He made an early attempt to square the circle and was the first to propose a method of exhaustion. He proposed successively doubling the number of sides of a regular polygon inscribed in a circle so that the difference in areas would eventually become exhausted.
Antiphon was involved in an anti-democratic revolution which failed and, despite his profession as a writer of defence speeches, his brilliant speech failed to save his life when he was tried for treason and he was executed.
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The method of exhaustion was developed by Archimedes and led to an early determination of an approximation for .
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