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

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### Common terms and phrases

a-Ha a-Hb according added adfected algebraic quantities arithmetical becomes binomial changing the signs coefficient completing the square compound quantities consequently cube root difference digits dividend division equa equal exponent expression extracting the root extracting the square factors find the values formula fourth given equation greater greatest common divisor Hence improper fraction least common multiple less lesser letter logarithm lowest terms lues magnitudes manner mixed quantity multiplied negative number of terms observed positive Prob problem proportion proposed equation quadratic equation quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the number Required the square required to find result rules second equation shillings side simple equations solution square root substituting subtraction surd third tion tities transposition travelled unity unknown quantity values of z whence whole number yards

### 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 150 - Find the value of one of the unknown quantities, in terms of the other and known quantities...

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 355 - 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 353 - 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 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 35 - 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 343 - 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 349 - 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 345 - 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...