Algebra for Schools and Colleges

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Longmans, Green & Company, 1895 - Algebra - 309 pages
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Page 20 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 21 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 217 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 271 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 220 - If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x b с bb Or r
Page 214 - In any proportion, the product of the means equals the product of the extremes.
Page 284 - For the first place can be filled in n ways, the second in n - 1 ways, the third place in n - 2 ways, and the rth place in n - (r - 1) ways.
Page 258 - If the coefficient of any term be multiplied by the exponent of a in that term, and the result divided by the exponent of x in the term increased by 1, the quotient will be the coefficient of the next following term.
Page 82 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

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