. The principles of projective geometry applied to the straight line and conic . If ABODE he a pentagon in-scribed in a conic and BG meetsthe connector of AB. DE (= K)and CD. EA (= L) in M, then theline ME is the tangent at E. Hence given any five points ona conic the tangents at any ofthese points can be constructed. If abcde be a pentagon circum-scribed to a conic and m is theconnector of be to the point ofintersection of (= fc) (= I), then m passes throughthe point of contact of e. Hence given any five tangentsto a conic the points of contactof any of these tangents can becon
. The principles of projective geometry applied to the straight line and conic . If ABODE he a pentagon in-scribed in a conic and BG meetsthe connector of AB. DE (= K)and CD. EA (= L) in M, then theline ME is the tangent at E. Hence given any five points ona conic the tangents at any ofthese points can be constructed. If abcde be a pentagon circum-scribed to a conic and m is theconnector of be to the point ofintersection of (= fc) (= I), then m passes throughthe point of contact of e. Hence given any five tangentsto a conic the points of contactof any of these tangents can beconstructed. Deductions from Pascals Theorem 213 (ii) If two pairs of the six If two pairs of the six tangents points coincide, the properties of coincide, the properties of thethe complete quadrangle inscribed complete quadrilateral circum-in a conic are obtained, viz. scribed to a conic are obtained, // a quadrangle be inscribedin a conic, the points of inter-section of the tangents at the ver-tices lie two by two on the sidesof the diagonal points tnangle ofthe quadrangle. (iii) If three pairs of thesix points coincide, the followingtheorem is obtained: If a quadrilateral be circuni-scHbed to a conic, the connectorsof the points of contact of thetangents pass two by two throughthe points of intersection of thediagonals of the quadrilateral. If three pairs of the sixtangents coincide, the followingtheorem is obtained:
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
