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 Archimedes' Book of Lemmas: Proposition 8 - Angle trisection

If CD be any chord of a circle whose center is O, and if CD be produced to A so that AD is equal to the radius; if further AO meets the circle in B, then the angle BOC will be equal to three times the angle BAC.

This is the Archimedes' neusis construction to the angle trisection problem. "Neusis" means use of a marked ruler in Greek.





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Last updated: June 29, 2007