnto the West side , you shall obserue , that alwaies they kéepe their distance from the Pole starre , or the true pole vnchaunged : as if you mark the two hinder whéeles of Charles waine , you shall finde , howsoeuer they be situated in the heauen , that their distance from the Pole starre is alwaies one , and the same not néerer or further of at one time then an other , and therefore euery starre or poynt , by such motion in a Globe or Sphere , his superficies describeth the circumference of a circle : so that the whole heauens must seeme to turne vpon the poles , and make a circular motion or reuolution . This motion in diuers respects hath diuers names , called sometime the Diurnall motion , sometime the motion of the first moueable heauen , sometime Notus captus . Againe , euery Starre or peynt by this conuersion describing a circle , if you take some starre , or poynt , which lieth betwéene the poles iust 90. degrées from either of them , that will describe a circle , passing by the poynts of East and West , which for some reasons hereafter to bee expressed , is called the Equinoctiall . The other poynts or starres describe circles parallel to the Equinoctiall circle , which be called circles of declination , because , if from the poles of the world , by any point taken in any of the parallels , a greatest circle be drawne to the Equinoctiall , that portion of it , which lieth betwéene the Equinoctiall and the Parallel , is called the declination of the poynt so taken . Some of these Parallels towards the North , described by reuolution of the poynts or starres , that neuer set , are whole aboue the Horizon , and one of them , which some name the Arctick circle , toucheth it onely : about the Antarcticke pole there be some wholy vnder the Horizon , and one , which some call the Antarcticke circle , only toucheth it in the South poynt : other betwéene these two touching Parallels , which arise and set or goe downe , cut the Horizon , whose portion lying betwéene that poynt and the true East or West , is called the Amplitude or Latitude of the rising , or the setting of the poynt describing the Parallel . These things hitherto rehearsed , trauellers may euery where and in all countries obserue : and besides , in their iournies Southward or Northward , they shall see sometimes more , and sometimes fewer stars neuer to goe downe : more in going Northward , fewer in going Southward , yet alwaies without alteration kéeping one and the same distance one from another . Mary the Pole starre or the true pole , proportionablie to the length of the way trauelled , altereth his distance from the Horizon , and the Zenith appearing , the further you goe Northward , the higher , & the further you go Southward , the lower , and so accordingly that portion of the Meridian , betwéene the Equinoctiall and the Zenith , which is

