An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 63
iongiven in § 78. It will be convenient first to prove the follo^ving lemma: Iftwo chords A A, BR, of a circle meet in K, then KA : KA = AB. AB: AB. AB.Since the triangles KAB, KBA are similar: thereforeKA:KB=AB:BA.Again, since the triangles KAB, KB A ai-e similar; thereforeKA:KB = AB:BA. 46… … For the triangles KAS, KSA are similar, and thereforeKA:KS = AS:SA;that is KA: KS = AS: -S^^- But KS = KA . KA, therefore KA : KA = AS: AS. 85. If 0 \AA, BB, CC,...} be any pencil in involution, and ifa circle he drawn through the point 0 cutting the rays of the pencilin the points A, A, B, B,...,…
Geometry
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