An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 15
... of a letter in the dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in the Exponent equal to Zero . Negative Exponents . quotient becomes.
... of a letter in the dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in the Exponent equal to Zero . Negative Exponents . quotient becomes.
Page 16
... becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , amam ao = 1 . 36 38. Corollary . When , in example 6 of art . 30 , the ex- ponent n of a ...
... becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , amam ao = 1 . 36 38. Corollary . When , in example 6 of art . 30 , the ex- ponent n of a ...
Page 23
... becomes equal to an - 1 , which gives the peculiar result an n α = nan - 1 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord- ing to ...
... becomes equal to an - 1 , which gives the peculiar result an n α = nan - 1 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord- ing to ...
Page 33
... become 3 a x7 3 a2 x6 24 a5 x3 . 2 b2 c x4-2 a b2 c x3 + 4 a2 b2 c x2-6 a3 b2 c x - 20 a1 b2 c . The greatest common divisor of these two quantities , found as in the preceding example , is x - 2 a , which , mul- tiplied by the common ...
... become 3 a x7 3 a2 x6 24 a5 x3 . 2 b2 c x4-2 a b2 c x3 + 4 a2 b2 c x2-6 a3 b2 c x - 20 a1 b2 c . The greatest common divisor of these two quantities , found as in the preceding example , is x - 2 a , which , mul- tiplied by the common ...
Page 34
... become and xy - 2 x2 y3 - 3x2 | y2 + 2 x2 y - 3 3 3 + 28 2 + 8x 6 + 9x y3 3 x | y2 . 4 x y + 4x . +2 6 x The suppression of the factor ( x - 3 ) y in the first of these polynomials reduces it to y3-2xy2-3xy + 2x , +2 by which the second ...
... become and xy - 2 x2 y3 - 3x2 | y2 + 2 x2 y - 3 3 3 + 28 2 + 8x 6 + 9x y3 3 x | y2 . 4 x y + 4x . +2 6 x The suppression of the factor ( x - 3 ) y in the first of these polynomials reduces it to y3-2xy2-3xy + 2x , +2 by which the second ...
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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