sky chart

called the Latitude of the countrie , being alwaies equall to that which is betwéene the Horizon and the Pole , called his height , or eleuation , is of necessitie greater or lesser : so that your situation is apparantly chaunged in respect of the heauen , but yet stil you kéepe the same distance from it , wherby you may easily inferre the figure or shape of the Earth to bee like and answerable to the celestiall Sphere : and that how vast and huge soeuer it be in it self , yet in comparison of the large compasse of the heauen , it is iustly counted for no more but a small poynt , or pricke : for it neuer hindreth you from seeing the precise halfe of the celestiall Sphere , which , were the bignes thereof any thing of accompt , it would of necessitie doe . For better vnderstanding of these matters , imagine the circle B C D E , described on the center A , to represent the Meridian , and vpon the line E C , a semicircle erected perpendicularly to represent the Horizon , whose Pole , or the Zenith , the poynt B is , and let H be the North pole . From H to A the place of your standing ( being the center of the Horizon and the whole Sphere , and so consequently of al the greatest circles in the same Sphere described ) from the pole H to the center A draw a right line , and extend it vnto I : the line H I is the Axis of the world : the poles be H the North , and I the South , or Antarcticke pole . Let the poynt G , taken in the Meridian , be iust 90. degrees from either pole , so that the circumferences G H , G I , be iust quadrants : by the reuolution of the Sphere vpon the poles H I , which is the Diurnall motion , the line G A shall describe a circle passing by the center of the Sphere , and perpendicular to the Meridian : therefore it must passe by the poles thereof which be in the Horizon , the points of East and West , as the circle set plumbe vpon the Diameter F G will doe . Other poynts , as S , N , V , describes circles parallel to that standing vpon G F , of which that which standeth vpon C S , doth onely touch the Horizon , and is wholy aboue it : the other beyond it to the pole-ward , as V , W , be wholy aboue it , and come not néere . So likewise E , T , is alwayes vnder the Horizon , and only toucheth it : the other beyond it towards I , are vnder it , and neuer come néere it . Now if in going Northward the pole H grow higher , the Equinoctiall must go further from the Zenith : for seeing B C and G H be equall , that is the iust quarters of the same circle , if you take away the circumference B H common to them both , the residue G B , the distance of the Equinoctial from the Meridian , which is the Latitude of the countrie , whose Zenith is B , is equall to H C , the height of the pole aboue the Horizon , or the eleuation of the pole , and as the pole riseth higher , so is the circle S Cremoued from the Horizon further and further : whereby you see , that by that meanes more starres neuer set . The circumferences of the Meridian G N , G S , G V , are called the declinations of the points N , S , V , taken in the parallels N Z , S C , V W , and the portion of the Horizon betwéene the point of true East , and the poynt , where the parallel standing vpon N Z , cu●teth the Horizon , is the amplitude or latitude of rising of the poynt L , or any other taken in the parallel , standing vpon the Diameter N Z. These things being well conceiued , let vs consider againe , that as apparantly as any starre , the Sunne making his reuolution , ariseth on the East side of the Horizon , and mounting vp vnto the Meridian , at which time it is high noone , descendeth againe vnto the West side , which time of his continuance aboue the Horizon is called the artificiall day , then being hid from our sight , the night beginneth , which continueth till the Sunne , passing by that part of the Meridian , which is vnder the Earth , when it is midnight with vs , returneth againe vnto the East side , making vp the naturall day , which is the space of time from the Sunne rising to the Sunne rising againe , and may bee indifferently reckoned from Sunne set to Sunne set , as the Iewes doe , or from midnight to midnight , which is our common accompt . The obscure light before the Sunnes rising , is called the dawning and breake of the day : after his setting is called the twilight , Crepusculum in Latin is a common name to both times . Although in the Sunnes daily reuolution we obserue all this , yet