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added affected algebraic apply approximating arithmetical arrangements becomes binomial called changing co-efficient consequently considered contain contrary corresponding cube root decimal denominator denote determine difference divide dividend division entire enunciation equal equation example exponent expression extract factors figure formula four fourth fraction given gives greater greatest common divisor hence indicated involving known least less letters logarithm manner method monomial multiplied necessary negative observe obtain operation performed polynomial positive preceding principle problem progression proportion proposed question quotient radical raise ratio Reduce reference remainder represent resolved respect result rule satisfy second degree second term similar square root substituted subtract suppose taken tens term third tion transformed true units unity unknown quantity whence whole number write
Side 277 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Side 348 - 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.
Side 33 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Side 111 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Side 298 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Side 204 - 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.
Side 182 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Side 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.