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

### Contents

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### Common terms and phrases

algebraic algebraic quantity arithmetical progression Binomial Theorem coėfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number 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.