## An Elementary Treatise on Algebra: Theoretical and Practical ... |

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according added addition appears arise becomes calculation called changing the signs coefficient common denominator common measure compound consequently contains continued cube root demonstrated denominator determined difference divided dividend division equal equation evident example exponent expression extracting factors figure find the values formula four fourth fraction give Given greater greatest common divisor Hence indicated integral involving known least common multiple less letter lowest terms magnitudes manner means method miles multiplied necessary negative observed obtained operation performed positive preceding Prob problem proper proportion proposed question quotient radical ratio Reduce remainder represent respect result RULE shillings side simple equations solution square root substituting subtracted suppose surd taken third tion tities transposition travelled units unity unknown quantities values of x whence whole

### Popular passages

Page iv - 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 time therein mentioned." And also to an act, entitled, " an act, supplementary to an act, 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, and extending the benefits thereof...

Page 148 - Find the value of one of the unknown quantities, in terms of the other and known quantities...

Page 338 - 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 - XX. THEOR. IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less...

Page 341 - If the whole be to the whole, as a magnitude taken from the first is to a magnitude taken from the other ; the remainder...

Page 342 - 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 33 - 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 331 - 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, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...

Page 337 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.

Page 333 - 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 whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...