A briefe treatise for the measuring of glasse, board, timber, or stone, square or round being performed only by simple addition and substraction, and that in whole numbers, with[o]ut any multiplication, or division at all / by John Speidell ... Speidell, John, fl. 1600-1634. This text is an enriched version of the TCP digital transcription A12751 of text S998 in the English Short Title Catalog (STC 23059.5). Textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. The text has been tokenized and linguistically annotated with MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish. This text has not been fully proofread Approx. 66 KB of XML-encoded text transcribed from 9 1-bit group-IV TIFF page images. EarlyPrint Project Evanston,IL, Notre Dame, IN, St. Louis, MO 2018 A12751 STC 23059.5 ESTC S998 23161415 ocm 23161415 26321 2240910749

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 Early English books online. (EEBO-TCP ; phase 2, no. A12751) Transcribed from: (Early English Books Online ; image set 26321) Images scanned from microfilm: (Early English books, 1475-1640 ; 1782:2) A briefe treatise for the measuring of glasse, board, timber, or stone, square or round being performed only by simple addition and substraction, and that in whole numbers, with[o]ut any multiplication, or division at all / by John Speidell ... Speidell, John, fl. 1600-1634. [16] p. Printed by Thomas Harper, London : 164[0?] Date of imprint suggested by STC (2nd ed.) and NUC pre-1956 imprints. Signatures: [pi]² A², ²A⁴. Title in ornamental border. Includes: The use of a scale of fractions, invented by John Speidell ... Reproduction of original in the Henry E. Huntington Library and Art Gallery. eng Arithmetic -- Early works to 1900. Fractions -- Early works to 1800. eebo A briefe treatise for the measuring of glasse, board, timber, or stone, square or round. Being performed only by simple addition and substraction, and Speidell, John, 1640 18 5610 181 0 0 0 0 0 322.64 F The rate of 322.64 defects per 10,000 words puts this text in the F category of texts with 100 or more defects per 10,000 words. 2010-09 Assigned for keying and markup 2010-09 Keyed and coded from ProQuest page images 2011-02 Sampled and proofread 2011-02 Text and markup reviewed and edited 2011-06 Batch review (QC) and XML conversion

A briefe TREATISE for the measuring of Glasse , Board , Timber , or Stone , square or round . Being performed only by simple Addition and Substraction , and that in whole Numbers , with●ut any Multiplication , or Division at all .

By John Speidell Mathematitian , in Queenes-street , where you may have of these Books at all times .

LONDON , Printed by Thomas Harper . 164●

This I have written in briefe to helpe all such as can but only Adde and Substract in whole numbers , which if any cannot doe , if they please to repaire to my house in Queen-street , I will teach them so much Arithmetick in halfe an houre .

And for all such as desire to be more then ordinarily instructed in the Mathematicks ; Let them repaire unto me , and I shal ( God willing ) give them such satisfaction in all the rules of Arithmetick , both in whole Numbers and Fractions , with the extractions of roots , the rule of Coffe or Algebra , with such extraordinary briefe rules for exchange , interest , valueing of Lands , Leases , Rents , Annuities , and Purchases , and with a briefer way for casting up of Tower bills for gold or silver , then hath hitherto been taught by any . As also by a new invention of mine to teach women or children above 10 yeares of age , to cast up any ordinary question of the rule of 3. or practice , in whole numbers , and with Fractions in a few houres .

There also may any be instructed in Geometry and Astronomy , by practice and demonstration , with the use of severall instruments for surv●ying of Lands , and plotting the same sundry wayes , and taking of heights and distances by severall instruments , with the use of both the Globes , the projection of the Sphere in plaine by scale and compasse , and the doctrine of right lyned and spherificall Triangles , with the application thereof in dialling , navigation and fortification , after a briefer way then is extant by any writer of these times , with the use of the Ephemerides , and other secret inventions to be taught in private .

