14 months; and they gained $100: what is each man's share? Ans. A's $26,47+B's 39,21,5+C's 34,31,3+. 112. C's note for $635,75, was given July 4th, 1826, on which the following payments have been made, viz: $120,25 1. January 1st, 1827, 2. March 10th, do. What was due July 4th, 1828? 200, Ans. $366,93,5. 113. From six hundred and four dollars two cents, take four hundred and nine dollars and six mills. Ans. $195,01,4. 114. How much, in dollars and cents, will 475 yards of cloth come to, at 2 shillings per yard? Ans. $158,33,3+ 115. A person willing to distribute some money among a number of beggars, wanted 8 cents to give them 3 cents each; he therefore gave 2 cents each, and had 3 left: how many beggars were there? Ans. 11. 116. B buys of C a hogshead of coffee, weighing gross 9cwt. 2qr. tare 12lb. pcr cwt. what will it amount to at 23 cents per lb. Ans. $218,50. PROBLEMS. PROB. 1. The circumference of a circle given, to find the diameter. As 355 is to 113:: so is the circumference to the diameter. 1. If the circumference of the earth be 24913 miles, what is the diameter? Ans. 7930+ miles. 2. If the circumference of a wheel be 15 feet, what is its diameter? Ans. 4ft. 9,295 inches. 3. If the circumference of the earth's orbit be 596,902,100 miles, how far are we from the sun? Ans 95,000,000 miles, nearly. PROB. 2. The diameter of a circle given, to find the circumference. As 113 is to 355, :: so is the diameter to the circumference. 1. If the diameter of the earth be 7930 miles, what is the circumference? Ans. 24913 miles, nearly. 2. If the diameter of a wheel be 4 feet, what is its circumference? Ans. 12ft. 6,796 inches. 3. If the earth is 95,000,000 miles from the sun, what is the circumference of its orbit? Ans. 596,902,100+ miles. PROB. 3. The area of a circle given, to find the diameter. As 355 is to 452 :: so is the area to the square of the diameter:-or, multiply the square root of the area by 1,12837 and the product will be the diameter. 1. What is the diameter of a circular piece of ground, which contains one acre? Ans. 14,27+po. 2. What is the diameter of a circle whose area is 5460ft? Ans. 83,37ft.-+ PROB. 4. The area of a circle given, to find the circumference. As 113 is to 1420 so is the area to the square of the circumference:-or, multiply the square root of the area by 3,5419, and the product is the circumference. 1. When the area is 160, what is the circumference? Ans. 44,84. 2. When the area is 625, what is the circumference? Ans. 88,62.+ 3. What length of fence must be made round a circular field to inclose just 10 acres? Ans. 141,79+rods. PROB. 5. The diameter of a circle given, to find the area. Multiply the square of the diameter by ,7854. 1. What is the area of a circle whose diameter is 623? Ans. 304836,5+. 2. How many acres in a circular island, whose diameter is 124 rods? Ans. 75 acres, 76 rods. PROB. 6. To find the convex surface of a cylinder. Multiply the length into the circumference of the base. 1. What is the convex surface of a stick of timber, 5 feet in length, and 7 inches in diameter? Ans. 1320 inches. PROB. 7. To find the solidity of a cylinder. Find the area of the base, (by Prob. 5,) which multiply into the length. . 1. What is the solid contents of a round stick of timber, whose diameter is 18 inches, and length 20 feet? Ans. 35,343ft. PROB. S. To find the solidity of a sphere or globe. 1. What is the solidity of a sphere whose diameter is 12 Ans. 901,7808 inches. inches? Compound Addition Promiscuous Questions in do. 27 Extraction of the Square Root $6 28 Demonstration of do. Compound Subtraction 98 100 |