# Mathematician:Apollonius of Perga

## Contents

## Mathematician

Ancient Greek: **Ἀπολλώνιος**, also known (in the Latin form) as **Pergaeus**.

Greek geometer and astronomer best known for his work on conic sections, in which he uses techniques in analytic geometry which anticipated the work of Descartes.

Greatly influential, he provided the names of the ellipse, parabola and hyperbola.

Not to be confused with the philosopher **Apollonius of Tyana** (1st century CE), the fictional **Apollonius of Tyre**, or several other notable figures called Apollonius from that era.

## Nationality

Greek

## History

- Born: c. 262 BCE, Perga, Pamphylia, Greek Ionia (now Murtina, Antalya, Turkey)
- Died: c. 190 BCE, Alexandria, Egypt

## Theorems and Topics

Results named for **Apollonius of Perga** can be found here.

Definitions of concepts named for **Apollonius of Perga** can be found here.

## Publications

- c. 230 BCE:
*Conics*(also known as*Conic Sections*) *Λόγου ἀποτομή, De Rationis Sectione*("Cutting of a Ratio")*Χωρίου ἀποτομή, De Spatii Sectione*("Cutting of an Area")*Διωρισμένη τομή, De Sectione Determinata*("Determinate Section")*Ἐπαφαί, De Tactionibus*("Tangencies"), in which the Problem of Apollonius is discussed*Νεύσεις, De Inclinationibus*("Inclinations")*Τόποι ἐπίπεδοι, De Locis Planis*("Plane Loci")

### Other works

These works are referred to by other ancient writers, but are now believed lost:

*Περὶ τοῦ πυρίου*(On the Burning-Glass), which probably explored the focal properties of the parabola*Περὶ τοῦ κοχλίου*(On the Cylindrical Helix) (mentioned by Proclus);- A comparison of the dodecahedron and the icosahedron inscribed in the same sphere
*Ἡ καθόλου πραγματεία*, on the general principles of mathematics, probably discussing possible improvements to Euclid's*The Elements**Ὠκυτόκιον*(Quick Bringing-to-birth), in which, according to Eutocius, demonstrates how to find a better approximation to pi than Archimedes managed- A work describing a system for working on large numbers, supposedly more accessible than Archimedes'
*The Sand-Reckoner*(reported by Pappus) - A work on the theory of irrationals, expanding that discussed in Book $\text X$ of Euclid's
*The Elements*(reported by Pappus).

## Critical View

*He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.*

## Sources

- John J. O'Connor and Edmund F. Robertson: "Apollonius of Perga": MacTutor History of Mathematics archive

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 1*(2nd ed.) ... (previous) ... (next): Introduction: Chapter $\text{IV}$. Proclus and his Sources - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.6$: Apollonius (ca. $262$ – $190$ B.C.) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic Of Shape