is it not without much varietie and chaunge : his rising and setting is not alwayes in one place of the Horizon , nor his height in the Meridian alwayes the same at noone . In the middest of winter , about the 12. of our December , when the daies be shortest , and the nights longest , it riseth & setteth most Southerly , and is lowest in the Meridian at noone : towards the Spring , as the dayes waxe longer and longer , in rising and setting it continually groweth from the South , and mounteth higher and higher in the Meridian , till about the 11. of our March , making the day and night equall , it riseth and setteth iust East and West , comming at noone to the common section of the Equinoctiall and the Meridian : then , as Summer commeth on , the dayes encreasing , it riseth and setteth more Northerly , mounting still higher and higher in the Meridian at noone , till in the middest of Summer , the dayes being at the longest , about the 12. of our Iune , it be at the highest in the Meridian at noone , and riseth and setteth furthest North : then , as the dayes shorten , it returneth backe againe , growing continually lower at noone , and rising and setting lesse Northerly , till the dayes and nights become equall againe , about the 13. of our September , when it riseth and setteth precisely East and West againe , and at noone will be in the common section of the Equinoctiall and the Meridian . From that poynt it groweth lower and lower at noone , rising & setting more and more Southerly , as the nights encrease , till about the 12. of our December the dayes being at the shortest , it becommeth lowest againe at noone , and in rising and setting most Southerly , as it was before . Of this returning from the highest in Summer , and the lowest in winter , the two Parallels , which it then describeth by the Diurnall reuolution , bee called Tropickes , and the Equinoctiall was so named , because in March and September the Sunne comming to it , the day is made equall to the night . By these varieties it was easily gathered , that the Sunne made a peculiar course beside his Diurnall reuolution , in a greatest circle touching the two Tropicks , and declining from the Equinoctiall , which it diuideth ( as all greatest circles doe one another ) into two equall parts , or semicircles . This declining circle , because when the Sunne and Moone either méete or be opposite in it , there happeneth an Eclipse , is called the Eclipticke , and sometime the Zodiacke : but the Zodiacke properly is a superficies like a fillet or a girdle , laid vpon this circles circumference , comprehending on either side of it sixe , or ( as some say ) eight degrées . The poles of this circle , which decline from the poles of the world , as the circle it selfe declineth from the Equinoctiall , describeth by the Diurnall reuolution two Parallels , which some , in stead of them afore described , take for the Arctick and Antarcticke circles . That section of the Equinoctial and the Eclipticke , which the Sunne commeth to in the Spring time , is called the Vernall section : that which is opposite to it , by which the Sunne passeth in the end of Haruest , is the Autumnall section : the poynts which touch the Tropickes , bee commonly called Solstitiall poynts . The greatest circle , passing by the Equinoctiall sections and the poles of the world , is the Equinoctiall Colure : that which passeth by the poles of the world and the Solstitiall poynts , is called the Solstitiall , or Tropicall Colure , the portion thereof lying betwéene the two Tropickes , is the distance of the Tropickes , whose halfe is the Sunnes greatest declination , otherwise called the Obliquitie of the Zodiacke , which by obseruation made with large instruments , is in this our age found by great Artes-men to be 23. degrées and 30. minutes , whose report it shall be sufficient to accept of , and commit to memorie , without taking or trying it by any small instrument : though some writers of the vse of the Astrolabe haue made that one of their speciall conclusions . The Equinoctiall and the Eclipticke , are circles of chiefe accompt : the first being the rule and measure of the first motion , or the motion of Primum mobile , otherwise called the Diurnall reuolution : and the other as it were the Standard , whereby all secondarie motions are examined : therefore the degrées of these circles haue peculiar names , called in the Equinoctiall Tempora , times , because