Diocles (Greek: Διοκλῆς; c. 240 BC – c. 180 BC) 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 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 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.^[2]

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”).^[3] 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.^[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]

Notes

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.; Robertson, Edmund F., "Diocles of Carystus", MacTutor History of Mathematics Archive, University of St Andrews
Malik, Saira (2021-01-01). "Diocles". Encyclopaedia of Islam, THREE

Ancient Greek mathematics

Mathematicians
(timeline)

Treatises

Problems

Concepts
and definitions

Results

In Elements	Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon
Apollonius	Apollonius's theorem
Other	Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Ancient Greek astronomy Attic numerals Greek numerals Latin translations of the 12th century Non-Euclidean geometry Philosophy of mathematics Neusis construction
History of	A History of Greek Mathematics by Thomas Heath algebra timeline arithmetic timeline calculus timeline geometry timeline logic timeline mathematics timeline numbers prehistoric counting numeral systems list
Other cultures	Arabian/Islamic Babylonian Chinese Egyptian Incan Indian Japanese

Ancient Greece portal • Mathematics portal

Authority control databases
International	FAST ISNI VIAF 2 3 4
National	Norway France BnF data Germany Italy Israel United States
Academics	CiNii MathSciNet zbMATH
People	Deutsche Biographie
Other	IdRef