An Elementary Treatise on Conic Sections |
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Page ix
... Confocal conics Osculating conics Pairs of common chords of two conics . Invariants Examples on Chapter XI . CHAPTER XII . ENVELOPES . Envelopes , how found . Tangential co - ordinates and equations Director - circle of envelope ( cf ...
... Confocal conics Osculating conics Pairs of common chords of two conics . Invariants Examples on Chapter XI . CHAPTER XII . ENVELOPES . Envelopes , how found . Tangential co - ordinates and equations Director - circle of envelope ( cf ...
Page x
... confocal conics 322 Projection . Definition of projection • 323 The projection of any curve is a curve of the same degree 323 Projections of tangents , poles and polars 324 Straight lines meeting in a point projected into parallel ...
... confocal conics 322 Projection . Definition of projection • 323 The projection of any curve is a curve of the same degree 323 Projections of tangents , poles and polars 324 Straight lines meeting in a point projected into parallel ...
Page xi
Charles Smith. A system of conics inscribed in a quadrilateral projected into confocal conics Cross ratios of pencils and ranges unaltered by projection Conics through four fixed points are cut by any straight line in pairs of points in ...
Charles Smith. A system of conics inscribed in a quadrilateral projected into confocal conics Cross ratios of pencils and ranges unaltered by projection Conics through four fixed points are cut by any straight line in pairs of points in ...
Page 110
... confocal parabola . 50. If the circle described on the chord PQ of a parabola as diameter cut the parabola again in the points R , S , then will PQ and RS intercept a constant length on the axis of the parabola . 51. If the normals at P ...
... confocal parabola . 50. If the circle described on the chord PQ of a parabola as diameter cut the parabola again in the points R , S , then will PQ and RS intercept a constant length on the axis of the parabola . 51. If the normals at P ...
Page 178
... confocal conic . Prove that these conics all touch two fixed conics , the reciprocals of whose latera recta are the sum and difference respectively of those of the variable conic and their fixed confocal and which have the same ...
... confocal conic . Prove that these conics all touch two fixed conics , the reciprocals of whose latera recta are the sum and difference respectively of those of the variable conic and their fixed confocal and which have the same ...
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
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