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

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according added addition algebraic answer appears arise becomes calculation called changing the signs coefficient common denominator completing compound consequently consisting contains continued cube root DEMONSTRATION determined difference divided dividend division equa equal equation evident example exponent expression extracting fact factors figures find the values formula four fourth fraction give Given greater greatest common divisor Hence indices infinite integral involving known least common multiple less letter magnitudes manner means measure method miles multiplied necessary negative observed obtained operation positive preceding Prob problem proper proportion question quotient ratio Reduce remainder represent respect result RULE shillings side simple equations solution square root substituting subtraction suppose surd taken third tion transposition travelled 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 146 - Find the value of one of the unknown quantities, in terms of the other and known quantities...

Page 336 - 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 341 - 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 339 - 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 340 - 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 31 - 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 329 - 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 335 - 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 331 - 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...