An Easy Algebra

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University Publishing Company, 1890
 

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Page 101 - In a proportion the antecedents and consequents of the two ratios are respectively the antecedents and consequents of the proportion. The first and fourth terms are called the extremes, and the second and third the means.
Page 21 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, 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 26 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Page 136 - To what is the square of the difference of two quantities equal ? 82. To what is the product of the sum and difference of two quantities equal ? 83. How may the reciprocal of any quantity be expressed ? How may any factor be transferred from one term of a fraction to the other? In what other form may a"1 be written ? a—'
Page 64 - Three methods of elimination are usually given. such numbers as will make the coefficients of one of the unknowns the same in both.
Page 103 - Hence if any three terms of a proportion are given, the fourth may be found. Thus...
Page 108 - Multiply one half the sum of the first and last terms by the number of terms. Thus, the sum of eight terms of the series whose first term is 3 and last term 38 is 8 x * (3 + 38) = 164.
Page 82 - ... the divisor. Multiply the divisor thus increased, by the second term of the root, and subtract the product from the remainder.
Page 35 - ... thing, viz. 12 : so, likewise, 3 multiplied by 4 multiplied by 5 is 60, and will be 60 in whatever order we take them — -3 by 4 by 5, or 4 by 3 by 5, or 5 by 3 by 4 ; when, therefore, we have obtained one denominator, it is sufficient. Hence the usual rule to reduce fractions to a common denominator : Multiply each numerator by all the denominators except its own for new numerators, and all the denominators together for the common denominator. 6. We are now prepared to add two or more fractions...
Page 125 - A purse of eagles is divided among three persons, the first receiving half of them and one more, the second half of the remainder and one more, and the third 6.

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