# A Complete Algebra: For High Schools, Academies and Normal Schools

E.H. Butler & Company, 1895 - Algebra - 344 pages
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### Contents

 Exercises 9 Definitions 16 Algebraic Expressions 21 Equations and Problems 31 Use of the Parentheses 37 Equations and Problems 48 Special Method of Dividing a Binomial by a Binomial 57 General Application 65
 PAGE 161 The Binomial Theorem 167 Square Root of Polynomials 173 Cube Root of Polynomials 179 Theory of Exponents 186 Radicals 196 Rationalization 209 Square Root of a Binomial Surd 215

### Popular passages

Page 61 - 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 60 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Page 56 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 257 - The sum of all the terms. Any three of which being given, the other two may be found.
Page 241 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards ; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.
Page 275 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 93 - To reduce fractions to their lowest terms. A fraction is in its lowest terms when its numerator and denominator are prime to each other; that is, when both terms have no common divisor. 1. Reduce the fraction -|| to its lowest terms.
Page 49 - The Dividend is the quantity to be divided. The Divisor is the quantity by which we divide. The Quotient is the result, •which shows how many times the divisor is contained in the dividend.
Page 253 - 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: 6 = c: d = e :/. Then, by Art.
Page 22 - 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.