absolute numbers affected algebraic algebraic quantities arithmetical binomial binomial formula coefficient common factor consequently contains contrary signs cube root deduce denote difference divide dividend division entire functions entire number entire polynomials enunciation equa equal equation involving example exponent expression extract formula fraction given number gives greater greatest common divisor greyhound Hence hypothesis infinite number logarithm manner method monomial multiplied necessary negative nomials nth root number of terms obtain perfect square performing positive preceding prime principle problem proposed equation proposed polynomials question quotient radical rational and entire reduced relative divisor remainder resolved result rule second degree second member second term solution square root substituting subtract suppose take the equation tion transformations unity unknown quantities verified whence whole number
Page 26 - 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 14 - ... first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
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.