## Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |

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### Common terms and phrases

added algebraic applied arithmetical assumed balls becomes binomial called changed coëfficients common complete consists containing continued corresponding cube root decimal denominator denotes derived determine difference Divide dividend division divisor equal equation evident EXAMPLES exponent expressed extract the square factors figure Find the square find the value formula four fourth fraction given gives greater Hence increased least less letters logarithm manner means method minus monomial Multiply negative obtained operation perfect performed permutations places polynomial positive PRACTICE preceding principle problem progression proportion prove question quotient radical ratio Reduce remainder REMARK represent required to find result second degree second term side solution solved square root substituting subtract suppose taken term theorem third tion transformed travels true units unknown quantity variations whence whole zero

### Popular passages

Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Page 42 - 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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...

Page 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.

Page 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...

Page 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.