The interest of 50 dollars for 6 months, is And, the interest of 1 dol. 50 cts. for 6 months, is 3 $cto 1 50 4 Ans. Rebate, $1 46 2. What is the rebate of 150. for 7 months, at 5 per cent.? Interest of 1507. for 7 months, is £. s. d. 47 6 2 61 Ans. £4 4 11nearly By the above Rule, those who use interest tables in their counting-houses, have only to deduct the interest of the in terest, and the remainder is the discount. A concise Rule to reduce the currencies of the different States, where a dollar is an even number of shillings, to Federal Money. RULE. I.-Bring the given sum into a decimal expression by inspection, (as in Problem I. page 80) then divide the whole by 3 in New-England, and by,4 in New-York currency, and the quotient will be dollars, cents, &c. EXAMPLES. 1. Reduce 541. 8s. 34d. New-England currency, to fo deral money. ,3)54,415 decimally expressed. Ans. $181,38 cts. 2. Reduce 78. 113d. New-England currency, to federal money. 7s. 113d.-£0,399 then,,3),399 Ans $1,33 3. Reduce 5137. 16s. 10d. New-York, &c. currency, to ,4)513,842 decimal. federal money. Ans. $1284,60 4. Reduce 19. 53d. New-York, &c. currency, to Fedeval Money. ,4)0,974 decimal of 19s. 53d. $2,431 Ans. 5. Reduce 647. New-England currency, to Federal Money. ,3)64000 decimal expression. $213,331 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. 6d. New-England currency, to Federal Money. 6×8+2=50 to be annexed. 6)45,50 or 6)4550 $7,583 Ans. 758 cents. 2. Reduce 21. 10s. 9d. New-York, &c. currency, to Federal Money. 9x8+2=74 to be annexed. Then 8)5074 $cts. Or thus, 8)50,74 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 be fore, &c. 3. Reduce 31. 5s. New-England currency, to Federal Morey 31 58-659. Then 6)6500 Ans. 1083 cents. SOME USEFUL RULES, FOR FINDING THE CONTENTS OF SUPERFICES AND SOLIDS. SECTION I.-OF SUPERFICES. The superfices or area of any plane surface, is compo sed or made up of squares, either greater or less, 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, 12 × 12=144 the square inches in a superficial 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 ? 20×20=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, 26×26—676 sq. rods, and 676÷160=4 a 36 r. the Answer. ART. 2. To measure a parallelogram, 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 feet long, and 54 wide; how many square feet of ground are contained in it? Ans. 96×54-5184 square feet. 2. A lot of land, in form of a long square, is 120 rods in ength, and 60 rods wide; how many acres are in it? 120 × 60=7200 sq. rods, then 200-45 acres. Ans. 3. If a board or plank be 21 feet long, and 18 inche broad ; how many square feet are contained in it? 18 inches 1,5 feet, then, 21 × 1,5=31,5. Ans. Or, in measuring boards, you may multiply the length in feet by the breadth in inches, and divide by 12, the quotient will give the answer in square feet, &c. Thus, in the foregoing example, 21×18÷12=31,5 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? 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. 32×7=224 square inches the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 514 rods; the perpendicular from the corner opposite the base measures 44 rods; how many acres doth it contain? 51,5×22=1133 square rods,=7 acres, 13 rods. * 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 perpendicu fas, by marking it down on the slate, 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 circum ference. 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 diameter is 4 feet?-as 7: 22:: 4 : 12,57 the circumference. 2. What is the circumference of a circle whose diameter is 35?-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 cir cumference, 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 diame ter is 11 rods? ,7854 By the second method, 11 x11 = 121 Ans. 95,0334 rods SECTION 2.-OF SOLIDS. Solids are estimated by the solid inch, solid foot, &c. 1728 of these inches, that is, 12 × 12 × 12 make 1 cubic or solid foot. |