An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 15
... exponent 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.
... exponent 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
... 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 in the ...
... 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 in the ...
Page 20
... zero , and the larger the absolute value of the expo- nent the lower the power . Thus a5x - 6 - a4x - 3 + a3 + a - 1x + a - 2x2 , a − 2x2 , is arranged according to the ascending powers of x , and according to the descending powers of ...
... zero , and the larger the absolute value of the expo- nent the lower the power . Thus a5x - 6 - a4x - 3 + a3 + a - 1x + a - 2x2 , a − 2x2 , is arranged according to the ascending powers of x , and according to the descending powers of ...
Page 33
... zero , and the last divisor 2x + 3 a is the greatest common divisor . - 2. Find the greatest common divisor of 21 a3 b x7 21 a4 b x6 - 168 a7 b x3 and 14 a2 b3 c x4 14 a3 b3 c x3 + 28 a4 b3 c x2 . -42 a5 b3 c x 140 a6 b3 c ...
... zero , and the last divisor 2x + 3 a is the greatest common divisor . - 2. Find the greatest common divisor of 21 a3 b x7 21 a4 b x6 - 168 a7 b x3 and 14 a2 b3 c x4 14 a3 b3 c x3 + 28 a4 b3 c x2 . -42 a5 b3 c x 140 a6 b3 c ...
Page 63
... zero in the other member ; and the polynomial thus formed may be reduced to its simplest form , by arts . 20 and 110 . Equations reduced to their simplest forms . 119. EXAMPLES . CH . III . § II . ] 63 REDUCTION OF EQUATIONS .
... zero in the other member ; and the polynomial thus formed may be reduced to its simplest form , by arts . 20 and 110 . Equations reduced to their simplest forms . 119. EXAMPLES . CH . III . § II . ] 63 REDUCTION OF EQUATIONS .
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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