An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 21
... known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with an exponent ...
... known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with an exponent ...
Page 60
... known quantities or their powers enter otherwise than as factors , it is said to be transcendental ; and the consideration of such equations belongs to the higher branches of mathematics . Thus , ax = b ( x + a ) y + b = c , are ...
... known quantities or their powers enter otherwise than as factors , it is said to be transcendental ; and the consideration of such equations belongs to the higher branches of mathematics . Thus , ax = b ( x + a ) y + b = c , are ...
Page 65
... known quantities , whether positive or negative , and x is the unknown quantity . 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 ...
... known quantities , whether positive or negative , and x is the unknown quantity . 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 ...
Page 66
... known terms to the second member , and all its unknown terms to the first member ; and the value of the un- known quantity is equal to the quotient arising from the division of the second member by the multiplier of the unknown quantity ...
... known terms to the second member , and all its unknown terms to the first member ; and the value of the un- known quantity is equal to the quotient arising from the division of the second member by the multiplier of the unknown quantity ...
Page 78
... known quantity , and that it may have any value whatever . In some cases , however , there are limi- tations to the change of value of the unknown quantity . Cases in which the value of an unknown quantity is 78 [ CH . III . § III ...
... known quantity , and that it may have any value whatever . In some cases , however , there are limi- tations to the change of value of the unknown quantity . Cases in which the value of an unknown quantity is 78 [ CH . III . § III ...
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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