An elementary treatise on algebra (Google eBook)

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Chapman and Hall, 1875 - Algebra - 165 pages
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Page 111 - The base of the common system is 10, and, as a logarithm is the exponent of the power to which the base must be raised in order to be equal to a given number, all numbers are to be regarded as powers of 10; hence, 10 = 1, we have logarithm of 1 = 0. 101 = 10, we have logarithm of 10 = 1. 10" = 100, we have logarithm of 100 = 2.
Page 48 - С :D::A ; B, signify the same proportion the only difference being, that the extremes of one expression are the means of the other. Since magnitudes cannot be compared, except they be of the same kind, it is manifest that the first and second terms of a proportion must be of the same kind, as also the third and fourth ; yet the first and third may be of different kinds : eg lOlbs ; 6lbs::l5 ft.
Page 48 - ... whatever of the second and fourth, it is found, that if the multiple of the first be >, =, < that of the second, that of the third is always >, =, < that of the fourth, then these four quantities are proportionals. For, let a, b, c, d...
Page 120 - An infinite series of positive terms is divergent, if, after some particular term, the ratio of each term to the preceding be equal to unity, or greater than unity. In the series ui + HS 4 из + + n 4 -, let the ratio of each term after the fcth be equal to 1.
Page 46 - A ratio is called a ratio of greater inequality, of less inequality, or of equality, according as the antecedent is greater than, less than, or equal to, the consequent.
Page 47 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.
Page 46 - The terms of this fraction are called the terms of the ratio. The first term of a ratio is called the antecedent; the second term, the consequent. Thus, in the ratio of 2 to 3, commonly written 2 : 3, the first term 2 is the antecedent, and the second term 3 is the consequent.
Page 116 - An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be.
Page 130 - Three points are taken at random on the circumference of a circle. Find the probability that they lie in the same semicircle.
Page 152 - Find the sum of the squares of the coefficients in the expansion of (1 + x)", where n is a positive integer.

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