An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 65
... Solution of Equations of the First Degree , with one unknown quantity . 120. Theorem . Every equation of the first de gree , with one unknown quantity , can be reduced to the form Ax + B = 0 ; in which A and B denote any known ...
... Solution of Equations of the First Degree , with one unknown quantity . 120. Theorem . Every equation of the first de gree , with one unknown quantity , can be reduced to the form Ax + B = 0 ; in which A and B denote any known ...
Page 75
... solution of a problem gives zero for the value of either of the unknown quantities , this value is sometimes a true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is ...
... solution of a problem gives zero for the value of either of the unknown quantities , this value is sometimes a true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is ...
Page 76
... solution . 3. In what cases would the value of one of the unknown quantities in example 38 of art . 126 become zero ? and what would this value signify ? Ans . When either a = c , or b = c ; and , in either case , these equations ...
... solution . 3. In what cases would the value of one of the unknown quantities in example 38 of art . 126 become zero ? and what would this value signify ? Ans . When either a = c , or b = c ; and , in either case , these equations ...
Page 81
... solution of a problem gives a negative value to either of the unknown quantities , this value is not generally a true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is ...
... solution of a problem gives a negative value to either of the unknown quantities , this value is not generally a true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is ...
Page 87
... Solution . Having reduced the equation to the form Ax + By + Cz + & c . + M = 0 , find , as in art . 137 , the value of either of the unknown quantities , as z , for instance , which is , by art . 121 , x By - Cz - & c . - M A , and any ...
... Solution . Having reduced the equation to the form Ax + By + Cz + & c . + M = 0 , find , as in art . 137 , the value of either of the unknown quantities , as z , for instance , which is , by art . 121 , x By - Cz - & c . - M A , and any ...
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Common terms and phrases
126 become zero 3d root arithmetical mean arithmetical progression Binomial Theorem 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 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