For ABBC AD , , AB dc^^bc —-, from similarCX BAO, BCX; ah AD —, from similar AS DAO, DCY; DC.. CX-CY. The consti-netion for the harmonic division of a line(Prop. 23) would have suggested the truth of the pre-ceding, sinee XA, XP, XB, XQ form a harmonicpencil. . 262 Geomeiky. Prop. 25. If A, B, C, D… … Through C and C di-aw XCY, XCY, paraUel to OA.Then since CX = CY (Prop. 24), therefore CX = CY. Also 4^, = ^,; (sim. AS BAO, BCX.)B C C X and ^ = 1^, (Sim. As OAD, YCD.) ^AO. CX .•.|| = ^^, a^^ A, B, C, D for7,i a har-monic range. Additional Propositions. 263 Hence if we start vnth tlie harmonic…
Geometry · Geometry, Plane
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