An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 6
... 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 b2 + 2 a2b + c + ...
... 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 b2 + 2 a2b + c + ...
Page 16
... substituted for the usual fractional form of the quotient . Thus , if m is zero , we have a ° : a : = 1 ÷ an = 1 an In the same way we should have a b2 c3 ÷ a5 b2 c8 d a1 b2 c3 ÷ a5 b2 c8 d1a - 4 c - 5 d - 1 . = Any quotient of ...
... substituted for the usual fractional form of the quotient . Thus , if m is zero , we have a ° : a : = 1 ÷ an = 1 an In the same way we should have a b2 c3 ÷ a5 b2 c8 d a1 b2 c3 ÷ a5 b2 c8 d1a - 4 c - 5 d - 1 . = Any quotient of ...
Page 86
... substituted for the other unknown quantities , and the corresponding value of the chosen unknown quantity is thus obtained . 138. Corollary . An equation which contains sev- eral unknown quantities is not , therefore , sufficient to ...
... substituted for the other unknown quantities , and the corresponding value of the chosen unknown quantity is thus obtained . 138. Corollary . An equation which contains sev- eral unknown quantities is not , therefore , sufficient to ...
Page 87
... substituted for y , z , & c . 142. Problem . To solve several equations with several unknown quantities . First Method of Solution called that of Elimina- tion by Substitution . Find the value of either of the unknown quantities in one ...
... substituted for y , z , & c . 142. Problem . To solve several equations with several unknown quantities . First Method of Solution called that of Elimina- tion by Substitution . Find the value of either of the unknown quantities in one ...
Page 88
... Substitution . The new equations thus formed , together with those in which this unknown quantity does not occur ... substituted in the values of the other quantities , will lead to the determination of the values of all the unknown ...
... Substitution . The new equations thus formed , together with those in which this unknown quantity does not occur ... substituted in the values of the other quantities , will lead to the determination of the values of all the unknown ...
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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