An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 14
... the dividend is positive , and it must be the reverse of that of the divisor when the dividend is negative ; whence we readily obtain the rule . CH . I. § V. ] 1440 119 DIVISION . 14 [ CH . I. § V. ALGEBRA . Division.
... the dividend is positive , and it must be the reverse of that of the divisor when the dividend is negative ; whence we readily obtain the rule . CH . I. § V. ] 1440 119 DIVISION . 14 [ CH . I. § V. ALGEBRA . Division.
Page 26
... reverse of the preceding process , and cannot therefore change the value of the frac- tion or ratio . 56. The terms of a fraction can often be simplified Greatest Common Divisor . by dividing them by a common 26 [ CH . II . § 1 ...
... reverse of the preceding process , and cannot therefore change the value of the frac- tion or ratio . 56. The terms of a fraction can often be simplified Greatest Common Divisor . by dividing them by a common 26 [ CH . II . § 1 ...
Page 81
... reverse . 134. EXAMPLES . 1. In what case would the value of the unknown quan- tity in example 25 of art . 126 be negative ? why should it be so ? and could the enunciation be corrected for this case ? Ans . When ́ a > b ; that is ...
... reverse . 134. EXAMPLES . 1. In what case would the value of the unknown quan- tity in example 25 of art . 126 be negative ? why should it be so ? and could the enunciation be corrected for this case ? Ans . When ́ a > b ; that is ...
Page 85
... reverse is the case , when the terms are increased instead of being diminished . SECTION IV . Equations of the First Degree containing two or more unknown quantities . 136. In the solution of complicated problems in- volving several ...
... reverse is the case , when the terms are increased instead of being diminished . SECTION IV . Equations of the First Degree containing two or more unknown quantities . 136. In the solution of complicated problems in- volving several ...
Page 144
... reverse order of its terms , gives ( x + a ) " = x2 + n a xn − 1 + ` n ( n - 1 ) a2xn − 2 + & c . 2 whence it appears that The coefficients of two terms which are equally distant , the one from the first term , and the other from the ...
... reverse order of its terms , gives ( x + a ) " = x2 + n a xn − 1 + ` n ( n - 1 ) a2xn − 2 + & c . 2 whence it appears that The coefficients of two terms which are equally distant , the one from the first term , and the other from the ...
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Common terms and phrases
126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence