Although little is known about the life of Diocles, it is known that he was a contemporary of
Apollonius and that he flourished sometime around the end of the 3rd century BC and the beginning of the 2nd century BC. Diocles is thought to be the first person to prove the focal property of the
parabola. His name is associated with the geometric
curve called the
Cissoid of Diocles, which was used by Diocles to solve the problem of
doubling the cube. The curve was alluded to by
Proclus in his commentary on
Euclid and attributed to Diocles by
Geminus as early as the beginning of the 1st century. Fragments of a work by Diocles entitled
On burning mirrors were preserved by
Eutocius in his commentary of
Archimedes'
On the Sphere and the Cylinder and also survived in an
Arabic translation of the lost Greek original titled
Kitāb Dhiyūqlīs fī l-marāyā l-muḥriqa (lit. “The book of Diocles on burning mirrors”). Historically,
On burning mirrors had a large influence on Arabic mathematicians, particularly on
al-Haytham, the 11th-century polymath of Cairo whom Europeans knew as "Alhazen". The treatise contains sixteen propositions that are proved by
conic 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 certain
cubic 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 just
burning mirrors, it may be the case that
On burning mirrors is the aggregate of three shorter works by Diocles. 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. == Notes ==