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

Ivison, Phinney, Blakeman & Company, 1868
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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 142 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 Radical Equations 212
 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 41 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
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.
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 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 266 - ... quantities are said to be in continued proportion, and any one of them is a mean proportional between the two adjacent ones. Thus, if a...
Page 401 - VARIATIONS of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of variations of the signs, p the number of permanences ; we shall have m=n+p. Moreover, let n' denote the number of positive roots, and p' the number...
Page 300 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 84 - A Literal Equation is one in which some or all of the known quantities are represented by letters.
Page 343 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.