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affected algebraic quantities arithmetical arithmetical progression arrangements binomial binomial theorem called co-efficient common difference consequently continued fraction contrary signs cube root decimal deduced divide dividend division entire number enunciation equa equal equation involving equation x2 example exponent factors figure find the values formula fourth given equation given number gives greater greatest common divisor hence last term least common multiple less logarithm manner merator method monomial multiply nth root number of terms number of variations obtain operation ounces perfect square permutations positive roots preceding problem progression proposed equation quan quotient radical sign real roots Reduce remainder required to find resolved result satisfy second degree second member second term simplest form square root substituted subtract superior limit suppose supposition take the equation taken third tion total number transformed transposing unity unknown quantity whence whole number
Page 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.
Page 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.
Page 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.
Page 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.
Page 298 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Page 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.
Page 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.
Page 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.