The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.

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Title: The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.
Author: Brown, John, philomath.
Publication: London, :: Printed by W.G. for William Fisher ...,; 1667.
Rights/Permissions: This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. Searching, reading, printing, or downloading EEBO-TCP texts is reserved for the authorized users of these project partner institutions. Permission must be granted for subsequent distribution, in print or electronically, of this text, in whole or in part. Please contact project staff at eebotcp-info@umich.edu for further information or permissions.
Subject terms: Mensuration -- Early works to 1800.; Mathematical instruments -- Early works to 1800.; Navigation -- Early works to 1800.
Cite this Item: "The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A77649.0001.001. University of Michigan Library Digital Collections. Accessed May 8, 2024.

Pages

CHAP. V. The use of the line of numbers in mea∣suring of Solid measure such as Tim∣ber, Stone, or such like Solids.

PROB. 1. By Foot-measure. A peice of ••imber being to be mea∣sured and not just square, how to make it square.

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Divide the Space between the breadth, and the thickness, into two equal parts, and the Compasses shall stay at the side of the Square, equal to the oblong made of that breadth and thickness; which is the mean pro∣portional between them. The breadth being 18, and thickness 6, the side of the Square will be found to be 10, 38.

PROB. 2. Having the side of a square, equal to the base of any Solid given in Foot-measure, to find how much makes a Foot Solid in Foot-measure.

As the side of the square in Foot-measure unto 1, so is 1 to a 4^th num∣ber, and that 4^th to the length. As 2 120 unto 1.000, so 1.000 unto 0, 471, and that to 0. 222. or thus, the extent from 2. 120 to 1, will reach from 1, twice repeated to 0. 222, ••nd so much is the length to make a Foot Solid, (at that squareness.)

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PROB. 3. To find how much in length makes a Foot, any breadth and depth with∣out squaring.

As 1 to the breadth in Foot-mea∣sure, so is the depth to a fourth num∣ber, as that 4^th number to 1 so is 1 to the lenth in Foot-measure.

Example.

As 1 is to 2. 50, so is 1. 80, to 4 50, then as 4. 50 to 1, so is 1 unto o•• 222. the length required.

PROB. 4. Having the side of a square, equal to the Base of a Solid given, and the length thereof in Foot- measure, to find the content in Feet.

As 1 to the side of the square in Foot-measure, so the length in Feet to a fourth number, and that fourth to the content in Foot-measure. The extent from 1 to 2. 12, twice repea∣ted from 15.25, shall reach unto 68.62.

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PROB. 5. Having the length breadth and depth of a Square Solid given in Foot-measure, to find the content in Feet.

As 1 to the breadth in Foot-mea∣sure, so is the depth to the Base in Feet; as 1 to that Base, so the length in Feet to the content in Feet.

As 1 to 2, 50, so 1. 80 to 4. 50, then as one 1 to 4. 50, so is 15.25, unto 68. 625. The content required.

PROB. 6. By Inches, (only) and Feet and Inches. Having the side of a Square, equal to the base of any Solid given in Inches, to find how many Inches in length will make one Foot.

The side of the Square is found as in the first Problem of this Chapter, or by the 7^th of Board measure. Then as the side of the square in Inches to 41, 57, so is one Foot to a 4^th number, and that 4^th to the length in Inches, and tenth parts of an Inch.

The extent from 25, 45 unto 41, 57 twice repeated from 1 will reach to

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2, 67, or more easie if it be squared, as ••he side of the square is to 12, so is 12 to a 4^th and that fourth to the length required. The extent from 25, 45 to 12 being twice repeated from 12, will stay at 2, 667, or more short 267.

PROB. 7. Having the breadth and depth of a squared Solid given in inches, to find the length of a Foot in Feet and Inches.

As 1 to the breadth in Inches, so the depth to a fourth number, which is the content of the base in Inches, then as this 4 number is to 1728, so is 1 to the length of a Foot Solid in Inch measure. As 1 to 21, 6, so is 30 to 648, then as 648 to 1728, so is 1 to 2, 667.

Or again thus.

As 12 to the breadth in Inches, so the depth in Inches to a fourth num∣ber; then as this fourth number is to 144 so 1 to the length of a foot solid; as 12 to 21, 6, so 30 to 54; then as 54

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is to 44, so is 11 unto 2, 667. the length required.

Example.

The side of a square given in inches to find how much is in a foot long. Extend the Compasses from 12 to the Inches square the same extent turned the same way from the Inches square shall shew how much is in a foot long. At 18 inches square in every foot long, is 27 inches, or 2 foot 3 in∣ches: But if the side of the square be given in feet and parts, Say, as 1 to the feet and parts square, so is that to the quantity in 1 foot long, which multiplyed by the feet long gives the whole content.

PROBL. 8. Having the side of the square and the length thereof given in Inch-mea∣measure, to find the content in Feet.

As 41.57, to the side of the square in Inches, so is the length to a fourth Number, and that fourth to the con∣tent in Foot-measure. As 41. 57, to 25. 45, so 183, twice repeated unto 68, 62.

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PROB. 9. Having the side of a Square equal to the base of any solid given in Inch∣measure and the length in Foot-mea∣sure, to find the content in Feet.

As 12 to the side of the square in Inches, so the length in Feet to a fourth Number, and that fourth to the content in Foot-measure. As 12 to 25, 45, so 15. 25 to 32. 55, and 32. 55 to 68. 62. Or the extent from 12 to 25, shall reach to 68. 62, the con∣tent sought.

PROB. 10. Having the length, breadth and depth, of a Squared Solid given in Inches, to find the content in Inches.

As 1 to the breadth in Inches, so the depth to the base, then as 1 to the base, so the length to the content in Inches. As 1 to 21. 6, so 30 to 648. as 1 to 648, so that 183 to 118584.

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PROBL. 11. Having the length, breadth, and depth given in Inches, to find the content in Feet.

As 1 to the breadth in Inches, so the depth in Inches to the base in In∣ches; Then as 1728 to the base, so is the length in Inches to the content in Feet. As 1 to 21, 6, so 30 to 648, as 1728 to 648, so 183 to 68. 62.

Or you may say,

As 12 to 21.6, so 30 to 54, as 144 to 54, so 18, 3 to 68.62.

PROB. 12. Having the breadth and depth of a squared solid given in Inches, and the length in Feet, to find the con∣tent.

As 1 to the breadth in Inches, so the depth in Inches to a fourth number. Then as 144 to that fourth, so is the length in Feet to the content in Feet.

As 1 to 216, so is 30 to 648; then as 144 to 15.25, so is 648 unto 68.62, Or as 144 to 21.6, so 30 to 4. 50: as 1 to 4. 50, so 15.25 to 68.62. Or again,

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As 12 to 21.6, so 30 to 54: then as 12 to 54, so 15.25 to 68.62, the content required.