An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 14
... the 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.
... the 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.
Page 16
... 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 divisor is greater than its exponent m in the dividend , the exponent m ...
... 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 divisor is greater than its exponent m in the dividend , the exponent m ...
Page 46
... whence B2AX C ; B = √ A x C ; that is , the mean proportional between two quantities is the square root of their product . 92. A succession of several equal ratios is called a continued proportion . Thus , A : B = C : D = E : F , & c ...
... whence B2AX C ; B = √ A x C ; that is , the mean proportional between two quantities is the square root of their product . 92. A succession of several equal ratios is called a continued proportion . Thus , A : B = C : D = E : F , & c ...
Page 47
... whence A + C + E + & c . B + D + F + & c . A C E = M = & c . B D F 94. Corollary . Either antecedent may be repeat- ed any number of times in the above sum , provided its consequent is also repeated the same number of times . 95 ...
... whence A + C + E + & c . B + D + F + & c . A C E = M = & c . B D F 94. Corollary . Either antecedent may be repeat- ed any number of times in the above sum , provided its consequent is also repeated the same number of times . 95 ...
Page 52
... whence , by art . 88 , distance gone by 1st courier = 3 ( x + 8 ) . The distance gone by the second courier is obtained from the proportion whence 3 : x = 221 distance gone by 2d courier ; distance gone by 2d courier - 15 x . But as ...
... whence , by art . 88 , distance gone by 1st courier = 3 ( x + 8 ) . The distance gone by the second courier is obtained from the proportion whence 3 : x = 221 distance gone by 2d courier ; distance gone by 2d courier - 15 x . But as ...
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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