A Treatise on Infinitesimal Calculus ... |
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Page 214
... radius vector of E and is denoted by r , and the angle Eoz , at which OE is inclined to oz , = 0. Let a plane be drawn through oz and OE , and let on be the line in which this plane cuts the fundamental plane ; then as these two planes ...
... radius vector of E and is denoted by r , and the angle Eoz , at which OE is inclined to oz , = 0. Let a plane be drawn through oz and OE , and let on be the line in which this plane cuts the fundamental plane ; then as these two planes ...
Page 215
... radius vector OE revolve through an infinitesimal angle de in the meridian plane thus determined , so that E describes the small circular arc EF which = rde ; and finally let the meridian plane revolve through an infinitesimal angle do ...
... radius vector OE revolve through an infinitesimal angle de in the meridian plane thus determined , so that E describes the small circular arc EF which = rde ; and finally let the meridian plane revolve through an infinitesimal angle do ...
Page 232
... radius vector of the point of contact . y2 ( 1+ dy dx ± = 0 ; y y b dx2 dy3 ) = y2 + x2 . ... log ± log == = 0 . ( 2 ) xy = ab ; ( 1 ) % / = 2/3 ; so that the required line is either straight , or an equilateral hy- perbola , according ...
... radius vector of the point of contact . y2 ( 1+ dy dx ± = 0 ; y y b dx2 dy3 ) = y2 + x2 . ... log ± log == = 0 . ( 2 ) xy = ab ; ( 1 ) % / = 2/3 ; so that the required line is either straight , or an equilateral hy- perbola , according ...
Page 234
... radius vector and the curve = 0 , the curve is a circle . Ex . 16. If the subnormal is equal to the abscissa , the curve is a hyperbola . Ex . 17. If the radius of curvature = p , the curve is the involute of the circle . CHAPTER VII ...
... radius vector and the curve = 0 , the curve is a circle . Ex . 16. If the subnormal is equal to the abscissa , the curve is a hyperbola . Ex . 17. If the radius of curvature = p , the curve is the involute of the circle . CHAPTER VII ...
Page 309
... radius vector ; fig . 25 . Let P , to which the radius vector is drawn be ( x , y ) ; and let the limits of x be denoted by x , and xo ; then the equation to OP is x = y = xo ; Yn x2 y2 a2 b2 1 , = Xni and as the equation to the ...
... radius vector ; fig . 25 . Let P , to which the radius vector is drawn be ( x , y ) ; and let the limits of x be denoted by x , and xo ; then the equation to OP is x = y = xo ; Yn x2 y2 a2 b2 1 , = Xni and as the equation to the ...
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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