A first course in projective geometry . = 4-1 in each case Pig. 9. It follows then that AF BD CEBF ? DC ? EA or AF . BD . CE = - FB . DC . EA. Conversely. If D, E, F be taken on the sides so as to fulfilthis condition, these points are let EF meet BC in D. Then AF. BD. CE = - FB . DC. EA by the AF . BD . CE = - FB. DC. EA by hypothesis. Bp_DC_BD + DC BD ~ ~ DC BD-fDC .. D and D coincide. 1 in each case. METRICAL RELATIONS 27 Ex. 1. Prove that the sides of tlie triangle formed hy joining thepoints of contact of the inscribed circle of a triangle with the sides,inters
A first course in projective geometry . = 4-1 in each case Pig. 9. It follows then that AF BD CEBF ? DC ? EA or AF . BD . CE = - FB . DC . EA. Conversely. If D, E, F be taken on the sides so as to fulfilthis condition, these points are let EF meet BC in D. Then AF. BD. CE = - FB . DC. EA by the AF . BD . CE = - FB. DC. EA by hypothesis. Bp_DC_BD + DC BD ~ ~ DC BD-fDC .. D and D coincide. 1 in each case. METRICAL RELATIONS 27 Ex. 1. Prove that the sides of tlie triangle formed hy joining thepoints of contact of the inscribed circle of a triangle with the sides,intersect the sides in three collinear points. Ex. 2. Prove that the sides of the pedal triangle intersect those ofthe given triangle in collinear points. Ex. 3. Examine the case in which the transversal is parallel to aside of the triangle. § 5. A Theorem of Desargues. If the joins of corresponding vertices of two coplanar trianglesare concurrent, the intersections of cmrespoTuUng sides are collinear,aiul conversely. [In § 4 of the
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
