A Treatise on Infinitesimal Calculus ... |
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Page xxi
... progression 180. If the terms of a series decrease in magnitude and are alternately positive and negative , the series is con- vergent 235 236 237 240 181. u is convergent or divergent according as the ratio OF CONTENTS . xxi.
... progression 180. If the terms of a series decrease in magnitude and are alternately positive and negative , the series is con- vergent 235 236 237 240 181. u is convergent or divergent according as the ratio OF CONTENTS . xxi.
Page xxii
Bartholomew Price. 181. u is convergent or divergent according as the ratio of Ux + 1 to Ux1 when x = ∞ , is less or greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite ...
Bartholomew Price. 181. u is convergent or divergent according as the ratio of Ux + 1 to Ux1 when x = ∞ , is less or greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite ...
Page xxv
... according to other laws 256. The cubature of a solid of revolution when the generating area is referred to an axis parallel to that of revolution 353 SECTION 2. - Cubature of Solids bounded by any curved Surface . 257. Investigation of ...
... according to other laws 256. The cubature of a solid of revolution when the generating area is referred to an axis parallel to that of revolution 353 SECTION 2. - Cubature of Solids bounded by any curved Surface . 257. Investigation of ...
Page 1
... according to the doctrine of infinitesimals and infinities , which has been established in Vol . I , if relatively to a given base the orders of infinity and of infinitesimal are the same , the sum will be finite ; and as the order of ...
... according to the doctrine of infinitesimals and infinities , which has been established in Vol . I , if relatively to a given base the orders of infinity and of infinitesimal are the same , the sum will be finite ; and as the order of ...
Page 9
... according to the index law which the symbol is subject to , -1 dx Jdx = ( d ) 1 = d - 1dr : dx . ' . S = √ = d1 ; ( 14 ) ( 15 ) and represents an operation which is the reverse of differen- tiation * . Hence also Ja and d are symbols ...
... according to the index law which the symbol is subject to , -1 dx Jdx = ( d ) 1 = d - 1dr : dx . ' . S = √ = d1 ; ( 14 ) ( 15 ) and represents an operation which is the reverse of differen- tiation * . Hence also Ja and d are symbols ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα