A first course in projective geometry . Fig. 60. I the vanishing line in the plane of the circle. a, h the axes of the conic. ^, ^ the asymptotes of the conic. C the centre of the conic. For convenience we repeat the construction of § 13 for theaxes. Take the inverse of V with respect to the circle, centre V and this point describe a circle having its centreon the vanishing line. (This cuts the circle, centre O, ortho-gonally.) Join O to the points R, R, where this circle cutsthe vanishing line. Join R and R to the points where these 120 PROJECTIVE GEOMETRY lines cut the circle again
A first course in projective geometry . Fig. 60. I the vanishing line in the plane of the circle. a, h the axes of the conic. ^, ^ the asymptotes of the conic. C the centre of the conic. For convenience we repeat the construction of § 13 for theaxes. Take the inverse of V with respect to the circle, centre V and this point describe a circle having its centreon the vanishing line. (This cuts the circle, centre O, ortho-gonally.) Join O to the points R, R, where this circle cutsthe vanishing line. Join R and R to the points where these 120 PROJECTIVE GEOMETRY lines cut the circle again, and let the joining lines meet in TR, TR are a pair of conjugate lines with respect to thecircle, centre O, such that the intercept RR on the vanishing. Fig. 61. line between them subtends a right angle at V. They there-fore project into conjugate lines for the conic at right angles,which, as proved in § 13, are the axes. We get the axes thenby joining to C the points where TR, TR meet the axis ofprojection. Examples on Chapter VIII. DRAWING EXERCISES. 1. Draw the actual form of the section of a right circular cone ofheight 10 inches and radius of base 3 inches, made by a plane inclinedat 30° to the base, the line of intersection of the planes being a tangentto the base. 2. The circle oiP-^-ip — ^ is projected from a point 5 units verticallyabove the point (4, 0), the plane of xy being horizontal. Draw theprojection of the circle upon the vertical plane through the line y = 2^this projection being rabatted about the latter line into the horizontalplane. 3. Draw a figure in plane perspective with the circle :i(?-\-{y - 2)^ = 4,being given that the origin and ( - 1, 1) are corresponding points, that EXAMPLES 121 the lines 2/ = 0, y
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