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By the Sliding rule.

Set 1 on B to 20 on A, then against 32 on B, is 640, the area of the greater bafe on A.

Set 1 on B to 6 on A, then against 10 on B is 60, the area of the leffer bafe or end on A.

Set 1 on B to 60 on A, then against 640 on B is 38400, the product of the two areas on A.

1Set 60 on C to 60 on D, then against 640 on C is 195.959, (a mean proportional between the greater and leffer areas,) on D, which being added to the two areas, the sum is 895.959, one third is 298.653 a mean area.

Set 144 on B to 298.653 on A, then against 18 feet the length on B is 37.3 feet the content on A, true way.

Common way.

Half the fum of the breadths is 21, which is the breadth in the middle, and half the fum of the thickneffes is 13, which is the thickness in the middle.

Set 1 on B to 13 on A, then against 21 on B is 273, the area of the middle bafe.

Set 144 on B to 273 on A, then against 18 feet, the length on B, is 34.1 feet the content on A, common way. By the Scale and Compaffes.

Extend the compaffes from 1 to 20, that extent will reach from 32 to 640, the area of the greater base. Then extend from 1 to 6, that extent will reach from 10 to 60 the area of the leffer bafe. Extend from 1 to 60, that extent will reach from 640 to 38400, the product of the two areas: Find the fquare root thereof by dividing the space between 1 and 38400 into two equal parts, fo you will find the middle point at 195.959, the root fought; or divide the space between 60, the area of the leffer base, and 640, the area of the greater bafe, into two equal parts, you will find the middle point at 195.959 as before, which is a mean proportional between the greater and lesser areas: Then add the mean proportional and two areas together, and the fum is 895.959; one third of which 298.653 a mean area. Laftly, extend from 144 to 298.653, that extent will reach from 18 feet, the length, to 37.3 feet, the content, by the true method.

Common method.

Half the fum of the breadths is 21, which is the breadth in the middle; and half the fum of the thickneffes is 13, which is the thickness in the middle: Extend from 1 to

H

13, that extent will reach from 21 to 273, the area of the middle bafe: Then, extend from 144 to 273, that extent will reach from 18 feet, the length, to 34.1 feet the con tent, by the common method.

Ex. 2. What is the content of a piece of timber that is 18 feet long, the greater end being 18 by 15 inches, and the leffer end 15 by 12 inches.

Content true way

28.711575F. Ans.

Content common way 28.6171873F. Ans.

Explanation and ufe of the following Table.

In the columns of quarter girts, or fides of squares, find the quarter girt, or fide of your fquare log or piece of timber; and oppofite thereto, in the column under Areas reduced to cubick feet, you will find the area of the end or bafe in fquare feet, &c. or the folid content of one foot in length, both in feet and decimal parts, and feet, inches, parts, &c. This content for one foot in length, being mul tiplied by any other length or number of feet, will produce the content for that length or number of feet; which the examples following the Table will illuftrate.

A TABLE.

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A TABLE of the Areas of Squares, or the Contents of Square Prifms, reduced to Cubick feet and parts, both in Decimals and Duodecimals, for all quarter girts, or fides of fquares from 3 to 30 inches, and for the length of 1 foot.

Areas reduced to cubick

feet.

Decimals. Duodecimals.
0.0625

0 0 90 O

3 0.073351 0 0 10 6 9 0.085069 0 1

girt,or side of sqr.

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10

9 230

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0.097656 0 1

209

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0.1111110

44.0.1254340 4 0.1406250

1

400

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1

609

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A TABLE of the Content of Prisms, &c. Continued.

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4445

girt, or

side

of sqr.

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24/

244

4.253906 4 3 0 69

25

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19

2.506944/2

6

100

25

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Required the folid content of a log that is 21 feet long, and 21 inches the fide of the fquare, or quarter girt.

The operation by Table.

For fide of the fquare or quarter girt 21 inches,

Decimally.

the content for one foot is

3.0625F.

Multiplied by the length,

21

30625

61250

The content required is 64.3125F,

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