Apollonius of Perga

Apollonius of Perga (Greek: Ἀπολλώνιος ὁ Περγαῖος; Latin: Apollonius Pergaeus; late 3rd – early 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections. Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today.

Apollonius worked on many other topics, including astronomy. Most of the work has not survived except in fragmentary references in other authors. 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eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance.

Life

For such an important contributor to the field of mathematics, scant biographical information remains. The 6th century Palestinian commentator, Eutocius of Ascalon, on Apollonius’ major work, Conics, states:^[1]

“Apollonius, the geometrician, ... came from Perga in Pamphylia in the times of Ptolemy Euergetes, so records Herakleios the biographer of Archimedes ....”

Perga at the time was a Hellenized city of Pamphylia in Anatolia. The ruins of the city yet stand. It was a center of Hellenistic culture. Euergetes, “benefactor,” identifies Ptolemy III Euergetes, third Greek dynast of Egypt in the diadochi succession. Presumably, his “times” are his regnum, 246-222/221 BC. Times are always recorded by ruler or officiating magistrate, so that if Apollonius was born earlier than 246, it would have been the “times” of Euergetes’ father. The identity of Herakleios is uncertain. The approximate times of Apollonius are thus certain, but no exact dates can be given.^[2] The figure Specific birth and death years stated by the various scholars are only speculative.^[3]

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 Kingdom of Pergamon to the north, ruled by the Attalid dynasty. Someone designated “of Perga” might well 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.^[4]

"Basilides of Tyre, O Protarchus, when he came to Alexandria and met my father, spent the greater part of his sojourn with him on account of the bond between them due to their common interest in mathematics. And on one occasion, when looking into the tract written by Apollonius about the comparison of the dodecahedron and icosahedron inscribed in one and the same sphere, that is to say, on the question what ratio they bear to one another, they came to the conclusion that Apollonius' treatment of it in this book was not correct; accordingly, as I understood from my father, they proceeded to amend and rewrite it. But I myself afterwards came across another book published by Apollonius, containing a demonstration of the matter in question, and I was greatly attracted by his investigation of the problem. Now the book published by Apollonius is accessible to all; for it has a large circulation in a form which seems to have been the result of later careful elaboration."

"For my part, I determined to dedicate to you what I deem to be necessary by way of commentary, partly because you will be able, by reason of your proficiency in all mathematics and particularly in geometry, to pass an expert judgment upon what I am about to write, and partly because, on account of your intimacy with my father and your friendly feeling towards myself, you will lend a kindly ear to my disquisition. But it is time to have done with the preamble and to begin my treatise itself."

The times of Apollonius

Apollonius lived toward the end of a historical period now termed the Hellenistic Period, characterized by the superposition of Hellenic culture over extensive non-Hellenic regions to various depths, radical in some places, hardly at all in others. The change was initiated by Philip II of Macedon and his son, Alexander the Great, who, subjecting all of Greece is a series of stunning victories, went on to conquer the Persian Empire, which ruled territories from Egypt to Pakistan. Philip was assassinated in 336 BC. Alexander went on to fulfill his plan by conquering the vast Persian empire.

The short autobiography of Apollonius

The material is located in the surviving false “Prefaces” of the books of his Conics. These are letters delivered to influential friends of Apollonius asking them to review the book enclosed with the letter. The Preface to Book I, addressed to one Eudemus, reminds him that Conics was initially requested by a house guest at Alexandria, the geometer, Naucrates, otherwise unknown to history. Naucrates had the first draft of all eight books in his hands by the end of the visit. Apollonius refers to them as being “without a thorough purgation” (ou diakatharantes in Greek, ea non perpurgaremus in Latin). He intended to verify and emend the books, releasing each one as it was completed.

Hearing of this plan from Apollonius himself on a subsequent visit of the latter to Pergamon, Eudemus had insisted Apollonius send him each book before release. The circumstances imply that at this stage Apollonius was a young geometer seeking the company and advice of established professionals. Pappus states that he was with the students of Euclid at Alexandria. Euclid was long gone. This stay had been, perhaps, the final stage of Apollonius’ education. Eudemus was perhaps a senior figure in his earlier education at Pergamon; in any case, there is reason to believe that he was or became the head of the Library and Research Center (Museum) of Pergamon. Apollonius goes on to state that the first four books were concerned with the development of elements while the last four were concerned with special topics.

There is something of a gap between Prefaces I and II. Apollonius has sent his son, also Apollonius, to deliver II. He speaks with more confidence, suggesting that Eudemus use the book in special study groups, which implies that Eudemus was a senior figure, if not the headmaster, in the research center. Research in such institutions, which followed the model of the Lycaeum of Aristotle at Athens, due to the residency of Alexander the Great and his companions in its northern branch, was part of the educational effort, to which the library and museum were adjunct. There was only one such school in the state. Owned by the king, it was under royal patronage, which was typically jealous, enthusiastic, and participatory. The kings bought, begged, borrowed and stole the precious books whenever and wherever they could. Books were of the highest value, affordable only to wealthy patrons. Collecting them was a royal obligation. Pergamon was known for its parchment industry, whence “parchment” is derived from “Pergamon.”

Apollonius brings to mind Philonides of Laodicea, a geometer whom he introduced to Eudemus in Ephesus. Philonides became Eudemus' student. He lived mainly in Syria during the 1st half of the 2nd century BC. Whether the meeting indicates that Apollonius now lived in Ephesus is unresolved. The intellectual community of the Mediterranean was international in culture. Scholars were mobile in seeking employment. They all communicated via some sort of postal service, public or private. Surviving letters are abundant. They visited each other, read each other’s works, made suggestions to each other, recommended students and accumulated a tradition termed by some “the golden age of mathematics.”

Preface III is missing. During the interval Eudemus passed away, says Apollonius in IV, again supporting a view that Eudemus was senior over Apollonius. Prefaces IV–VII are more formal, omitting personal information and concentrating on summarizing the books. They are all addressed to a mysterious Attalus, a choice made “because”, as Apollonius writes to Attalus, “of your earnest desire to possess my works.” By that time a good many people at Pergamum had such a desire. Presumably, this Attalus was someone special, receiving copies of Apollonius’ masterpiece fresh from the author’s hand. One strong theory is that Attalus is Attalus II Philadelphus, 220-138 BC, general and defender of his brother’s kingdom (Eumenes II), co-regent on the latter’s illness in 160 BC, and heir to his throne and his widow in 158 BC. He and his brother were great patrons of the arts, expanding the library into international magnificence. The dates are consonant with those of Philonides, while Apollonius’ motive is consonant with Attalus' book-collecting initiative.

Apollonius sent to Attalus Prefaces V–VII. In Preface VII he describes Book VIII as “an appendix” ... “which I will take care to send you as speedily as possible.” There is no record that it was ever sent or ever completed. It may be missing from history because it was never in history, Apollonius having died before its completion.

 Published by Laiza Cruz

Source:: https://en.wikipedia.org/wiki/Apollonius_of_Perga