# First Lessons in Algebra: Embracing the Elements of the Science

A.S. Barnes, 1841 - Algebra - 252 pages
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Page 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 214 - A merchant bought cloth for which he paid £33 15s, which he sold again at £2 8s per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy 1 Ans.
Page 175 - 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 155 - 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 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Page 138 - 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 35 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Page 79 - Ibs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and t.ail together : what was the weight of the fish ? Let 2x = the weight of the body, in pounds.
Page 197 - That the sum of the two roots is equal to the coefficient of x in the second term, taken with a contrary sign. 4th. That the product of the roots is equal to the known term in the second member, taken with a contrary sign. EXAMPLES. 1.
Page 45 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.