they be the first measures of time , euery 15. degrées ascending making an houre , and so the whole reuolution of 360. which is performed euery naturall day , make 24. houres . Astronomers begin to accompt the parts or degrées , as well in the Equinoctiall , as in the Eclipticke , from that poynt common to them both , which is called the Vernall section : and though in the Equinoctiall there be no chaunge of names , yet in the Eclipticke or Zodiacke euery thirtie degrées is called a signe , and hath a peculiar name . The first 30. immedtatly following the Vernall section , is called Aries : the next 30. Taurus , the third 30. Gemini , the fourth 30. ( whose first point begin a new quadrant , and toucheth the Summer Tropicke ) is termed Cancer : the fift 30. Leo , the sixt Virgo . These sixe Signes make vp the semicircle of the Zodiacke , which leaneth or declineth from the Equinoctiall toward the North pole . The first 30. after this semicircle , beginning at the Autumnall section , make the seuenth signe , named Libra : the next or eight 30. is the signe Scorpio : the ninth 30. is Sagittarius : the tenth 30. ( beginning a new quadrant with the first poynt , which toucheth the winter Tropicke ) is Capricornus : the eleuenth 30. is Aquarius , and the twelfth 30. is Pisces . There be characters vsed to expresse euery Signe with , which are found in euery Almanacke . The Sunne passeth in the Ecliptick from poynt to poynt , making his continuall reuolution in it , without swaruing to the one side or the other : other Starres for the most part decline from it , but yet haue their places determined by Longitude and Latitude in respect thereof thus : By any poynt or Starre , a greatest circle being drawne from the pole of the Ecliptick to his circumference , the section there made , or the portion of the Ecliptick betwéene that section and the Vernall section , is the Longitude of the poynt , or Starre , by which the greatest circle is drawne : his Latitude is that portion of the same greatest circle lying betwéene the Starre and the Eclipticke . The Sunne being in any poynt of the Eclipticke , and the poynt it selfe , with all other Starres , wheresoeuer placed besides , are in like manner compared to the Equinoctiall , and in respect therof , not onely their declination , which hath béen touched before , but also their right Ascension is considered . A greatest circle being drawne from the Poles of the world to the Equinoctiall , by any poynt or Starre , his right Ascension is that portion of the Equinoctiall , taken betwéen that poynt where the greatest circle cutteth , and the Vernall section . The declination is the portion of the greatest circle so drawne , which lieth betwéene the Equinoctiall and the Starre , which ( as before was noted ) is also determined by a Parallel to the Equinoctiall , passing by the Starre . The right Ascension is so called , because vnder the Equinoctiall , that is , in a Situation where the Equinoctiall passeth by the Zenith , and the Horizon by the Poles of the world , the Horizon ( by which once in 24. houres euery poynt ascendeth ) doth the office of any greatest circle so drawne , as is appoynted , and agréeth with it most exactly . This Situation is called Sphaera recta , the right Sphere ; and the Horizon in that Situation , Horizon rectus , the right Horizon : but when the Equinoctiall declineth from the Zenith , and the Poles bée one aboue , the other beneath the Horizon , that Situation is called the Oblique , or Declining Sphere ; and the Horizon , the Oblique Horizon , which neuer agréeth with the foresayd greatest circle , drawne by the Poles of the world : and therefore with the Starre there is another poynt of the Equinoctiall in the Horizon , betwéene which and the Vernall section is contained that portion of the Equinoctiall , that is called the Starres Oblique Ascension , and the portion of the Equinoctiall betwéene the ends of the right and Oblique Ascension , is called the Difference Ascensionall . But for helping the conceit of these things , I will vse a linearie example , taking the former figure , where E C is the Meridian line , and the Diameter on which the Horizon standeth , now in the middest of winter the Sun being lowest in the Meridian , in the point K , by the Diurnall reuolution , describeth a Parallel standing vpon the Diameter K M , which cutteth the Horizon from the East towards the South : it continually groweth higher and

