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abstract numbers abstract products algebraic arithmetic means arithmetic series axioms base coefficients commensurable number commensurable power concrete number concrete product cube root decimal denominator diagonal difference dividend division dollars entire function entire numbers exponent expression figures find the number find the value four geometric progression geometric series groups harmonic mean harmonic series highest common measure incommensurable integer power larger letter of arrangement logarithm lowest common multiple lowest terms mantissa monomial multiplicand negative number number of combinations number of permutations operator polynomial positive integer positive number prime factors prime numbers principle PROB probability proof of theor proper fraction proportion Prove q things quadratic equation quadratic surd QUESTIONS quotient radical reciprocal relation remainder result Show simple equations simple fraction square root subtract taken theorem third trial divisor type-form unit unknown elements variables wherein write yards zero
54 ページ - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
246 ページ - IV. PERMUTATIONS AND COMBINATIONS. § 1. DEFINITIONS. THE different orders in which several things or elements can be put, are their permutations or arrangements; the different groups that can be made of them, without regard to order, are their combinations. Two permutations are different when either the things themselves are different or their order of arrangement is different ; but two combinations are different only when at least one of the things contained in one of them is not found in the other....
144 ページ - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
73 ページ - A shepherd being asked how many sheep he had in his flock, said, if I had as many more, half as many more, and 7 sheep and a half, I should have just 500; how many had he?
81 ページ - Divide the number 90 into 4 such parts, that the . first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal.
232 ページ - The logarithm of a product is the sum of the logarithms of the factors. 10™ 2. —— =10™~r. The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor. 3. (10"')r = 10"'.
144 ページ - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
81 ページ - B engage in play ; in the first game A wins as much as he had and four shillings more, and finds he has twice as much as B ; in the second game B wins half as much as he had at first and one shilling more, and then it appears he has three times as much as A : what sum had each at first...
89 ページ - C are three towns forming a triangle. A man has to walk from one to the next, ride thence to the next, and drive thence to his starting point. He can walk, ride, and drive a mile in a, b, c minutes respectively.