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algebraic algebraic quantity annuity arithmetical progression Binomial Theorem coefficients complete equation completing the square converging fraction cube root cubic equation denotes dividend division equa equation whose roots evident EXAMPLES FOR PRACTICE exponent expressed extract the cube extracting the square Find the cube Find the greatest find the number Find the square Find the sum find the value following Rule geometrical geometrical progression given equation given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply number of balls number of permutations number of terms obtained operation perfect square polynomial positive root principle proposed equation quotient ratio real roots Reduce remainder Required the numbers required to find result second degree second term solution solved square root Sturm's theorem substituting subtract theorem third tion transformed transposing unknown quantity Whence whole number zero
Pàgina 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Pàgina 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Pàgina 128 - 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.
Pàgina 43 - 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.
Pàgina 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Pàgina 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Pàgina 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Pàgina 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...