## Elements of Algebra: For Colleges, Schools and Private Students |

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### Common terms and phrases

added addition algebraic apply arithmetical assume balls becomes binomial called changed coefficients common consists contains continued courses cube root decimal denominator derived difference distance divide dividend division divisor Elimination equal equation evident examples Expand exponent expressed factors figure find the value formula four fourth fraction given gives greater greatest Hence hour known less letters logarithms manner means method miles minus monomial Multiply negative obtain operation perform pile places polynomial positive preceding principle problem proportion Proposition prove question quotient radical raised ratio Reduce remainder represent required to find result Rule separated side similar simple solution solved square root Substituting subtracted suppose taken tens term Theorem third tion transposing travels true units unity unknown quantity Whence whole

### Popular passages

Page 152 - 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 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 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 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 325 - The characteristic of the logarithm of any number greater than unity, is one less than the number of integral figures in the given number.

Page 148 - No binomial can be a perfect square; for the square of a monomial is a monomial, and the square of a binomial is a trinomial. Thus...

Page 255 - Given, the first term a, the common difference d, and the number of terms n, to find s, the sum of the series. If we take an arithmetical series, of which the first term is 3, common difference 2, and number of terms 5, it may be written in the following forms : 3, 5, 7, 9, 11, 11, 9, 7, 5, 3.

Page 37 - Since, in multiplying a polynomial by a monomial, we multiply each term of the multiplicand by the multiplier ; therefore, we have the following RULE, FOR DIVIDING A POLYNOMIAL BY A MONOMIAL. Divide each term of the dividend, by the divisor, according to the rule for the division of monomials.

Page 39 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.