An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
From inside the book
Results 1-5 of 23
Page 26
... Proof . For dividing both these terms by a quantity is the same as striking out a factor common to the two terms of a quotient , which , as is evident from art . 35 , does not affect the value of the quotient . Also multiplying both ...
... Proof . For dividing both these terms by a quantity is the same as striking out a factor common to the two terms of a quotient , which , as is evident from art . 35 , does not affect the value of the quotient . Also multiplying both ...
Page 63
... Proof . For suppressing it in the member in which it at first occurs is the same as subtracting it from that member ; and annexing it to the other member with its sign reversed is , by art . 26 , subtracting it from the other member ...
... Proof . For suppressing it in the member in which it at first occurs is the same as subtracting it from that member ; and annexing it to the other member with its sign reversed is , by art . 26 , subtracting it from the other member ...
Page 65
... Proof . When an equation of the first degree with one unknown quantity is reduced , as in art . 118 , its first mem- ber is composed of two classes of terms , one of which con- tains the unknown quantity , and the other does not . If ...
... Proof . When an equation of the first degree with one unknown quantity is reduced , as in art . 118 , its first mem- ber is composed of two classes of terms , one of which con- tains the unknown quantity , and the other does not . If ...
Page 87
... Proof . When an equation of the first degree is reduced , as in art . 118 , the aggregate of all its known terms may be denoted by M. Each of the other terms must have one of the unknown quantities as a factor ; and , by art . 106 ...
... Proof . When an equation of the first degree is reduced , as in art . 118 , the aggregate of all its known terms may be denoted by M. Each of the other terms must have one of the unknown quantities as a factor ; and , by art . 106 ...
Page 110
... Proof . Since the equation A + Bx + Cx2 + D x3 + & c . = 0 is true for every value which can be given to x , it must be true when we make x = 0 ; in which case all the terms of the first member vanish ex- cept the first , and we have A ...
... Proof . Since the equation A + Bx + Cx2 + D x3 + & c . = 0 is true for every value which can be given to x , it must be true when we make x = 0 ; in which case all the terms of the first member vanish ex- cept the first , and we have A ...
Other editions - View all
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