Person: Diocles Of Carystus
Diocles was a Greek mathematician who was the first to prove the focal property of a parabolic mirror and studied the cissoid curve as part of an attempt to duplicate the cube.
Mathematical Profile (Excerpt):
- In this work we are told that Diocles studied the cissoid as part of an attempt to duplicate the cube.
- The extracts quoted by Eutocius from Diocles' On burning mirrors showed that he was the first to prove the focal property of a parabolic mirror.
- Although Diocles' text was largely ignored by later Greeks, it had considerable influence on the Arab mathematicians, in particular on al-Haytham.
- Latin translations from about 1200 of the writings of al-Haytham brought the properties of parabolic mirrors discovered by Diocles to European mathematicians.
- Recently, however, some more information about Diocles' life has come to us from the Arabic translation of Diocles' On burning mirrors whose discovery is described below.
- From this work we learn that Zenodorus travelled to Arcadia and entered into discussions with Diocles, so that certainly Diocles was working in Arcadia at the time.
- It is only recently that an Arabic translation of Diocles On burning mirrors has been found in the Shrine Library in Mashhad, Iran.
- The first of these propositions proves what has long been known to have been first established by Diocles, namely the focal property of the parabola.
- These constructions are again properties of the parabola that Diocles was the first to give.
- The duplication of the cube problem, again referred to by Eutocius, is studied by Diocles in Proposition 10.
- The next two propositions solve the problem of inserting two mean proportions between a pair of magnitudes using the cissoid curve which was invented by Diocles.
- In On burning mirrors Diocles also studies the problem of finding a mirror such that the envelope of reflected rays is a given caustic curve or of finding a mirror such that the focus traces a given curve as the Sun moves across the sky.
Born about 240 BC. Died about 180 BC.
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Tags relevant for this person:
Ancient Arab, Ancient Greek, Geometry, Origin Greece
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive