An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 111
... Theorem . If two polynomials : A + B x + Cr2 + Dr3 + E x2 + & c . , A ' + B ' x + C ' x2 + D ' x3 + E ' x2 + & c . are identical , that is , equal , independently of x , it must always be the case that A = A ' , B = B ' , C = C ' , D ...
... Theorem . If two polynomials : A + B x + Cr2 + Dr3 + E x2 + & c . , A ' + B ' x + C ' x2 + D ' x3 + E ' x2 + & c . are identical , that is , equal , independently of x , it must always be the case that A = A ' , B = B ' , C = C ' , D ...
Page 141
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . 3. Solve the equation 2 1 ( 2 x + 13 ) = 3 ( 2 x + 13 ) ... Theorem . Secondly . To find the form in CH . V. § III . ] POWERS OF POLYNOMIALS . 141.
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . 3. Solve the equation 2 1 ( 2 x + 13 ) = 3 ( 2 x + 13 ) ... Theorem . Secondly . To find the form in CH . V. § III . ] POWERS OF POLYNOMIALS . 141.
Page 142
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . Secondly . To find the form in which a enters into the ... Theorem . The combination of these results gives Sir 142 [ CH . v . § III . ALGEBRA ,
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . Secondly . To find the form in which a enters into the ... Theorem . The combination of these results gives Sir 142 [ CH . v . § III . ALGEBRA ,
Page 143
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . The combination of these results gives Sir Isaac Newton's Binomial Theorem . The first term of any power of a binomial is the same power of the ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . The combination of these results gives Sir Isaac Newton's Binomial Theorem . The first term of any power of a binomial is the same power of the ...
Page 144
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . 213. Corollary . If x is changed into -x in the pre- ceding formula , it ... Theorem . ( 2ab - 2c - 4b c2 144 [ CH . v . § III . ALGEBRA .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Binomial Theorem . 213. Corollary . If x is changed into -x in the pre- ceding formula , it ... Theorem . ( 2ab - 2c - 4b c2 144 [ CH . v . § III . ALGEBRA .
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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