A first course in projective geometry . Pig. 48, § 7. General Properties. I. Any straight line cuts a conic in two points, real,coincident, or imaginary. From any point two tangents, real, coincident, or imaginary,can be drawn to any conic. These follow at once by projection from the circle (§§ 2 and 3). A conic is therefore a curve of the second order and ofthe second class. II. The locus of the intersection of tangents at the endsof chords of a conic which pass through a fixed point is astraight line. 100 PROJECTIVE GEOMETRY This theorem has been proved for the circle in Chap. VI.§ 1. It fol
A first course in projective geometry . Pig. 48, § 7. General Properties. I. Any straight line cuts a conic in two points, real,coincident, or imaginary. From any point two tangents, real, coincident, or imaginary,can be drawn to any conic. These follow at once by projection from the circle (§§ 2 and 3). A conic is therefore a curve of the second order and ofthe second class. II. The locus of the intersection of tangents at the endsof chords of a conic which pass through a fixed point is astraight line. 100 PROJECTIVE GEOMETRY This theorem has been proved for the circle in Chap. VI.§ 1. It follows at once for the conic by projection, sincetangents project into tangents (Fig. 49). (Compare Fig. 28.).
Size: 1543px × 1620px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
