An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 6
... corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + a b2 - 8 c is the same as 8 a2 b — 2 c . 21 . EXAMPLES . 1. Reduce the polynomial 10 a1 + 3 a1 + 6 aa — a1 — 5 a to its simplest ...
... corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + a b2 - 8 c is the same as 8 a2 b — 2 c . 21 . EXAMPLES . 1. Reduce the polynomial 10 a1 + 3 a1 + 6 aa — a1 — 5 a to its simplest ...
Page 10
... corresponding term , the number of times which it occurs as a factor in the product must be equal to the sum of the exponents . Hence every letter which is contained in any of the given factors must be written in the product , with an ...
... corresponding term , the number of times which it occurs as a factor in the product must be equal to the sum of the exponents . Hence every letter which is contained in any of the given factors must be written in the product , with an ...
Page 28
... corresponding divisor , quantities smaller and small- er are found , which are all divisible by the greatest common divisor , until at length the common divisor itself must be attained . Greatest Common Divisor . The greatest common ...
... corresponding divisor , quantities smaller and small- er are found , which are all divisible by the greatest common divisor , until at length the common divisor itself must be attained . Greatest Common Divisor . The greatest common ...
Page 46
... corresponding consequents , as one antecedent is to its consequent . Demonstration . Denote the value of each of the ratios in the continued proportion of the preceding article by M , and we have MA : B = = C : D E : F , & c .; whence A ...
... corresponding consequents , as one antecedent is to its consequent . Demonstration . Denote the value of each of the ratios in the continued proportion of the preceding article by M , and we have MA : B = = C : D E : F , & c .; whence A ...
Page 77
... corresponding absurdity in the enunciation of the problem ? 1 Ans . When @ = b , and the absurdity is , that , while the couriers are travel- ling at the same rate , it is required to determine the time in which one will overtake the ...
... corresponding absurdity in the enunciation of the problem ? 1 Ans . When @ = b , and the absurdity is , that , while the couriers are travel- ling at the same rate , it is required to determine the time in which one will overtake 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