# Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the Cadets of the U. S. Military Academy, Volume 1

E. B. Clayton, 1831 - Algebra - 389 pages

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### Contents

 INTRODUCTION 1 Of Algebraic Operations 8 96 14 Rule for Multiplication 17 unknown quantity 45 45 104 62 Resolution of Problems and Equations of the Second 104 114 111
 CHAPTER IV Formation of Powers and Ertraction of Roots 163 156 174 160 180 ties 200 189 218 198 233 Resolution of JNumerical Equations involving 328

### Popular passages

Page 12 - In the first operation we meet with a difficulty in dividing the two polynomials, because the first term of the dividend is not exactly divisible by the first term of the divisor. But if we observe that the co-efficient 4...
Page 79 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Page 316 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. 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 to , the number of permanences.
Page 131 - There are other problems of the same kind, which lead to equations of a degree superior to the second, and yet they may be resolved by the aid of equations of the first and second degrees, by introducing unknown auxiliaries.
Page 81 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 145 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Page 249 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Page 213 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.