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

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

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### Contents

 Factoring 66 To Factor Trinomials 74 Highest Common Divisor 82 Lowest Common Multiple 88 Keduction of Fractions 95 Clearing Equations of Fractions 102 Multiplication of Fractions 109 Complex Fractions 116 SIMPLE EQUATIONS 122 Simple Equations containing Two Unknown Quantities 139 Literal Simultaneous Equations 147 Equations containing Three or More Unknown Quantities 155 PAGE 161
 Equations in Quadratic Form 228 Problems producing Affected Quadratics 231 Theory of Quadratic Equations 246 RATIO AND PROPORTION 252 Additional Theorems 259 Table of Formulas 266 Infinite Series 272 LOGARITHMS 279 Table of Common Logarithms 285 Exponential Equations 291 Zero and Infinity 297 Indeterminate Equations 303 ANSWERS 311

### 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.