## Ray's Algebra, Part Second: An Analytical Treatise, Designed for High Schools and Academies, Part 2 |

### Other editions - View all

### Common terms and phrases

ALGEBRAIC QUANTITIES arithmetical progression Binomial Theorem coefficients complete equation Completing the square converging fraction cube root cubic equation decimal denotes dividend divisible equa equal equation whose roots evident 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 formula geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root number of balls number of permutations number of terms obtained operation perfect square polynomial preceding principle proposed equation quotient ratio real roots Reduce remainder Required the number required to find result second degree second term solution solved square root Sturm's theorem substituting subtracted taken third tion transposing unknown quantity Whence whole number zero

### Popular passages

Page 73 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

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 130 - ... 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 130 - 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 29 - 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 173 - 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 25 - 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 18 - 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.

Page 19 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.

Page 118 - ... and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.