An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 4
... greater than b ; and the inequality ab denotes that a is less than b ; the greater quantity being always placed at the opening of the sign . 11. An algebraic quantity is any quantity written in algebraic language . 12. An algebraic ...
... greater than b ; and the inequality ab denotes that a is less than b ; the greater quantity being always placed at the opening of the sign . 11. An algebraic quantity is any quantity written in algebraic language . 12. An algebraic ...
Page 6
... greater , may be substituted as a single term for the terms from which it is obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a ...
... greater , may be substituted as a single term for the terms from which it is obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a ...
Page 16
... greater than its exponent m in the dividend , the exponent m - n in the quotient is nega- tive ; and a negative exponent is thus substituted for the usual fractional form of the quotient . Thus , if m is zero , we have a ° : a : = 1 ...
... greater than its exponent m in the dividend , the exponent m - n in the quotient is nega- tive ; and a negative exponent is thus substituted for the usual fractional form of the quotient . Thus , if m is zero , we have a ° : a : = 1 ...
Page 22
... greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true for the 6th , 7th , 8th , & c . powers ; that is , for any positive integral power ...
... greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true for the 6th , 7th , 8th , & c . powers ; that is , for any positive integral power ...
Page 28
... greater than the other ; and must therefore be equal . 60. Problem . To find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of the ...
... greater than the other ; and must therefore be equal . 60. Problem . To find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of 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