A Treatise on Infinitesimal Calculus ... |
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Page xxi
... curve . 166. Determination of the equation of a curve when 8 is a given function of x and y 167 , 168. The intrinsic equation of a curve 210 211 212 214 217 219 SECTION 5. - Involutes of Plane Curves . 169 , 170. Investigation of ...
... curve . 166. Determination of the equation of a curve when 8 is a given function of x and y 167 , 168. The intrinsic equation of a curve 210 211 212 214 217 219 SECTION 5. - Involutes of Plane Curves . 169 , 170. Investigation of ...
Page xxiv
Bartholomew Price. 222. Quadrature of a plane surface contained between two given . curves .. 223. Examples in ... curve , its evolute , and two bounding radii of curvature 316 .. 317 SECTION 3. - Quadrature of Surfaces of Revolution ...
Bartholomew Price. 222. Quadrature of a plane surface contained between two given . curves .. 223. Examples in ... curve , its evolute , and two bounding radii of curvature 316 .. 317 SECTION 3. - Quadrature of Surfaces of Revolution ...
Page 5
... plane of xy referred to the rectangular axes , ox and oy . H is a point ( x ... plane superficies ; and is an element of a plane area bounded by any lines in ... curve is y = f ( x ) . We must find the sum of all the elements , similar to ...
... plane of xy referred to the rectangular axes , ox and oy . H is a point ( x ... plane superficies ; and is an element of a plane area bounded by any lines in ... curve is y = f ( x ) . We must find the sum of all the elements , similar to ...
Page 142
... plane curve represented in fig . 16 ; let OM , X。, OM = x , OM1 = x1 ; MN dx , MP = y = F ( x ) : so that r ' ( x ) dr expresses n ; = dx the area of MPQN , when MN = dx = an infinitesimal . Evidently therefore will curve , the extreme ...
... plane curve represented in fig . 16 ; let OM , X。, OM = x , OM1 = x1 ; MN dx , MP = y = F ( x ) : so that r ' ( x ) dr expresses n ; = dx the area of MPQN , when MN = dx = an infinitesimal . Evidently therefore will curve , the extreme ...
Page 197
... Plane Curves referred to Rect- angular Coordinates . 154. ] IN the present Chapter I propose to consider some of the most simple applications of single integration to questions of ... curve is of the 154 ] 197 RECTIFICATION OF PLANE CURVES .
... Plane Curves referred to Rect- angular Coordinates . 154. ] IN the present Chapter I propose to consider some of the most simple applications of single integration to questions of ... curve is of the 154 ] 197 RECTIFICATION OF PLANE CURVES .
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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