An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 8
... increasing C - A by the excess of A above A - B , that is , by B , and it is thus found to be C- A + B. The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B . Hence , To ...
... increasing C - A by the excess of A above A - B , that is , by B , and it is thus found to be C- A + B. The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B . Hence , To ...
Page 23
... increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal to an - 1 , which gives the peculiar result an n α ...
... increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal to an - 1 , which gives the peculiar result an n α ...
Page 51
... increased he took away the fourth part , and put again in its stead $ 70 . He then counted his money , and found $ 120 . What was the original sum ? Method of putting into equations . Let the original sum expressed in dollars . After ...
... increased he took away the fourth part , and put again in its stead $ 70 . He then counted his money , and found $ 120 . What was the original sum ? Method of putting into equations . Let the original sum expressed in dollars . After ...
Page 60
... increased , diminished , multiplied , or divided by the same quan- tity , without destroying the equality . 110. Corollary . If all the terms of an equation have a common factor , this factor may be suppressed . 111. EXAMPLES . 1. If ...
... increased , diminished , multiplied , or divided by the same quan- tity , without destroying the equality . 110. Corollary . If all the terms of an equation have a common factor , this factor may be suppressed . 111. EXAMPLES . 1. If ...
Page 78
... increasing them both by the same quantity . 4. In what case would the denominators of the fractional values of the unknown quantities in example 48 of art . 126 become zero ? and what is the corresponding absurdity of the enunciation ...
... increasing them both by the same quantity . 4. In what case would the denominators of the fractional values of the unknown quantities in example 48 of art . 126 become zero ? and what is the corresponding absurdity of the enunciation ...
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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