There also may you have particular rules and scales for measuring of glasse , board , wainscot , plastering , tyling , brickworke , stone , or ti●ber , square or round , and for reducing one figure into another , and cutting of any part or parts thereof sundry waies , for valuing of rents , leases , annuities , and purchases , and for intrest , with rebat●s , after any rate per centum , to be done onely by scale and comp●sse , also gauging rods for all kinde of Caske great or small , and pr●sently taught at first sight , for the helpe of such as are not seene in Arthmetick at all .

There also may you have of the best Mathematicall paper , &c.

To measure glasse or board .

THis is 2 severall wayes to be done : First , by having only the breadth of your gl●sse or board , and thereby to finde how much in length sh●ll make a superficiall or square foot , or having the length and breadth to finde how much that whole pane of glasse , or that whole board containeth .

Example .

Let a board or a pane of glasse be broad 9. inches , and it is required to finde how much in length shall make a square foot : substract ●ver from , 33625. the number belonging to the breadth of your board or glasse , and the remainder being looks , sheweth how much in length shall make a square foot .

Example .

The breadth being 9. inches , the number thereunto belonging is , 15563. which taken from , 33625. leaveth , 18062. which being lookt out against it stands , 1. fo. and 4. inches , and so much in length shall make a square or superficiall foot : And after the same manner , if a glasse or board be 8. inches broad , there will be found 1. foot and 6. inches in length to make a foot :

And if your glasse or board be broad 13½ inches there shall be found 10¾ inches in length to make a foot .

The second way .

Suppose a pane of glasse to be broad 16. inches , and long 2 foot and 6. inches , and it is required to finde how many square foot therein is contained .

Take the numbers belonging to both the length and breadth , and adde them together , and from that addition substract ever the ●●●ber belonging to 1. foot , and the remaynder being looke sheweth h●w many squ●re foot that whole pa●●e containeth . Example . Against . 2 fo. 6 , is . 20792 Against 1 4. is ● . 18062 t●g●●●er . 38854 Against . 1. fo. is . 16812 — ●●st . 22●42
to which answers 3. fo. 4. in . and so much is contained in that whole pane of glasse required .

Againe , suppose a board to be long 18. foot , and broad 16. inches , and it is required to finde how many square foot that whole board containeth . Against . 18. fo. is . 29365 Against . 16. inches . 18062 together . 47427 Against . 1. fo. is . 16812 rest . 30615
to which answers 24. foot to be therein contained .

And after the same manner , if a board be broad 14. ¼ . inches , and long 17. fo. 5. ●/● . inches , then shall be therein contained 20. fo. 8. ¾ . inches .

To measure Timber or Stone .

This is also to be done 2. wayes .

First , having the breadth and depth of your Timber to finde how much in length shall make a sollid or cubicall foot ; or having the length , breadth , and depth , to finde how many sollide foot the whole piece of Timber containeth .

Forasmuch as almost no Timber is so broad and deepe above as below , therefore take both the breadth and thicknesse about the middle of the peece , and suppose you finde it thereabouts to be 15. inches broad , and 11 deepe , and it is required to finde howmuch in length shall make a sollide foot .

Adde the Numbers belonging to the breadth and depth together , and substract that addition ever fiō 50437 , and the remaynder lookt sheweth how much in length shall make a sollid foot . Against . 15. inches is . 17782 Against . 11. stands . 16435 together . 34217 Which substract from . 50437 so rest . 16220
to which answers 10 ½ . inches , and so much in length shall make a sollid foot required .

And after the same manner , if a peece be broad 18. inches , and deepe 16 , there is found that 6. inches in length shall make a sollid foot .

And being broad 9 ¼ . inches , and deepe 7. ¼ . by proceeding after the same manner there shall be found 24. inches in length to make a s●llid foot , and not 1/● . quarter more .

The other way by having the le●gth , breadth , and thicknesse to finde how much the whole piece containeth .

