A Treatise on Algebra: For the Use of Schools and Colleges

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Appleton, 1849 - Algebra - 336 pages

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Page 181 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 80 - 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 180 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 50 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 118 - 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.
Page 140 - Divide the first term of the remainder by three times the square of the root already found, and write the quotient for the next term of the root.
Page 242 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a
Page 176 - The quantities which are compared together are called the terms of the proportion. The first and last terms are called the two extremes, and the second and third terms, the two means.
Page 104 - ... multiply each numerator by all the denominators, except its own, for a new numerator, and under it write the common denominator.
Page 187 - That is, the last term is equal to the first term, plus the product of the common difference by the number of terms less one.

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