An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 14
... least exponent , and re- tain it in the other term , giving it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent ...
... least exponent , and re- tain it in the other term , giving it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent ...
Page 27
... least of them , and of their remainder after division . Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the ...
... least of them , and of their remainder after division . Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the ...
Page 37
... least common multiple of given quantities . Solution . When the given quantities are decom- posed into their simplest factors , as is the case with monomials , their least common multiple is readily obtained ; for it is obviously equal ...
... least common multiple of given quantities . Solution . When the given quantities are decom- posed into their simplest factors , as is the case with monomials , their least common multiple is readily obtained ; for it is obviously equal ...
Page 38
... least common multiple of a2 + 2 a b + b2 , a2 + 4 a b + 4 b2 , a2 — b2 , a2 + 3 a b + 2 b2 , a3 + a2 b ------ a b2 - . h3 . Ans . ( a + b ) 2 ( a — b ) ( a + 2 b ) 2 . SECTION II . Addition and Subtraction of Fractions . 73. Problem ...
... least common multiple of a2 + 2 a b + b2 , a2 + 4 a b + 4 b2 , a2 — b2 , a2 + 3 a b + 2 b2 , a3 + a2 b ------ a b2 - . h3 . Ans . ( a + b ) 2 ( a — b ) ( a + 2 b ) 2 . SECTION II . Addition and Subtraction of Fractions . 73. Problem ...
Page 83
... least expensive wine is more than that of the mixture . In either case the problem is altogether impossible , for two wines cannot be mixed together so as to produce a wine more valuable than either of them without a gain , or less ...
... least expensive wine is more than that of the mixture . In either case the problem is altogether impossible , for two wines cannot be mixed together so as to produce a wine more valuable than either of them without a gain , or less ...
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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