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

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### Common terms and phrases

added algebraic applied arithmetical assumed balls becomes binomial called changed coëfficients common complete consists containing corresponding cube root decimal denominator denotes derived determine difference distance 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 known least less letters logarithm manner means method miles minus monomial Multiply negative obtained operation perfect perform permutations places polynomial positive PRACTICE preceding principle problem progression proportion prove question quotient radical ratio Reduce remainder represent required to find result RULE second degree side solution solved square root substituting subtracted suppose taken term theorem third tion transformed travels true units unknown quantity variations Whence whole zero

### Popular passages

Page 140 - 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 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 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 317 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 204 - The conception of a force acting directly as the quantity of matter, and inversely as the square of the distance...

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 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.

Page 45 - Now, if this remainder is divisible by a—b, it is obvious that the dividend is divisible by a — b; that is, if the difference of the same powers of two quantities is divisible by the difference of the quantities, then will the difference of the powers of the next higher degree be divisible by that difference.

Page 90 - How many days did he work, and how many days was he idle?