Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the Cadets of the U. S. Military Academy, Volume 1 |
Common terms and phrases
a²-b² absolute numbers affected algebraic quantities arithmetical bc² binomial Binomial Formula coefficients common factor consequently contains contrary signs cube root deduce denominator denote determine difference divide dividend division entire functions entire number entire polynomials enunciation equa equation involving example extract final equation formula fraction given number gives greater greatest common divisor Hence hypothesis indeterminate infinite number letter logarithm manner method mial monomial multiplicand multiplied necessary negative nomial nth root number of terms obtain operation perfect square performing positive preceding prime problem proposed equation proposed polynomials question quotient radical rational and entire reduced relative common divisor relative divisor remainder resolved result rule satisfy second degree second member second term solution square root substituting suppose tain third tion transformations trinomial units expressed unity unknown quantities verified whence whole number
Popular passages
Page 2 - 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 67 - 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 304 - 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 119 - 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 69 - 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 133 - 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 237 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Page 201 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.