Algebra for Colleges and Schools

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Macmillan, 1897 - 516 páginas

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Página 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Página 262 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Página 349 - The logarithm of a product is the sum of the logarithms of its factors.
Página 350 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Página 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Página 287 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 326 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Página 320 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Página 288 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...

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