An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 2
... negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting 2 from 7 ...
... negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting 2 from 7 ...
Page 6
... negative terms . - When the first term is not preceded by any sign it is to be regarded as positive . 20. The following rule for reducing polynomials , which contain similar terms , is too obvious to require demonstration . Find the sum ...
... negative terms . - When the first term is not preceded by any sign it is to be regarded as positive . 20. The following rule for reducing polynomials , which contain similar terms , is too obvious to require demonstration . Find the sum ...
Page 8
... negative terms ; then A -B is the quantity to be subtracted , and let C denote the quantity from which it is to be taken . If A alone be taken from C , the remainder C - A is as much too small as the quantity subtracted is too large ...
... negative terms ; then A -B is the quantity to be subtracted , and let C denote the quantity from which it is to be taken . If A alone be taken from C , the remainder C - A is as much too small as the quantity subtracted is too large ...
Page 11
... negative terms - C and D ; but the negative terms of the product , as – BC and — AD , are obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two ...
... negative terms - C and D ; but the negative terms of the product , as – BC and — AD , are obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two ...
Page 13
... negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is , as in examples 18 and 19 , equal to the ...
... negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is , as in examples 18 and 19 , equal to the ...
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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