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A Limit Proof of the Theorem Euc. III, 35

Published online by Cambridge University Press:  31 October 2008

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Let AB be any chord passing through the fixed point P. Draw the diameter AOC, join CP and let it meet the circumference at D Then in triangle ACP, AC2 = AP2 + CP2 together with either 2AP. PB or 2 CP. PD according as CP is projected on AP or AP on CP. Hence AP.PB = CP.PD. Now draw the diameter DOE, join EP and let it meet the circumference at F. Then the theorem is true for chords CD. EF.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1925