Diocles (mathematician)
Diocles was a Greek mathematician and geometer, who probably flourished sometime around the end of the second century and the beginning of the first century BC. He was probably the first to prove the focal property of a parabola. His name is associated with the geometric curve called the Cissoid of Diocles. It was used by Diocles for doubling the cube. The curve was alluded to by Proclus in his commentary on Euclid and attributed to Diolcles by Geminus as early as the the beginning of the first century. Fragments of a work by Diocles titled On burning mirrors were preserved by Eutocius in his commentary of Archimedes' On the Sphere and the Cylinder. One of the fragments contains a solution, using conic sections to solve the problem of dividing a sphere by a plane to so that the resulting two volumes were a given ratio. This was equivalent to solving a certain cubic equation. Another fragment uses the cissoid to find two mean porportionals.
ReferencesHeath, Sir Thomas, A History of Greek Mathematics (2 Vols.) Dover Publications, Inc.(1980), Oxford (1921) ISBN 0486240738O'Connor, John J. and Edmund F. Robertson, Diocles [1], 1999.
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