# Diocles (mathematician): Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

Diocles (Διοκλῆς in Ancient Greek, ca. 240 BCE - ca. 180 BCE) was a Greek mathematician and geometer.

## Life and work

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 third century and the beginning of the second 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 first 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. Historically, On burning mirrors had a large influence on Arabic mathematicians, particularly on al-Haytham. 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.[1]

## Citations and footnotes

1. ^ G J Toomer

## References

• Heath, Sir Thomas, A History of Greek Mathematics (2 Vols.) Dover Publications, Inc.(1980), Oxford (1921) ISBN 0-486-24073-8
• G J Toomer, Diocles On Burning Mirrors, Sources in the History of Mathematics and the Physical Sciences 1 (New York, 1976).
• O'Connor, John J. and Edmund F. Robertson, Diocles, 1999.