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

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### Common terms and phrases

aČ+ab+bČ according added algebraic quantities arithmetical becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root cubic equation DEMONSTRATION difference digits divi divided dividend division equa equal exponent expression extracting the root factors find the values formula fourth given equation greater greatest common divisor greatest common measure Hence integral least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative number of terms observed positive Prob problem proportionals proposed equation quadratic equations 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 solution square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number

### Popular passages

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 498 - 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 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...