Apollonius of Perga ( ; ) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.
Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.
Life
Despite his momentous contributions to the field of mathematics, scant biographical information on Apollonius remains. The 6th century Greek commentator Eutocius of Ascalon, writing on Apollonius' Conics, states:
Apollonius, the geometrician, ... came from Perga in Pamphylia in the times of Ptolemy III Euergetes, so records Herakleios the biographer of Archimedes ....
From this passage Apollonius can be approximately dated, but specific birth and death years stated by modern scholars are only speculative. Ptolemy III Euergetes ("benefactor") was third Greek dynast of Egypt in the Diadochi succession, who reigned 246–222/221 BC. "Times" are always recorded by ruler or officiating magistrate, so Apollonius was likely born after 246. The identity of Herakleios is uncertain.
Perga was a Hellenized city in Pamphylia, Anatolia, whose ruins yet stand. It was a center of Hellenistic culture. Eutocius appears to associate Perga with the Ptolemaic dynasty of Egypt. Never under Egypt, Perga in 246 BC belonged to the Seleucid Empire, an independent diadochi state ruled by the Seleucid dynasty. During the last half of the 3rd century BC, Perga changed hands a number of times, being alternatively under the Seleucids and under the Attalids of Pergamon to the north. Someone designated "of Perga" might be expected to have lived and worked there; to the contrary, if Apollonius was later identified with Perga, it was not on the basis of his residence. The remaining autobiographical material implies that he lived, studied, and wrote in Alexandria.
A letter by the Greek mathematician and astronomer Hypsicles was originally part of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements.
Autobiographical prefaces
Some autobiographical material can be found in the surviving prefaces to the books of Conics. These are letters Apollonius addressed to influential friends asking them to review the book enclosed with the letter. The first two prefaces are addressed to Eudemus of Pergamon.
Eudemus likely was or became the head of the research center of the of Pergamon, a city known for its books and parchment industry from which the name parchment is derived. Research in Greek mathematical institutions, which followed the model of the Athenian Lycaeum, was part of the educational effort to which the library and museum were adjunct. There was only one such school in the state, under royal patronage. Books were rare and expensive and collecting them was a royal obligation.
Apollonius's preface to Book I tells Eudemus that the first four books were concerned with the development of elements while the last four were concerned with special topics. Apollonius reminds Eudemus that Conics was initially requested by Naucrates, a geometer and house guest at Alexandria otherwise unknown to history. Apollonius provided Naucrates the first draft of all eight books, but he refers to them as being "without a thorough purgation", and intended to verify and correct the books, releasing each one as it was completed.
Having heard this plan from Apollonius himself, who visited Pergamon, Eudemus insisted Apollonius send him each book before release. At this stage Apollonius was likely still a young geometer, who according to Pappus stayed at Alexandria with the students of Euclid (long after Euclid's time), perhaps the final stage of his education. Eudemus may have been a mentor from Appolonius' time in Pergamon.