An Elementary Treatise on Conic Sections |
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Page viii
... respect to a conic Conjugate points and conjugate lines 194 · 195 A chord of a conic is cut harmonically by a point and its polar 195 Diameters of a conic 196 Condition that two given lines may be parallel to conjugate diameters 196 ...
... respect to a conic Conjugate points and conjugate lines 194 · 195 A chord of a conic is cut harmonically by a point and its polar 195 Diameters of a conic 196 Condition that two given lines may be parallel to conjugate diameters 196 ...
Page ix
... respect to any inscribed conic Centre - locus of conics touching four fixed lines . [ See also 137 , 270 , and 297 ] Parabola touching the axes of co - ordinates . Confocal conics Osculating conics Pairs of common chords of two conics ...
... respect to any inscribed conic Centre - locus of conics touching four fixed lines . [ See also 137 , 270 , and 297 ] Parabola touching the axes of co - ordinates . Confocal conics Osculating conics Pairs of common chords of two conics ...
Page x
... respect to a circle 318 Reciprocal of a circle with respect to a point 320 Co - axial circles reciprocated into confocal conics 322 Projection . Definition of projection · 323 The projection of any curve is a curve of the same degree ...
... respect to a circle 318 Reciprocal of a circle with respect to a point 320 Co - axial circles reciprocated into confocal conics 322 Projection . Definition of projection · 323 The projection of any curve is a curve of the same degree ...
Page 37
... respect to the sign of the area of a triangle , but the equation ( ii ) is universally true . The student should convince himself of the truth of this by drawing different figures . Now also OK == C A ' C OL = -B ' Ᏼ ; LKOK2 + OL2 ...
... respect to the sign of the area of a triangle , but the equation ( ii ) is universally true . The student should convince himself of the truth of this by drawing different figures . Now also OK == C A ' C OL = -B ' Ᏼ ; LKOK2 + OL2 ...
Page 53
... respect to P and Q. * 55 . If four straight lines intersecting in a point O be cut by any straight line in the points P , Q , R , S , the cross ratio of the range P , Q , R , S will be equal to that of the pencil OP , OQ , OR , OS . EC ...
... respect to P and Q. * 55 . If four straight lines intersecting in a point O be cut by any straight line in the points P , Q , R , S , the cross ratio of the range P , Q , R , S will be equal to that of the pencil OP , OQ , OR , OS . EC ...
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre circumscribing coefficients College confocal conics conjugate diameters conjugate hyperbola constant corresponding cross ratio Crown 8vo curve diagonals directrix distance eccentric angles Edition ellipse envelope equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four points given points given straight line harmonic Hence imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals pair of conjugate parabola pass pencil perpendicular point of intersection point Q points at infinity points of contact polar pole Professor projection prove quadrilateral radical axis rectangular hyperbola required equation right angles shew sides square subtend tangents triangle of reference values vertex zero
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