. The principles of projective geometry applied to the straight line and conic . (iv) If the projective pencils are oppositely equal the conic istermed a rectangular hyperbola. (v) If the projective pencils are directly equal the conic isa circle. In Art. 93 it was shown that the correlative of a conic is a proof there given does not apply to the case when the conic breaksup into a pair of straight lines. Hence to the above should be added (vi) If the projective pencils are in plane perspective the conicbecomes a pair of straight lines, viz. the axis of perspective and theconnector o
. The principles of projective geometry applied to the straight line and conic . (iv) If the projective pencils are oppositely equal the conic istermed a rectangular hyperbola. (v) If the projective pencils are directly equal the conic isa circle. In Art. 93 it was shown that the correlative of a conic is a proof there given does not apply to the case when the conic breaksup into a pair of straight lines. Hence to the above should be added (vi) If the projective pencils are in plane perspective the conicbecomes a pair of straight lines, viz. the axis of perspective and theconnector of the vertices. If the ranges, which determine the correlative curve, are in planeperspective, the conic becomes a pair of points, viz. the centre ofperspective and the point of intersection of the bases. In Art. 37 it Avas shown how pencils of this nature could beconstructed. The following are the figures of the three kinds of coniesconstructed by the method there explained as the loci of the points ofintersection of projective pencils. 170 Principles of Projective Geometry. The Conic 171
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
