Or, in moasuring boards, you may multiply the length in feet by the breadth in inches, and divide by 12, the quotient will give square feet, &c. Thus, in the foregoing example, 21x18-12-31,5 as before. 4. If a boarıl be 8 inches wide, how much in leagth will make a square foot: Rule.- Divide 144 by the breadth, thus, 8)144 Ans. 18 ine 5. If a piece of land be 5 rods wide, how many rods in length will make an acre? . Rule-Divide 160 by the breadth, and the quotient will be the length required, thus, 5) 160 Ans. 32 rods in length. ART. 3. To measure a Triangle. Definition.--A Triangle is any three cornered 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. 32x7=224 square inches, the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 51} rods; the perpendicular trom the corner opposite the base measures 44 rods; how niany acres doth it contain: 51,5 x 22=1133 square rods,=7 acres, 13 ruds. *A Triangle may be either right angled or oblique ; in either case the teacher can easily give the scholar a right idea of the base and perpendicular, by marking it doun on a slatk, paper, &c. 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 in As 7 : 22 :: 4 : 12,57 the circumfe. rence. 2. What is the circumference of a circle whose diame Ler is 35 mAs 7 : 22 : : 55 : 110 Ans..and inversely as 22 : 7 : : 110 : 35, the diameter, &c. ART. 5. To find the area of a Circle. RULE. Multiply half the diameter by half the circumference, and the product is the area ; or if the diameter is giver without the circumference, multipy 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 inchos, and circumference 37,7 inches. 18,85=half the circumference. 6=half the diameter. 115,10 area in square inches. 2. Required the area of a circular garden whose diame fer is 11 rods? ,7854 By the second method, 11x11 = 121 Ans. 95,0334 rods. SECTION 2. OF SULIDS. Solids are estimated by the solid inch, solid foot, &c 128 of these inches, that is 12x12x12 make 1 eubic solid foot. ART. 6. To measure a Cabe. 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 by the same side, and this last product will be the solid content of the cube. LXAMPIES. . 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. Ans. Or, 18x18x18=5832 solid inches, and 44=3,375 2. Suppose a cellar to be dug that shall contain 12 feet erery way, in length, breadth and depth ; how many solid feet of earth inust be taken out to complete the same ? 12x12x12=1728 solid feet, the Ans. 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 thickness, and that product by the length, which gives the solid content. EXAMPLES. 1. A square piece of timber, being one foot 6 inches, or 18 inches broad, 9 inches thick, and 9 feet or 108 inches iong; how many solid feet doth it contain ? I ft. 6 in=1,5 foot. 9 inches ,75 foot. Prod. 1,125x9=10,125 solid feet, the Ans. in. in. in solid in. But, in measuring timber, you may multiply the breadlth in inches, and the depth in inches, and that product by the length in feet, and divide the last product by. 141, which will give the solid content m feet, &c. 2. A piece of timber being 16 inches broad, 11 inches thick, and 20 feet long, to find the content ? Breadth 16 inches. Prod. 176x20=3520 then, 5520-144=24,4 feet, the Answer. 3. A piece of timber 15 inches broad, 8 inches thick, and 25 feet long; how many solid feet doth it contain ? Ans. 20,8+feet. ART. 8. 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. RULE. Divide 1728 by the product of the breadth and depth, and the quotient will be the length making a solid foot. a a EXAMPLES. a 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, Ans. 2. If a piece of timber be 18 inches broad and 14 inches deep, how many inches in length will make a solid foot ? 18x11=252 divisor, then 252)1728(6,8 inches, Ans ART. 9. To measure a Cylinder. Definition.-A Cylinder is a round body whose bases are circles, a round column or stick of tiinber, of equal bigness from end to end. RULE. Multiply the square of the diameter of the end by 37854 which gives the area of the base; then multiply the area of the base 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 biyness from end to end, whose diameter is 1& inches, and length 20 feet? Square 2,25X,7854-1,76715 area of the bass, x 20 length Ans. 35,34300 solid content. Or, 18 inches. 18 inches. 324 X,7854=254,4696 inches, area of the base. £0 length in feet. hewn square: 144)5089,3920(35,343 solid feet. Ans. ART. 10. To find how many solid feet a round stick of timber, equally thick fruin end to end, will contain when hewn square. RULE. Multiply twice the square of its semi-diameter'in nches by the length in feet, then divide the product by 144, and the quotient will be the answer. EXAMPLE. 'If the diameter of a round stick of timber be 22 inches and its length 20 feet, how many solid feet will it contain when hewn square ? 11x11x2x206144=33,6+ feet, the solidity when Art. 11. To find how many feet of square edged boards of a given thickness, can be sawn from a log of a given diameter. RULE. Find the solid content of the log, when made snuare, by the last article-Then say, As the thickness of the buard including the saw calf : is to the solid feet : : so is 12 (inches) to the number of feet of boards. llow many feet of square edged boards, 14 inch thick, including the saw call, can be sawn from a log 20 feet long and 24 inches diameter ? 12x12x2x20+144=40 feet, solid content. As 11': 40 : : 18 : 384 feet, the EXAMPLE. |