4. Reduce 199. 544. New-York, &c currency to Federal Money. ,490 974 decimal of 198. 5 d. $2,431 Ans. 5. Reduce 641. New England currency to Federal Money. ,3)64000 decimal expression. $213,33} Ans. Note.-By the foregoing rule you may carry on the decimal to any degree of exactness ; but in ordinary practice, the following Contraction may be useful. RULE II. To the shillings contained in the given sum, annex 8 times the given pence, increasing the product by 2 ; then divide the whole by the number of shillings contained in a dollar, and the quotient will be cents. EXAMPLES. 1. Reduce 45s. 6. New-England eurrency, to rew eral Money, 6 X8+2 * 50 to be annexed. $ cls. 758 cents.=7,58, 2. Reduce 21. 10s. 9d. New-York, &c. currency to Federal Money. 9X8+274 to be annexed. Then 8)5074 Or thus, 8)50,74 $cts. Ans. 634 cents. = 6 34 $6,34 Ans. N. B. When there are no pence in the given sum, you must annex two.ciphers to the shillings; then divide as before, &c. 3. Reduce 31. 58. New-England currency, to Federal Money 31. 55.658. Then 6)6500 Ans. 1083 SOME USEFUL RULES, TOR FINDING THE CONTEXT'S OF SUPERFICES AND BOLIDS. SECTION 1. OF SUPERFICES. The superfices or area of any plane surface, is conposed or made up of squares, either greater or lesz, according to the different measures by which the dimensions of the figure are taken or measured : and because 12 inches in length make 1 foot of long measure, therefore, 12X12=144, the square inches in the surperficial foot, &c. Art. I. To find the area of a square having equal sides. RULE, Multiply the side of the square into itself and the product will be the area, or content. EXAMPLES. 1. How many square feet of boards are contained in the floor of a room which is 20 feet square ? 20 X 20–400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres, doth it contain? Note.--160 square rods make an acre. Therefore, 26 X26=676 sq. rods, and 676-160=4a, 36r. The Answer. ART. 2. To measure a parallellogram, or long square. RULE. Multiply the length by the breadth, and the product will be the area, or superficial content. EXAMPLES. 1. A certain garden, in form of a long square, is 96 fto long, and 54 wide ; hoiv many square feet of ground arë contained in it? Ans. 96 X 54=5184 square feet. 2. A lot of land, in form of a long square, is 120 rods in length, and 60 iods wide ; how many acres are in it? 120 X 60=7200 sq. rods, then 21812=45 acres. Ans. 3. If a board or plank be 21 feet long, and 18 inches broad how many square feet are contained in it? 18 inches=1,5 feet, then, 21 x 1,5.431,5. Ang Or, in measuring beards, you may multiply the length in feet by the breadth in rches, and divide by 12, the quotient will give the answer ir. square feet, &c. Thus, in the foregoing example, 21 X18-12-1,5 as before. 4. If a board be 8 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 ? ŘULE. -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=221 square inches the Answer. 2. There is a triangular or three cornered lot of land wbose base 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=1133 square rods,=7 acres 13 rods. * A triangle may be either right angled or oblique ; in cither case the teacher can easily give the scholar a a right idea of the base and perpendicular, by marking it down on a slalc, paper, &c. TO MEASURE A CIRCLE. ART. 4. The diameter of a Circle being given, to And the circumference. RULE. 487 : is to 22 : : so is the given diameter : totho circumference. Or, more exactly, As 113 : is to 355 : ; &c. the diameter is found inversely. Note.-The diameter isa right line drawn across the circle through its centre. EXAMPLES. 1. What is the circumference of a wheel whose diameter is 4 feet?-as 7 : 22 : :4: 12,57 the circumference. 2. What is the circumference of a circle whose diayre. ter is 351-As 7 : 22 :: 35 : 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, 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 inches, and circumference 37,7 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 di. ameter is 11 rods ? ,7854 By the second method, 11xil= 121 Ans. 95,0334 rods. SECTION 2. OF SOLIDS. Solids are estimated by the solid inch, solid foot, &Cm 729 of these inches, that is 12X12X12 make 1 cubie or solid foot. ÅRT. 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 by the same side, and this last product will be the solid content of the cube. EXAMPLES. 1. The side of a cubic block being 18 inches, or 1 foot and 6 inches, how many solid inches doth it contain? st. in. ft. 1 6=1,5 and 1,5X1,5X1,5–3,375 solid feet. Ans. Or, 18 X 18 X 18=5832 solid inches, and =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 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 long'; how many solid feet doth it contain ? 1 ft. 6 in=1,5. foot. Prod. 1,125 X 9=10,125 solid feel, the Ans. in. in. in. solid in. Or, 18 X9X108517496_1728=10,125 feet. But, in measuring timber, you may multiply the breadth in inches, and the depth in inches, and that preduct by the length in feet, and divide the last product by 144, which will give the solid content in feet, &c. |