cover image: Lectures on the Theory of Plane Curves

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20.500.12592/4c2x9c

Lectures on the Theory of Plane Curves

1919

The Oval of Cassini The equation of the Cassinian Properties of Cassini's ovals The Cartesian Ovals The equation of the Cartesian Generation of a Cartesian Foci of Cartesians . Points of inflexion on Cartesians The Lemniseate of Bernoulli The Limacon The Cardioid . The Conehoid of Nicomedes Trisection of an angle 316 . 316 317 318 . 319 321. [...] The points of contact of the tangents drawn from C' are the required points C. But in general four tangents can he drawn from C' to the curve, and the point of contact of any one of these tangents will be the required point C. But three of these points will give the solution of the problem ; for A B intersects the cubic at a third point D, the tangent at which also passes through C'. [...] A', or as we say, C' is the second tangential of A. Hence to construct a conic having a four-pointic contact at A and a simple contact elsewhere, we proceed as follows :—Draw the tangent at A to the cubic and let A' be the tangential of A and let C' be the tangential of A' i. e. , the second tangential of A. Then the four points of contact of the tangents drawn from C' to the curve will be the requi [...] The equation of a cubic having the vertex A of the triangle of reference as a point of inflexion is- -1-xitiv,± 713 =0. 161 The first polar or the polar conic'of A is 4r- . e. , the polar conic breaks up into (Ix two right lines, one of which n 1 =---0 is the tangent at A, and the other line 2. : + n =0 passes through the points of contact of the tangents drawn from A. Definition : The line (2. r+vi)= [...] The polar conic in question consists of the side of the triangle which passes through the point, and of the polar line cf the point of inflexion with respect to two other sides of the triangle.
technology medicine science
Pages
239
Published in
India
SARF Document ID
sarf.100014
Segment Pages Author Actions
Preface
i-xiii Surendramohan Ganguly view
Chapter X Curves or the Third Order—Cubiu Curves
139-157 unknown view
Chapter XI Harmonic Properties of Curic Curves
158-168 unknown view
Chapter XII Canonical Forms
169-203 unknown view
Chapter XII Unicursal Cubics
204-215 unknown view
Chapter XIV Special Cubics
216-231 unknown view
Chapter XV Invariants and Covarlants of Cubic Curves
232-243 unknown view
Chapter XVI Curves of the Fourth Order—Quartic Curves
244-266 unknown view
Chapter XVII Trinodai Quartices
267-275 unknown view
Chapter XVIII Bicircular Quartics
276-305 unknown view
Chapter XIX Circular Cubics as Degenerate Bicircular Quartics
306-315 unknown view
Chapter XX Special Quartic Curves
316-328 unknown view
Appendix
329-346 unknown view
Index
347-350 unknown view
The Theory of Plane Curves
1-14 unknown view

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