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 146 - 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 169 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Page 42 - ... 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 183 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 47 - The exponent of x in the second term is 1, and increases by 1 in each succeeding term.
Page 34 - Division, in Algebra, is the process of finding one of two factors, when their product and the other factor are given.
Page 228 - If any number of quantities are proportional, 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 Now ab = ab (1) and by Theorem I.
Page 225 - 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 3 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Page 42 - 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.

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