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… … OA, OB, OC, OD form a harmonic pencil; andtherefore A, B, C, D form a harmonic range; andso on. Thus we may proceed from a harmonic rangeto a harmonic pencil, thence to a harmonic range, andso on indefinitely, by constructing pencils and draw-ing transversals, alternately. The Complete…
Geometry · Geometry, Plane
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