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An Elementary Treatise on Algebra, Theoretical and Practical: Adapted to the ...
No preview available - 2017
a-Ha a-Hb according added adfected algebraic quantities arithmetical becomes binomial changing the signs coefficient completing the square compound quantities consequently cube root cubic equation DEMONSTRATION denoted difference digits divided dividend division equa equal exponent expressed extracting the root factors find the values formula fourth given equation greater greatest common divisor Hence improper fraction integral involving least common multiple less letter logarithm lowest terms lues manner method miles mixed quantity multiplied number of terms observed operation positive PRob problem PROP proportion proposed equation quadratic equation quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations square root substituting subtraction THEOR third tion tities transposition unity unknown quantity whence whole number
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 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...