Let the breadth and depth about the midle be 16. ½ and 10. ●/● . inches , and the whole length 17. fo. 8 ¼ . inches , and it is required to finde how many solid feet that whole piece containeth .

Adde the Numbers belonging to the length , breadth , and dep●h together , and from that Addition substract ever this Number 33625. and the remainder lookt , sheweth how many foot that whole peece containeth .

The number belonging to 17. fo. 8. in . ¼ . the length is . 29289 To the breadth 18195 To the depth 16335 together 63819 Substract ever 33625 so rest 30194
to which answers 21. fo. 9. in . ½ . to be therein contained .

For Stone .

Suppose a Stone to be long 5 fo. 7. in . ½ . broad 2. fo. 1. ¼ . in . and deep 1. fo. 3. in . ½ . and it is required to finde how many solid feet that stone containeth . To the length is 24314 To the breadth 20043 To the depth 17924 together 62281 Substract 33625 so rest 28656
to which answers 15. fo. 3. in . 1/● . to be therein contained .

And after the same manner the length being 4. fo. the breadth 18. inches , and the depth 16. there is found that whole stone to containe just 8. sollid foot .

To measure round Timber called girt measure .

This is also to be done a wayes , either by finding how much in length shall make a sollid foot , or to finde how many sollid foot the whole tree containeth ; Gird your tree about neare the middle thereof , and suppose you finde it to be 35. inches about , and you desire to finde how much in length shall make a sollid foot .

Take the number belonging to the circomference , and double it ever , which double substract from 61431. alwayes the remaynder being lookt , sheweth how much in length shall make a sollid foot , which by so working is found to be 1. fo. 5. ¾ . inches .

And after the same manner , a tree being 2 fo. 7. inches about , there shall be found 1. fo. 10 ½ . inches in length to make a sollid foot .

To finde how much the whole Tree containeth .

Suppose your tree neere the middle to be about 48. inches , and long 14. fo. and it is required to finde how many sollid foot that whole tree containeth .

Set downe alwayes twice the number belonging to the circumference , and under it the number belonging to the length , and under that ever this number 55381. then adde all together , and cast away alwaies the first figure thereof next your left hand , the rest lookt sheweth how many sollid ●o . the whole tree containeth .

Example .

It is 4. fo. about , and the number thereunto belonging is . 27833 which I set down again . 22833 to 14 fo. ●he length belongs 28274 and ever this number . ●5381 fa. ●●●●●
to which answers 17 fo. 9. ¾ . inches , and so many sollid foot that whole tree containeth , 〈◊〉 like manner worke for all other .

The use of a scale of Fractions , invented by John Speidell , Mathematitian , in Queen street .

THE scale containeth 120. equall partes , being numbred on the left hand by 4. 8. 12. to 120. and on the right hand by 1. 2. 3. to 20. whose uses follow .

Addition in Fractions .

Let it be required to adde ⅕ . and ⅙ . together : Take from the bottome the distance to ⅕ . and setting one foot in ⅙ . turne the other foot ever upwards , and it endeth now in 11/30. or you may take ⅙ . first , and then setting one foot in ⅕ . turne the other ever upwards , and it endeth also in 11/30. and so is found that ⅕ . and ⅙ . being added together doe make 11/30. of the whole .

In like manner ⅓ . and ¼ . of any thing being added together doe make 7/12. of the same thing , be it of an ell , a yard , a shilling , or a pound , &c.

Againe , let it be required to adde ⅔ . and ¼ . together ; if now you take ⅔ . from the bottom , and with that distance setting one foot in ¾ . and turne the other foot upwards , as before taught , you shall finde it to goe beyond your scale .

Therefore take only the distance between ⅔ , or ¾ . one of your Fractions given , and the top 120. and with that distance setting 1. foot in the other Fraction , turne downwards , and to what it sheweth adde ever 1. whole unite , as if you take the distance between ¼ . and the top of your scale 120. and with the same distance setting one foot in ⅔ . the other Fraction , turne downwards , and it endeth now in 5/12. to which adde 1. whole unite , so is it 1 ●/12. and so is found that ●/● . and ¼ . being added together doe make 1 ●/1● . the thing required .

