Elementary Algebra: Embracing the First Principles of the Science

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A.S. Barnes & Company, 1861 - Algebra - 303 pages
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Page 160 - 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 163 - Since the square or second power of a fraction is obtained by squaring the numerator and denominator separately, it follows that the square root of a fraction will be equal to the square root of the numerator divided by the square root of the denominator.
Page 16 - Similarly, any term may be transposed from one member of an equation to the other by changing its sign.
Page 197 - 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 138 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14JA days, B 17fa, and C 23JT.
Page 255 - BD we have — = -^, (Art. 169) ; and by clearing the equation of fractions, we have BC = AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Page 295 - The crew of a ship consisted of her complement of sailors, and a number of soldiers. There were 22 sailors to every three guns, and 10 over ; also, the whole number of hands was five times the number of soldiers and guns together.
Page 167 - These expressions may often be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square...
Page 76 - To reduce fractions having different denominators to equivalent fractions having a common denominator. RULE. Multiply each numerator into all the denominators except its own, for the new numerators, and all the denominators together for a common denominator.
Page 252 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order. Thus, in the last proportion, A and C are the antecedents, and B and D the consequents.

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