# New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications, for Colleges and High Schools

Ivison, Phinney & Company, 1863 - Algebra - 420 pages
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### Contents

 Reduction 66 Addition 74 Reduction of Complex Forms 81 SIMPLE EQUATIONS 83 Reduction of Simple Equations 89 Two Unknown Quantities 103 Three or more Unknown Quantities 118 General Solution of Problems 124 Discussion of Problems 130 Interpretation of Anomalous Forms 136 Inequalities 145 SECTION III 151 Powers of Polynomials 157 Square Root of Polynomials 164 Cube Root of Polynomials 172 SECTION IV 182 Subtraction of Radicals 189 General Theory of Exponents 197 Properties of Quadratic Surds 204
 Problems in Proportion 274 Examples of Permutations and Combinations 283 The Ten Cases 290 Problems 298 Decomposition of Rational Fractions 306 The Residual Formula 308 Method of Substitution 317 Expansion of Fractions into Series 323 Summation of Infinite Series 331 Interpolation 340 The Common System 346 Use of Tables 353 SECTION VIII 359 Commensurable Roots 370 Equal Roots 376 Detached Coefficients 388 Surd and Imaginary Roots 398 SECTION IX 405 Horners Method of Approximation 416

### Popular passages

Page 209 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Page 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
Page 178 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Page 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Page 77 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Page 266 - 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 169 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.