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

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absolute numbers acº affected algebraic quantities arithmetical binomial coefficients common factor consequently contains contrary signs cube root deduce denominator denote difference divide dividend division entire functions entire number entire polynomials enunciation equa equal equation involving evidently example formula fraction given number gives greater greatest common divisor Hence highest exponent hypothesis indeterminate infinite number logarithm manner mial monomial multiplicand multiplied necessary negative number of terms obtain ounces perfect square positive preceding prime primitive equation principle problem proposed equation proposed polynomials quotient radical rational and entire reduced relative divisor remainder resolved result rule satisfy second degree second member second term solution square root substituting subtract suppose third tion total number transformations trinomial units expressed unity unknown quantities verified whence whole number

### 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.