An Elementary Treatise on Algebra, Theoretical and Practical ...

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J. & H.G. Langley, 1838 - Algebra - 391 pages
 

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Page 382 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Page 375 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Page 148 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 386 - THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to CF.
Page 380 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 188 - 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 375 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...
Page 390 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
Page 173 - A farmer parting with his stock, sells to one person 9 horses and 7 cows for 300 dollars: and to another, at the same prices, C horses and 13 cows for the same sum.
Page 98 - Any term may be transposed from one side of an equation to the other by changing its sign.

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