5)120,000 800 killed. 600 taken prisoners. James gave to John 6 dollars, which was of all the money he had ; how much had be? You sell a watch for 18 dollars, which was 4 of what it cost you ; how much do you make by the bargain? Ans. 44 dollars.. How inuch did he give for it? Ans. 131 dollars. In the above sum, what would 3 thirds of what it east him be? Ans. As is a whole, to sell it for of what it cost him, is to sell it for what it cost. What does 4 thirds of what it cost mean? Ans. more than cost. In the above sum, is of 18=44 now, how much are 4 thirds? Ans. 4 times 41, i. e. 18. How much more than the whole is 4 of 18? Ans. 42. If he had sold his watch for 30 dollars, which was of what it cost him, how much would he have made? Ans. 12 dollars. How prove this? Ans. must be 6, i. e. 30 divided by 5, if is 30; and as is a whole, is equal to 3 times 6-18-of course he gained 12 dollars, or 4, which is equal to 12 dollars. A inan sold a horse for 4 fifths of what it cost him; did he gain or lose, and how much? A man sold a horse for 20 dollars, which was 10 fifths of what it cost him; did he make or lose, and how much? You give away 2 dollars, which is of all the money you have ; how much money have you? If of a yard of cloth is worth 2 dollars, how much is a whole yard worth, How much is worth? You buy a cow for 20 dollars, and sell her for of what she cost you; do you make or lose, and how A man wishing to purchase a horse, refused to give 24 dollars, the price asked; but to make a little display of his knowledge of fractions, said he would give of 24 dollars, on hearing of which the seller immediately told him it was a bargain, now which knew the most about fractions, the buyer or seller, and how much does the purchase price differ from what was asked? John says that he had as lief have of 20 apples, as to have 40 apples ; does John know much about fractions? How do you know that? John says again that he had as lief have 4 and 1 of 1 of 12 oranges, as to have 5; how near right is he now? How much is $ and } of ? Ans. 4. How prove this? Ans. 4 of fis ; and } multiplied by 2 is , and makes 8=. . INVOLUTION. What is the continual multiplication of any number into itself, called? Ans. Involution. What afe the several products called? Ans, Pow. ers. .. What is the number denoting the height of the power called? Ans. Index, or exponent. What is the second power called? Ans. A square. What is the fourth power called? Ans. A biquadrate. What is the fifth power called? Ans. A sursolid. What is a factor ? Ans. Either the multiplicand multiplier or both. How many times do you multiply any number into itself? Ans. Till it is taken as a factor as many times as there are units in the index of the required power. What is the square of 4? Ans. 16. How many times was 4 used as a factor? Ans. As many times as there are units in the exponent or index. How many units are there? 16. What is the sursolid or fifth power of 2? Ans. 32, Why is Land or Square Measure so called? Ans. Give an example? Ans. 144 is the square of 12 inches. What is 304 square yards the second power of ? Ans. 51. Why is Solid or Cubic Measure so called? Ans. Because the several denominations are powers, or cubes. Give an example-Ans. 1728 is the third power or cube of 12 inches. A father gave his son a piece of land 30 rods long and 15 rods wide ; but told him if he would tell how many rods would make a square, one side of which was to be the length of what he had already given him, he should have the lot, what must his answer be? Ans. 900 rods, A man bought a square piece of land for a build. ing spot, and by measurement one side was found to be 20 feet in length; how many rods did it contain? Ans. 400 feet. A piece of land is 60 rods square, how many rods does it contain? Ans. 3600. A Captain has in each rank and file 20 men, how many are there in the company. In your instructor's school-room, which is exactly square, 10 pupils may be accommodated on each side ; how many may be accommodated in the room. What are the solid contents of a pile of wood 6 feet in length, breadth and depth? Ans. 216 feet. What is the power to which 6 feet was raised, called? Ans. A cube. A boy, having purchased ten marbles, was told, that if he would tell how many it would take to fill a square box, so wide that ten marbles would lie in a row in the bottom, he should have the box filled with marbles; the boy got them, now, let us see if you would have gotten them by your answer, and how many did he get over and above what he had purchased for his mathematical knowledge. A farmer says to his son, our potatoes this year are all of a size, now (as you have cyphered considerably) if you will tell me how many bushels, allowing 200 to the bushel, our little square bin will hold, as you see that 20 lie along on the bottom in a straight line, you may go a fishing one half a day through the summer; the boy gave a correct answer, now I demand how many the bin held, and how many days the boy had to himself. John found a square piece of gold, which measured on each side 2 inches; and was offered 60 dollars for every solid inch it contained, how much was the lump worth at that rate? EVOLUTION Remark--As the design of this work is to embrace merely that portion of arithmetic, which is indispensible to the ordinary transactions of business; therefore the common rules, for the extraction of roots will be omitted. A few examples only will be - given, sufficient to initiate ihe pupil into the principles of their operations. By taking on trial a number, which is supposed will nearly make the given number, when multiplied • into itself continually; most sums which are of a practical cast may be generally answered in this way by one or two operations. What is Evolution? Ans. T'he opposite of Involution. Define it more particularly? Ans. It is finding what number multiplied into itself continually, as in Involution, will make the given sum or power. What is the number so found, called? Ans. The root. What are roots which cannot be perfectly evolved without leaving indefinite fractions, called? Ans. Irrational, or surd roots. What are those which can? Ans. Rational roots. What is a root? Ans. It is that number which by a continual multiplication into itself produces the given power. What is Evolution then? Ans. It is finding a root. |