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affected algebraic quantities arithmetical arithmetical progression becomes binomial binomial theorem called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent figure find the values formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner merator method monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect power perfect square permutations preceding problem progression proposed equation quan quotient radical sign Reduce remainder required to find resolved result rule second degree second member second term simplest form square root substituted subtract suppose take the equation third tion transformed units unity unknown quantity whence whole number
Page 275 - 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 346 - 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 31 - 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 109 - 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 296 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Page 202 - 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 180 - 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 25 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.