Diocles (Ancient Greek:Διοκλῆς; c. 240 BC – c. 180 BC) was aGreekmathematician andgeometer.
Although little is known about the life of Diocles, it is known that he was a contemporary ofApollonius and that he flourished sometime around the end of the 3rd century BC and the beginning of the 2nd century BC.[1]
Diocles is thought to be the first person to prove the focal property of theparabola. His name is associated with the geometriccurve called theCissoid of Diocles, which was used by Diocles to solve the problem ofdoubling the cube. The curve was alluded to byProclus in his commentary onEuclid and attributed to Diocles byGeminus as early as the beginning of the 1st century.[2]
Fragments of a work by Diocles entitledOn burning mirrors were preserved byEutocius in his commentary ofArchimedes'On the Sphere and the Cylinder and also survived in anArabic translation of the lost Greek original titledKitāb Dhiyūqlīs fī l-marāyā l-muḥriqa (lit. “The book of Diocles on burning mirrors”).[3] Historically,On burning mirrors had a large influence on Arabic mathematicians, particularly onal-Haytham, the 11th-century polymath of Cairo whom Europeans knew as "Alhazen". The treatise contains sixteen propositions that are proved byconic sections. One of the fragments contains propositions seven and eight, which is a solution to the problem of dividing a sphere by a plane so that the resulting two volumes are in a given ratio. Proposition ten gives a solution to the problem of doubling the cube. This is equivalent to solving a certaincubic equation. Another fragment contains propositions eleven and twelve, which use the cissoid to solve the problem of finding two mean proportionals in between two magnitudes. Since this treatise covers more topics than justburning mirrors, it may be the case thatOn burning mirrors is the aggregate of three shorter works by Diocles.[4] In the same work, Diocles, just after demonstrating that the parabolic mirror could focus the rays in a single point, he mentioned that It is possible to obtain a lens with the same property.[5]
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