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Page 350 - 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 343 - 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 96 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 146 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 342 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Page 348 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 186 - 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 354 - 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 347 - IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth...
Page 41 - 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.