. The principles of projective geometry applied to the straight line and conic . he Pascal hexagon ACABCB. (7) If the sides of a given triangle meet a conic in six points, the triangle formedby joining the six points in pairs is in perspective with the given triangle. (8) 0, O, 0 are three fixed coUinear points and A is any point on a fixedconic S. AO meets S in B, BO meets S in C, CCf meets B in D. Prove that ADwill always pass through a fixed point. Eange described by A is projectivewith range described by B, hence with range described by C,hence with range described by OD meet the con
. The principles of projective geometry applied to the straight line and conic . he Pascal hexagon ACABCB. (7) If the sides of a given triangle meet a conic in six points, the triangle formedby joining the six points in pairs is in perspective with the given triangle. (8) 0, O, 0 are three fixed coUinear points and A is any point on a fixedconic S. AO meets S in B, BO meets S in C, CCf meets B in D. Prove that ADwill always pass through a fixed point. Eange described by A is projectivewith range described by B, hence with range described by C,hence with range described by OD meet the conic in B and OBmeet the conic in C. Then OC willpass through A, for ABCDBC is a Pascalhexagon. Therefore A and D mutuallycorrespond. Therefore they are conjugate points of an involution on the conic andconsequently AD always passes through a fixed point. (9) If the conies of a system pass through four points A, B, C, D, and a fixedchord through A meet one of the conies in P and the tangent to the same conic atone of the points (C) in P, then P and P describe projective Deductions from Besargues Theorem •217
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