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higher in the Meridian pan , & riseth in the Horizon néerer and néerer the East , till about the 11. of March at noone it commeth to G , the section of the Equinoctiall and the Meridian , and then by the Diurnall reuolution describeth a circle iust answering the Equinoctiall , which passing by the poynts of East and West in the Horizon , standeth vpon the Diameter G F : from thence , a● Summer commeth on , it ascendeth in the Meridian , and riseth more Northerly vpon the Horizon , til about the 12. of our Iune , being at the highest in N , it describeth a Parallel standing vpon the Diameter N Z , in which it riseth vpon the Horizon furthest from the East to the Northward : from thence it descendeth againe by G , to K , and passeth in the Horizon by the true East to the furthest Southward , then it ascendeth againe till it come to N , continually returning from the highest to the lowest , & from the lowest to the highest : whereof the two Parallels standing vpon the Diameters K M , L N , be called Tropickes . By these changes it was easily gathered , that the Sunne ( besides the Diurnall reuolution ) made another proper to it selfe in a circle standing vpon the Diameter K L , drawne from Tropicke to Tropick by A the center of the Sphere : by reason whereof , this circle , called the Eclipticke , and the Equinoctiall , diuide the one the other into two semicircles . The Eclipticke is sometimes called the Zodiacke , though properly the Zodiacke be a superficies lying on either side of it , as you sée the superficies O P Q R , parted by the line Z K. The common Diameter of the Equinoctiall and the Ecliptick standing in A , perpendicular to the plaine of the circle B C D E , the poynts K and L being the Solstitiall poynts , the circle B C D E is the Solstitiall Colure . The circle standing vpon I H , and passing by the perpendicular Diameter , or the Equinoctial section , is the Equinoctiall Colure : the circumference K N is the distance of the Tropicke , the one halfe thereof G K , or G N , is the obliquitie of the Zodiacke , or the Suns greatest declination , for it groweth lesse & lesse as it commeth néerer the Equinoctiall section : where it hath no declination at al , it neuer declineth from the Eclipticke or circle standing vpon K Z , but make his motion in it , his place is named of the poynt wherein it is . Other Starres or poynts without the Eclipticke ( as for example , S ) haue their place determined by a greatest circle B C D E , drawne from X , the Pole of the Zodiacke , by S ●o K , a poynt in the Ecliptick circumference , the portion of the Ecliptick betwéene the Vernall section and K , or the poynt K is the Longitude of S , and the circumference S K , is his Latitude . In like manner , if by any starre or poynt Y , and the Poles of the worlde H I , there bee drawne a greatest circle B C D E , cutting the Equinoctiall in G , the portion of the Equinoctiall betwéene the Vernall section and G , is the right Ascension of Y , and the circumference G Y is his declination . Now if G , the section of the Meridian and the Equinoctiall , be the Zenith of any place , the Horizon must stand on I H , and passe by the Poles of the world , which situation is called the right Sphere , and the Horizon the right Horizon , wherein , by the Diurnall reuolution twice in 24. houres , the circle B C D E must ioyne close with it . But if G , the section of the Equinoctiall and the Meridian , decline from B the Zenith , which situation is called the Oblique Sphere , and the Horizon then standing on E C , being an Oblique Horizon , by the Diurnall motion made vpon the Poles H I , the circle B C D E can neuer agréene or match euenly with the Horizon : therefore of force some other poynt of the Equinoctiall , and not G , must be in the Horizon with Y : the circumference of the Equinoctiall betwéene that point in the Horizon , and the Vernall section , is the Oblique Ascension of Y : but the portion that lieth betwéene that poynt and G , is the difference Ascensionall . That poynt of the Zodiacke , where it is cut off the Meridian , is called Medium coeli , mid heauen ; Culmen and cor coeli aboue the Horizon , & Imum coeli vnder the Horizon , the lesser angle , made by that section , is called the Meridian angle . The poynt of the Eclipticke , that is in the East side of the Horizon , is called the Ascendent , and the Horoscope , the section there make the angles , of which the lesser is called the Horizontall angle : the quantitie thereof is equall to the Nonagesimus Gradus of the Eclipticke , which is peculiarly giuen to that poynt of it , which is iust 90. degrées from the Ascendent . There be moreouer other greatest circles to be considered , which are called circles of position , or circles of Station , sixe of them diuiding the heauen in twelue portions , which are called houses or Stations , though many times those names be restrained only to such parts of the Zodiack , as be intercepted by those circles . Though the Horizon be alwaies taken for one , and the beginning of the first house : yet are the rest by diuers diuersly drawne . Some will haue them all to haue the Meridian line for their common Diameter , and yet agréeing in this make difference in placing them . Campanus and Gazulus diuide the Verticall circle into twelue equall parts , and by euery two opposite sections draw a circle of position . Regiomontanus diuideth the Equinoctial into twelue equall parts , and will haue euery circle of position passe by two of those opposite sections : both these waies kéepe the Horizon and the Meridian for circles of position . Other diuide the Zodiacke into twelue equall parts , beginning at the Ascendent , and two of those opposite sections draw from the poles of the Zodiacke their circles of position : these kéepe the same Ascendent that the former doe , but must differ many times in the tenth house , or the Cardo medij coeli , though Gemma writeth that all agrée about the foruer Cardines , that is the Horoscope , seuenth house Culmen , and Imum coeli : for they cannot haue alwaies the Meridian & the Horizon for circles of position . Other draw these circles from the poles of the world , and that diuersly : but the thrée former wayes are in greatest estimation . A circle of position differeth from an angle of position , which ( after Prolomey ) is an angle at the Zenith , subtended of that portion of the Horizon , which lieth betwéene the Meridian and the Azimute , passing by the Zenith of the other place , vnto which the position belongeth . Gemma Frisius maketh it a right lined angle in the center of the Horizon , subtended of the same circumference : by it Topographicall descriptions are made , wherein sometimes the distance of two places is measured by a right line lying betwéene them , but in a Sphericall superficies by the portion of a greatest circle , because that is the shortest that can bee drawne in it . These things may be easily conceiued without linearie explication , if the former matters bee well vnderstood : therefore as it were besides the principall purpose , setting downe how by supputation you may readily gesse somewhat néere the Suns place , being a thing for many purposes to be had in a readines , I will end this first section : the thing is taken out of Clauius , but fitted to our common , or the Iulian yeere .

