A Complete Course in Algebra for Academies and High Schools

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Leach, Shewell & Sanborn, 1885 - Algebra - 349 pages
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Page 164 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Page 211 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 253 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the • proportion a : b = с : d, a and d are the extremes, and b and с the means.
Page 253 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 44 - 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 288 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 105 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Page 256 - 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: b = c: d = e:f.
Page 256 - 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.

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