A Treatise on Infinitesimal Calculus ... |
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Page 5
... plane superficies ; and is an element of a plane area bounded by any lines in the plane of xy . Thus the whole area will be the integral of these infinitesimal area - elements . If no limits of the area are given , the problem is ...
... plane superficies ; and is an element of a plane area bounded by any lines in the plane of xy . Thus the whole area will be the integral of these infinitesimal area - elements . If no limits of the area are given , the problem is ...
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 geometry , reserving the more complex problems of space ...
... 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 geometry , reserving the more complex problems of space ...
Page 198
... plane curves . Ex . 1. The circle ; see fig . 3 . Let the centre be the origin ; and let the arc APμ , whose length is required , begin at A , and be measured from A towards B ; so that , if APS , Oм = x , x decreases as s increases ...
... plane curves . Ex . 1. The circle ; see fig . 3 . Let the centre be the origin ; and let the arc APμ , whose length is required , begin at A , and be measured from A towards B ; so that , if APS , Oм = x , x decreases as s increases ...
Page 208
... ) ( 47 ) 0 = x cos a ― y sin a — ƒ ” ( a ) ; . where f represents an arbitrary function ; and hence we 208 [ 160 . RECTIFICATION OF PLANE CURVES . General character of rectifiable plane curves developed The explanation of the symbolism.
... ) ( 47 ) 0 = x cos a ― y sin a — ƒ ” ( a ) ; . where f represents an arbitrary function ; and hence we 208 [ 160 . RECTIFICATION OF PLANE CURVES . General character of rectifiable plane curves developed The explanation of the symbolism.
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A Treatise On Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2018 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³