Elements of Algebra: For Colleges, Schools and Private Students |
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Common terms and phrases
2d Bk algebraic ALGEBRAIC QUANTITIES arithmetical progression Binomial Theorem coefficient common divisor Completing the square Corollary cube root decimal degree denotes dividend division equa equal EQUATIONS CONTAINING evident examples exponent expressed extract the cube Extract the square Find the cube find the G.C.D. find the number Find the square Find the sum find the value following Rule formula fourth geometrical progression given number gives greater greatest common divisor Hence less letters logarithms method minus monomial Multiply negative nth root nth term number of balls number of terms order of differences perfect square polynomial preceding proportion Proposition quadratic equation quan quotient ratio Reduce remainder Required the number required to find result second term solved square root Substituting subtracted taken third tion tities transposing unity unknown quantity Whence whole number
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.