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according added addition appears arise becomes called changing coefficients common denominator common measure completing compound consequently consisting contains continued demonstrated determined difference divi divided dividend division equal equation evident example exponent expression extracting factors figure find the values formula four fourth fraction Given gives greater greatest common divisor Hence indicated integral involving known least common multiple less letter logarithm lowest magnitudes manner means method miles mixed multiplied necessary negative observed obtained operation partial positive preceding prefixed Prob problem proper proportionals proposed proposition quadratic quan quotient radical ratio Reduce remainder represent result RULE shillings side simple solution square root substituting subtracted suppose surd taken third tion tity transposition travelled units unity unknown quantity values of x whence whole
Page iv - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Page 57 - 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 162 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples...
Page 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 503 - 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 496 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 318 - 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 7 - NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. 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...