And after the same manner 4/● . and ⅚ . being added together doe make 1 19/●0 and 7/● . and ●/● being added together doe make 1 1●/24. parts , &c.

Substraction in Fractions .

Let it be required to take ⅖ . from ½ . and to finde what part of the whole is left .

Take only with your compasses the difference between ●/● . and ½ . your 2. Fraction given , and that distance applyed from the bottome , sheweth 1/10. and so is found that 2/● . of any thing being taken from the 1/● . of the same thing , there shall remaine 1/10 ; . of the same thing .

And in like manner , if you take ⅙ . from 3/● . there shall remaine 13/10. and 2/● . being taken from ⅞ . there shall remaine ●/●4 . and ●/5. from ⅚ . leaveth 1●/●● . &c.

Multiplication in Fractions .

Multiplication and Fraction of Fractions , is one and the same thing ; for it is all one question to say multiply ½ . by ●/● . or what is the 1/● . of 3/● . or the 3/● . of 1/● ? this is all one and the same demand , to doe this by your scale of Fractions .

Looke out ⅗ . on your scale , and against it on your left hand stands 72. whereof take ½ . that is 36. which looke also amongst the Numbers on your left hand , and by it stands ●/10. and so is found that ⅗ . being multiplyed by ●/● . or the 1/● . of ●/● . is ●/10. of the whole unite .

And after the same manner , ●/● . of ●/4. is ½ . of the whole , for against ●/● . stands 80. whereof ●/4. is 60. against which 60. stands 1/● .

In like manner , if ⅘ . be given to be multiplyed by ●/● . the product will be found to be ●/1● . and 7/● . being given to be multiplyed by ⅖ . the product will be 7/20. &c.

Division in Fractions .

Let it be required to divide ●/5. by ½ .

Against 3/● . stands 72. and against 1/● . stands 60. now so often as 60 is in 72. which is once , and 1/● . so often is ●/● . in ●/● . &c.

Againe , divide 4/● . by ●/● . against ⅘ . stands 96. and against ●/● . stands 40. now so often as 40. is in 96. which is two times , and ●/● . so often is ●/● . in ⅘ . &c.

Againe , divide ●/● . by ⅚ . against ●/● . stands 72. and against ⅚ . stands 100. Now 100. cannot be had in 72. set it therefor thus , 72/1●0 . parts , or being abreviated by 4. it is 18/25. parts , and so is found that ●/5. being divided by ⅚ . the Quotient is 18/25. &c.

After the same manner 2/● . being given to be divided by ●/4. the Quotient will be ●0/●0 . or abreviated by 10. it will be 8/9. &c.

To finde the value of a Fraction in shillings and pence .

Let it be required to finde how many shillings and pence the ⅝ of a pound is : Looke out ⅝ . on your scale , and among the Numbers on your right hand stands 12. below the ⅝ . and 13. above it , that is to say the ⅝ . of a pound is more then 12 shillings , and lesse then 13 shillings ; now right against 12 shillings stands ⅗ . count therefore in the small parts upwards , from ⅗ . to ⅝ . how many of them it is , and you find 3. which are two pences , so the 3. make ● pence , which put to the 12 shillings , so is it 12 shillings and 6 pence , and so is found that the ⅝ . of 20 shillings , or a pound , is 12 shillings and 6 pence .

Againe , let be required to finde how much the 2/● . of a pound is .

Looke ⅓ . and the Number next under it on your right hand is 13. which stands against 13/20. then count the small parts form thence upwards to ⅓ . which are 2. that is 2. two pences , which is 4 pence , so is found that ⅔ . of a l. is 13. s. 4. d. and after the same manner ⅚ . of a pound , is found to bee 16. s. 8. d. and ⅞ . to be 17. s. 6. d. &c.

FINIS .

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