Differential Calculus with Applications and Numerous Examples: An Elementary Treatise...Macmillan, 1886 - 439 páginas |
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Página 197
... equiangular spiral r = demo is another equiangular spiral . 30. In the curve 0 1 + tan 2 r = Ꮎ m + n tan 2 the locus of the extremity of the polar subtangent is a cardioide . [ PROFESSOR WOLSTENHOLME . ] 31. Show geometrically that the ...
... equiangular spiral r = demo is another equiangular spiral . 30. In the curve 0 1 + tan 2 r = Ꮎ m + n tan 2 the locus of the extremity of the polar subtangent is a cardioide . [ PROFESSOR WOLSTENHOLME . ] 31. Show geometrically that the ...
Página 277
... equiangular spiral , in which par , is included as the case in which B = 0 . 281. Polar Curves . . We shall next reduce the formula to a shape suited for application to curves given by their polar equations . We proved in Art . 181 1 ...
... equiangular spiral , in which par , is included as the case in which B = 0 . 281. Polar Curves . . We shall next reduce the formula to a shape suited for application to curves given by their polar equations . We proved in Art . 181 1 ...
Página 303
... equiangular spiral 29. Show that the chord of curvature through the pole of the r = = aemo is 2r . 2r rm = amcos me is m + 1 Examine the cases when m = - 2 , - 1 , − 1 , 12 , 1 , 2 . curve 30. Show that the radius of curvature of the ...
... equiangular spiral 29. Show that the chord of curvature through the pole of the r = = aemo is 2r . 2r rm = amcos me is m + 1 Examine the cases when m = - 2 , - 1 , − 1 , 12 , 1 , 2 . curve 30. Show that the radius of curvature of the ...
Página 304
... equiangular spiral is an equal equiangular spiral . 37. Given the pedal equation of a curve , viz . , p = f ( r ) ; show that the pedal equation of its evolute may be found by elimi- nating p and r between this equation and the ...
... equiangular spiral is an equal equiangular spiral . 37. Given the pedal equation of a curve , viz . , p = f ( r ) ; show that the pedal equation of its evolute may be found by elimi- nating p and r between this equation and the ...
Página 329
... equi- angular spiral and are reflected by the curve the caustic is a similar equiangular spiral . CHAPTER XII . CURVE TRACING . 315. Nature of the ENVELOPES . 329.
... equi- angular spiral and are reflected by the curve the caustic is a similar equiangular spiral . CHAPTER XII . CURVE TRACING . 315. Nature of the ENVELOPES . 329.
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Differential Calculus With Applications and Numerous Examples: An Elementary ... Joseph Edwards Sin vista previa disponible - 2006 |
Términos y frases comunes
algebraic angle asymptote axis Cambridge cardioide chord circle co-ordinates coincident points College conic conjugate point Crown 8vo cusp cuts the curve cycloid d²y denote differential coefficient dx dx dx dy dy dx Edition ellipse equiangular spiral evolute EXAMPLES expansion Extra fcap fcap Fellow function given curve Globe 8vo Hence homogeneous function independent variable infinite intersection intrinsic equation inverse limit locus Maclaurin's Theorem maxima and minima negative normal nth degree numerous obtain ordinate origin p(x+h parabola parallel pedal equation perpendicular point of contact point of inflexion polar positive pedal Professor prove quantity radius of curvature result roots Show straight line tangent Taylor's Theorem Trace the curve values vanish whence zero ди ди ду дх эф Эх