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added addition affected algebraic apply arranged becomes binomial called coefficients combinations composed consequently considered contains contrary corresponding cube deduce demonstration denominator denote determine difference divide dividend division entire enunciation equal equation involving evidently example exponent expression extract factor figures follows formula fourth fraction function given gives greater greatest common divisor Hence hypothesis independent indicated known less letters logarithm manner means method monomial multiplied necessary negative observe obtain operation particular performing polynomial positive preceding prime principle problem progression proposed equation question quotient radical rational reasoning reduced reference relation relative remainder remark represent resolution resolved respect result root rule satisfy second degree second term simple solution square square root substituting subtract suppose taken third tion transformations units unity unknown quantities whence whole
Σελίδα 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...
Σελίδα 306 - 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.
Σελίδα 121 - 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.
Σελίδα 71 - 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.
Σελίδα 135 - 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.
Σελίδα 239 - ... is equal to the sum of the products of the roots taken three and three ; and so on.