# 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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Page viii - 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 65 - 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 302 - 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 117 - 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 67 - 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 131 - 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 235 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Page 199 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.