Apollonius of Perga (c. 240-190 BCE) was a Greek mathematician and astronomer from Perga in Pamphylia (modern-day Antalya province, Turkey), active during the Hellenistic period. He is best known for his systematic treatment of conic sections in his eight-book work Conics, which classified and analyzed the ellipse, parabola, and hyperbola - terms he is credited with coining. His contributions to geometry and mathematical astronomy rank him alongside Euclid and Archimedes as one of the most significant mathematicians of antiquity.

Biographical information about Apollonius is sparse and derives largely from later writers, particularly Pappus of Alexandria (c. 4th century CE) and Eutocius of Ascalon (c. 6th century CE). He is believed to have studied at Alexandria under the successors of Euclid and later worked at Pergamon. The dates of his birth and death are uncertain; ancient sources place his floruit during the reign of Ptolemy III Euergetes (246-222 BCE) and into the reign of Ptolemy IV.

The Conics is Apollonius's only work to survive in substantial form. Of the eight books, seven survive - four in the original Greek and three in Arabic translation; the eighth is lost. The work systematically derived the properties of conic sections from a single cone with varying cutting planes, superseding earlier treatments by Menaechmus and Euclid. Books I-IV are considered introductory; Books V-VII treat more advanced topics including normals to conics. The Conics became a foundational text in European mathematics after its partial recovery through Arabic transmission and was instrumental in the development of analytic geometry by Descartes and Fermat in the 17th century.

Apollonius made contributions to mathematical astronomy, most notably in the development of epicycle and eccentric models to account for the apparent irregular motions of planets. A theorem attributed to him - sometimes called the “Apollonius theorem” in the astronomical context - establishes the equivalence between certain epicyclic and eccentric models of planetary motion. His astronomical work is known primarily through citations in Ptolemy's Almagest (c. 150 CE). The relationship of his models to the broader history of geocentric and heliocentric theories of the cosmos is discussed at Heliocentrism - History.

Ancient sources attribute several other works to Apollonius, all lost. These include:

• Cutting off a Ratio (De Sectione Rationis) - survives only in Arabic translation
• Cutting off an Area
• On Determinate Section
• Tangencies - source of the classical “Problem of Apollonius” (constructing a circle tangent to three given circles)
• Plane Loci
• Vergings (Neuseis)
• On the Burning Mirror
• A work on the mathematical foundations of a base-10000 number system, apparently extending methods from Archimedes

The Conics exerted sustained influence from antiquity through the early modern period. Islamic mathematicians preserved and extended his work; Ibrahim ibn Sinan and al-Khayyam engaged directly with conic theory. In the 17th century, Kepler's recognition that planetary orbits are ellipses - a result that undermined the epicyclic tradition Apollonius helped establish - depended on the geometric vocabulary Apollonius had systematized. Newton's treatment of conic orbits in the Principia likewise drew on this tradition.

• Apollonius of Perga - History
• Heliocentrism - History
• Conic Sections
• Epicycle
• Euclid
• Archimedes
• Claudius Ptolemy
• Greek Mathematics

1. Toomer, G. J. “Apollonius of Perga.” Dictionary of Scientific Biography, vol. 1. Scribner, 1970, pp. 179-193.
2. Heath, Thomas L. Apollonius of Perga: Treatise on Conic Sections. Cambridge University Press, 1896. (Classic English edition; for a more recent critical text see Fried and Unguru below.)
3. Fried, Michael N., and Sabetai Unguru. Apollonius of Perga's Conica: Text, Context, Subtext. Brill, 2001.
4. Pappus of Alexandria. Collection, Book VII. Trans. Alexander Jones. Springer, 1986.
5. Neugebauer, Otto. A History of Ancient Mathematical Astronomy. Springer, 1975, pp. 264-270.
6. Hogendijk, Jan P. “Arabic Traces of Lost Works of Apollonius.” Archive for History of Exact Sciences 35.3 (1986): 187-253.