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A Limit Proof of the Theorem Euc. III, 35

Published online by Cambridge University Press:  31 October 2008

G. D. C. Stokes
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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
Information
Edinburgh Mathematical Notes , Volume 23 , June 1925 , pp. 7 - 8
Copyright
Copyright © Edinburgh Mathematical Society 1925