An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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... PROGRESSIONS . SECTION I. Arithmetical Progression . II . Geometrical Progression . · 186 186 195 18 CHAPTER VIII . GENERAL THEORY OF EQUATIONS . SECTION I. Composition of Equations . II . Equal Roots . III . Real Roots . on 201 he 201 ...
... PROGRESSIONS . SECTION I. Arithmetical Progression . II . Geometrical Progression . · 186 186 195 18 CHAPTER VIII . GENERAL THEORY OF EQUATIONS . SECTION I. Composition of Equations . II . Equal Roots . III . Real Roots . on 201 he 201 ...
Page 185
... are they , the difference of whose fourth powers is 65 , and the square of the sum of whose squares is 169 . Ans . 2 , and ± 3 . 16 * 1 To find the last Term . CHAPTER VII . PROGRESSIONS CH . VI . 1. ] EQUATIONS OF THE SECOND DEGREE . 185.
... are they , the difference of whose fourth powers is 65 , and the square of the sum of whose squares is 169 . Ans . 2 , and ± 3 . 16 * 1 To find the last Term . CHAPTER VII . PROGRESSIONS CH . VI . 1. ] EQUATIONS OF THE SECOND DEGREE . 185.
Page 186
... Progression . 244. An Arithmetical Progression , or a progres- sion by differences , is a series of terms or quantities which continually increase or decrease by a constant ... PROGRESSIONS Arithmetical Progression Geometrical Progression.
... Progression . 244. An Arithmetical Progression , or a progres- sion by differences , is a series of terms or quantities which continually increase or decrease by a constant ... PROGRESSIONS Arithmetical Progression Geometrical Progression.
Page 187
... progression when its first term , last term , and number of terms are known . Solution . In this case , a , l , and n are supposed to be known , and S is to be found . To find the Sum of the Progression . Suppose the CH . VII . § 1 ...
... progression when its first term , last term , and number of terms are known . Solution . In this case , a , l , and n are supposed to be known , and S is to be found . To find the Sum of the Progression . Suppose the CH . VII . § 1 ...
Page 188
... Progression . Suppose the terms of the series to be written as follows , first in the regular order , and then in an inverted order : a , b , c , l , k , i , • i , k , l ; · c , b , a . The sum of the terms of each of these progressions ...
... Progression . Suppose the terms of the series to be written as follows , first in the regular order , and then in an inverted order : a , b , c , l , k , i , • i , k , l ; · c , b , a . The sum of the terms of each of these progressions ...
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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