[Page] [Page] 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.

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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

[Page] 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.

[Page] 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 breadth18195
To the depth16335
together63819
Substract ever33625
so rest30194

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 is24314
To the breadth20043
To the depth17924
together62281
Substract33625
so rest28656

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 [Page] 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 belongs28274
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 [Page] 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 [...]/ [...]. [Page] 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.

[Page] 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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By Iohn Speidell in Queen-streete.
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