An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 26
... ratio , and its divisor the consequent of the ratio ; and the antecedent and consequent of a ratio are called the terms of the ratio . 55. Theorem . The value of a fraction , or of a ratio , is not changed by multiplying or dividing ...
... ratio , and its divisor the consequent of the ratio ; and the antecedent and consequent of a ratio are called the terms of the ratio . 55. Theorem . The value of a fraction , or of a ratio , is not changed by multiplying or dividing ...
Page 43
... ratios by substituting the term antecedent for numerator , and consequent for denominator . SECTION IV . Proportions . 85. A proportion is the equation formed of two equal ratios . : Thus , if the two ratios A : B and C D are equal ...
... ratios by substituting the term antecedent for numerator , and consequent for denominator . SECTION IV . Proportions . 85. A proportion is the equation formed of two equal ratios . : Thus , if the two ratios A : B and C D are equal ...
Page 44
... ratio to B x D , and are consequently equal , that is , AX DBX C , or the product of the means of a proportion is ... ratios to lower terms , as in art . 40 , A : B = C : D ; that is , A , B , C , D form a proportion . 87. Corollary . If ...
... ratio to B x D , and are consequently equal , that is , AX DBX C , or the product of the means of a proportion is ... ratios to lower terms , as in art . 40 , A : B = C : D ; that is , A , B , C , D form a proportion . 87. Corollary . If ...
Page 46
... ratios is called a continued proportion . Thus , A : B = C : D = E : F , & c . is a continued proportion . 93. Theorem . The sum of any number of ante ... Ratio of Sum of Antecedents to Sum of Consequents . 46 [ CH . II . § IV . ALGEBRA .
... ratios is called a continued proportion . Thus , A : B = C : D = E : F , & c . is a continued proportion . 93. Theorem . The sum of any number of ante ... Ratio of Sum of Antecedents to Sum of Consequents . 46 [ CH . II . § IV . ALGEBRA .
Page 47
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Ratio of Sum of Antecedents to Sum of Consequents . whence A + C + E + & c . B + D + F ... Ratio of Sum of two first Terms to that of CH . II . § IV . ] 47 PROPORTIONS .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Ratio of Sum of Antecedents to Sum of Consequents . whence A + C + E + & c . B + D + F ... Ratio of Sum of two first Terms to that of CH . II . § IV . ] 47 PROPORTIONS .
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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