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Or, in measuring boards, you nicy nultipiy the length iu feet by the breadth ja incles, and divide by 12, the quotient will give the answer in square feet, &c.

Thus, in the foregoing example, 21x18+12=31,5 as before.

4. If a board be ő inches wide, how much in length will make a square

foot ? RULE.--Divide 144 by the breadth, thus, 8)144

Ans. 18 in. 5. If a piece of land be 5 rods wide, how many rods in length will make an acre ?

RULE. --Divide 160 by the brcult!, and the quotient will be the length required, thus, 5) 100

Ans. 32 rods in lengti. ART. 5. To measure a Triangle. Definition.- A Triangle is any three cernered figure which is bounded by three right lines.*

RULE. Multiply the base of the given triangle into half its perpendicular height, or half the base into the whole perpendicular, and the product will be the area.

EXAMPLES.

1. Required the area of a triangle whose base or longest side is 32 inches, and the perpendicular height 14 inches. 52x7=224 square inches, the Answer.

2. There is a triangular or threc cornered lot of land whose basc or longest side is 51 ) rods; the perpendicular from the corner opposite the base, measures 44 rods; how many acres doth it contain ?

51,5 x 22=1155 square rods, acres, 13 rods. *A Triangle anuy le either right anglıl or oblique ; in either case the teacher can easily give the scholar a right idea of the base and perpendicular, by anarking it dou'n on a slate, naper, goc

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TO MEASURE A CIRCLE. ART. 4. The diameter of a Circle being given, to find the Circumference.

RULE. As 7 : is to 22 : : so is the given diameter : to the circumference. Or, more exactly, As 113 : is to 355 • : &c. the diameter is found inversely.

Note. The diameter is a right line drawn across the circle through its centre.

EXAMPLES. 1. What is the circumference of a wheel whose diam. eter is 4 feet?-As 1 : 22 : : 4 : 19,57 the circumfe rence.

2. What is the circumference of a circle whescaliane. ter is 55 !-As 7 : 22 : : 55 : 110 Ins.--! intersely as 22 : 7 :: 110 : 55, the diameter, &c. Art. 5. To finil the area of a Circhi.

RULE. Multiply half the diameter by half the circumference, and the product is the area ; or if the diameter is given without the circumference, multiply the square of the diameter by ,7854 and the product will be the area.

EXAMPLES. 1. Required the area of a circle whose diameter is 12 jnches, and circunference 57,7 inches.

18,85=half the circumference.

6--half the diameter.

113,10 area in square

inches. 2. Required the area of a circular garden whose diame. ter is 11 rods.

854 By the second method, 11X11 191

Ans. 95,0354 rods. SUCTION 2. OF SOLIDS. Solids are estimated by the solid inch, solid fant, &r. 1728 of these inches, that is 12x12x12 make 1 cb Or solid foot.

ART. 6. To measure a Cube. Definition.A cube is a solid of six equal sides, each of which is an exact square.

RULE. Multiply the side by itself, and that product same side, and this last product will be the solid content of the cube.

EXAMPLES.

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1. The side of a cubic block being 18 inches, or 1 foot and 6 inches, how many solid inches doth it contain: ft. in. ft.

1 6=1,5 and 1,5X1,5X1,5=3,575 solid feet, Sus. Or, 18x18x18=5832 sulid inches, audi=3,375.

2. Suppose a cellar to be dug that shall contain 12 feet every way, in length, breadth and depth; how many solid feet of earth must be taken out to complete the saine?

12x12x19=1728 solid seet, Ilie Ansier. Art. 7. To find the content of any regular solid of three

dimensions, length, breadth and thickness, as a piece of timber squared, whose length is more than the breadth and depth.

RULE. Multiply the breadth by the depth or thicknes, and that product by the length, which gives the solid content.

EXAMPLES.

1. A square piece of timber, beings i firet 6 inches, or 18 inches broad, 9 inches thick, and 9 fert er 108 inches long; how many solid feet doth it contain:

1 ft. 6 in.=1,5 foot. 9 inches

,75 foot.

Prod. 1,125x9==10,125 solide finiti ?r.

irl, in. in. solid in. Or, 18X9X108=17496-:-1728=10,125 fect.

But, in measuring timber, you may multiply the breadth in inches, and the depth in inches, and that product by the length in feet, and divide the last product by 11-4, which will give the solid content in fcet, &c.

2. A piece of timber being 16 inches broad, 11 ischer thick, and 20 feet long, to find the centent?

Breadth 16 inches.
Depth 11
Prod. 176x20=3520 then, 5520-144=24,4 feet,

the Answer. 5. A piece of timber 15 inches broad, 8 inches thick, and 25 feet long; hoiy many solid fect doth it contain ?

Sns. 20,3+feet. Akr. S. When the breadth and thickness of a piece of

timber are given in inches, to find how much in length will make a solid foot.

NULE. Divide 1728 by the product of the breadth and depth, and the quotient will be the length making a sulid foot.

EXAMPIES.

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1. If a piece of timber be 11 inches broad and 8 inches deep, how many inches in length will make a solid foot ?

11x8=88)1728(19,6 inches, ins. 2. If a piece of timber be 18 inches broad and 14 inches deep, how many inches in length will make a solid foot: 18x19=252 livisor, then 252) 1728(6,8 inches, Ans.

ART. 9. To measure a Cylinder. Definition.--A Cylinder is aaround body whose bases are circles, like a round column or stick of timber, of equal biyness from end to end.

RULE. Multiply tie square of the diameter of the end by ,7854 which gives the area of the base; then multiply the area of the orse by the length, and the product will be the solid content.

EXAMPLE.

What is the solid content of a round stick of timber of equal bigness from end to end, whose diameter is 18 il.. clics, and length 20 feet?

18 in.=1,5 st.

X1,5

Square 2,25 x 1854 = 1,76715 area of the base.

7.90 length.

Ans. 35,54309 solid content. Or, 18 inches.

13 inches.

324 X,7934.054,4696 inches, area of the basc.

20 length in feet.

EXAMPLE.

1915030,2090/85,543 solid feet, ans. ST. 10. Tolia bom many soli fcet a round stick of

cimber, equally thick frou end to end, will contain when hewn square.

RULE. :Iultiply twice the square of its seini-diameter in ines by the length in feet, then divide the product by 144,

the quotient will be the answer. Tithe diameter of a round stick of timber be 22 inches 2 lits length 20 feet, how many solid feet will it contain

n hewn square: 11x11x2X20-=-111=35,0+ feet, the solidity when y? square. T. 11. To find how many ieetui saurre enged boards fa given thickness, can be syn from a leg of a given iameter.

RULE. Find the solid content of the long when made square, be the last article. The sur, As the thickness of the nud including the sa calf is to the solid feet : : so is C(inches) to the number of feet of bouds.

How many feet of square edged boards, 14 inch thick,

cluding the saw calf, can be sawn from a log 20 feet og and 24 inches diameter ?

12x12x2x20---144=40 feet, solid content.

As 11 : 40 : : 12 : 584 feet, the Airs,

EXAMPLE

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