Parergon primum . What moneth , and what day of it , the Sunne entreth euery signe of the Zodiacke .

FIrst tell the moneths vpon your fingers , seeking Innuarie on your thumbe , Februarie on your forefinger , and so the other in order , till you come to your moneth , which marke on which finger it falleth : in like manner tell the Signes , beginning with Aquarius on your thumb , Pisces on your forefinger , and so the rest in order , till you come to the finger , on which your moneth fell : the Signe which falleth on that finger , the Sunne entreth that moneth . Then learning these two verses by heart :

Inclyta Laus Iustis Impenditur , Haeresis Horret Garrula , Grex Gratus Faustos Gratatur Honores .

In like manner set Inclyta on your thumbe , and word by word in order , till you come to the finger , on which your moneth fell : then telling from A in the crosse row , till you come to the first letter of your word , take that number and subtract it from 20. the residue is the day of the moneth , when the Sunne entreth the Signe . For example : I would know what Signe the Sunne entreth in October , and what day it entreth , telling from Ianuarie vpon my fingers the meneths in order : at the second going ouer I finde October on my little finger : then taking the Signes , and telling from Aquarius , at the second going ouer my fingers , Scorpio falleth on my little finger , so I say that the Sunne entreth Scorpio in October : then taking the verses , and setting the words one by one in like manner on my fingers , I finde in the second going ouer , Faustos on my little finger : now telling in the crosse row the letters from A to F , I finde sixe : this sixe I subtract from 20. so rest 14. which the day of October the Sunne entreth Scorpio .

Parergon secundum . To know the Sunnes place in the Zodiacke vpon any day giuen .

FInde the Signe answering your moneth , and the word likewise , then to the day of the moneth put ten , and the number the first letter sheweth in the crosse row : if this be lesse then 30. the number is the degrée of the Signe next before that , which the Sunne entreth in your moneth ; if more , cast away 30. and the residue is the degrée of the Signe entred in your moneth . Example , I would know where the Sunne is the 9. of October , I finde in October he entreth Scorpio , and the word for it to be Faustos , whose first letter F is the sixt in the crosse row , I take ten and 6. vz. 16. which I put to , 9. there is made 25. therefore I say the Sun is in the 25. degree of the Signe before Scorpio , which is Libra . If I would know for the 18. day , putting 16. to 18. there would amount 34. from which abating 30. the 4. remaining sheweth me , that the Sunne is in the 4. degrée of the Signe belonging to October , which is Scorpio .

Parergon tertium . The place of the Sunne being giuen , to finde the day of the moneth .

TAke the day and moneth the Sun entreth the Signe giuen , the number of the degrées giuen put to the day , wherein the Sunne entreth the Signe , that product being lesse than the dayes in your moneth , shew the day : but being more , cast away the dayes of your moneth , the residue is the day of the moneth following . Example , I finde the Sunne in the 4. degrée of Scorpio . I would know what day of the moneth it is ; I finde that the Sunne entreth Scorpio the 14. of October , I put 4. to 14. there amounteth 18. so I say it is the 18. day of October . Againe , let it be in the 25. of Libra , I finde that the Sunne entreth Libra 13. Septembris : I put 13. to 25. there amounteth 38. from which I take 30. the dayes of September , and there remaineth 8. the day of October . These are but gesses , as you may see much after the way commonly taught by the backe of the Astrolabe . Let him that desireth exactnes , seeke the Sunnes place in some Ephemerides , or in the Regiment of the Sunne , published by E. W. painfully calculated vpon his owne diligent and exact obseruations .

The end of the first Section .