# New University Algebra

Ivison, Blakeman, Taylor & Company, 1875 - Algebra - 412 pages
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### Contents

 REDUCTION OF COMPLEX FORMS 81 TRANSFORMATION OF EQUATIONS 85 31 93 PROBLEMS 94 44 102 TWO UNKNOWN QUANTITIES 103 THREE OR MORE UNKNOWN QUANTITIES 112 52 117 PROBLEMS 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 64 175 SECTION IV 182 66 186 SUBTRACTION OF RADICALS 189
 DISCUSSION OF THE FOUR FORMS 250 PROBLEMS PRODUCING QUADRATIC EQUATIONS 258 SECTION VI 265 PROBLEMS IN PROPORTION 274 EXAMPLES OF PERMUTATIONS AND COMBINATIONS 283 THE TEN CASES 290 PROBLEMS 298 DECOMPOSITION OF RATIONAL FRACTIONS 306 APPLICATION OF THE BINOMIAL FORMULA 313 DEVELOPMENT OF SURD ROOTS INTO SERIES 320 REVERSION OF SERIES 328 DIFFERENTIAL METHOD 336 LOGARITHMS 343 79 353 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 167 - 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 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 176 - ... 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 167 - 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 141 - But the relations of these quantities will not be changed, if we suppose the path of motion to be a curve, instead of a straight line. The above formula will therefore apply to the hands of a clock moving around the dial-plate, or to the planets moving in the circle of the heavens. It will thus afford a direct solution to the following problems : 1. The hour and minute hands of a clock are together at 12 o'clock ; when are they next together ? The circumference of the dial-plate is divided into 12...
Page 36 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.
Page 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Page 36 - 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 264 - 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 266 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.