Diocles was a Greek

Hellenistic Greece

In the context of Ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by Rome in 146 BC...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and geometer.

Life and work

Although little is known about the life of Diocles, it is known that he was a contemporary of Apollonius

Apollonius of Perga

Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...

 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

Parabola

In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...

. His name is associated with the geometric curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

 called the Cissoid of Diocles

Cissoid of Diocles

In geometry, the cissoid of Diocles is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio. In particular, it can be used to double a cube. It can be defined as the cissoid of a circle and a line tangent to it with respect to the...

, which was used by Diocles to solve the problem of doubling the cube

Doubling the cube

Doubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...

. The curve was alluded to by Proclus

Proclus

Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...

 in his commentary on Euclid

Euclid

Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

 and attributed to Diocles by Geminus

Geminus

Geminus of Rhodes , was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the Introduction to the Phenomena, still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only...

 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

Archimedes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

' On the Sphere and the Cylinder. 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.