An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 6
... positive terms , and those which are preceded by the sign are called the 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 ...
... positive terms , and those which are preceded by the sign are called the 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 ...
Page 8
... positive terms of the quantity to be subtracted , and B the aggregate of all its 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 ...
... positive terms of the quantity to be subtracted , and B the aggregate of all its 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 ...
Page 11
... positive terms of one factor by A and of the other by B , and those of their negative terms respectively by C and D ... positive terms of this product , AB and CD , are ob- tained from the product of the positive terms A and B , or from ...
... positive terms of one factor by A and of the other by B , and those of their negative terms respectively by C and D ... positive terms of this product , AB and CD , are ob- tained from the product of the positive terms A and B , or from ...
Page 13
... positive , when the number of 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 ...
... positive , when the number of 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 ...
Page 14
... divisor when the dividend is positive , and it must be the reverse of that of the divisor when the dividend is negative ; whence we readily obtain the rule . CH . I. § V. ] 1440 119 DIVISION . 14 [ CH . I. § V. ALGEBRA . Division.
... divisor when the dividend is positive , and it must be the reverse of that of the divisor when the dividend is negative ; whence we readily obtain the rule . CH . I. § V. ] 1440 119 DIVISION . 14 [ CH . I. § V. ALGEBRA . Division.
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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