# Apollonius of Perga

Apollonius of Perga (also: Apollonius Pergaeus; * ca 262 BC in Perga, † about 190 BC in Alexandria ) was a Greek mathematician, known for his book on conic sections.

## Life

About his life little is known. He studied and worked in Alexandria under Ptolemy III. and Ptolemy IV and later lived for a short time in Pergamum, where a large library was like in Alexandria ( one Eudemus of Pergamum and the visit are in his book conics mentioned). Apollonius mentions in his conic sections and his son of the same name, which he sent with book 2 of conic sections to Eudemos to Pergamum. The conic sections are dedicated to Eudemus or death of a Attalos of Pergamon (probably the king Attalus I ).

The lunar crater Apollonius is named after him.

## Work

In his most important work Konika ( " About conic sections " ), he devoted himself depth research on conic sections, limit regulations and minimum-maximum problems. He showed that the four different conic sections ( ellipse, circle, parabola, and hyperbola ) whose names and definitions he introduced, derived from the same general cone type. According to Apollonius of Perge and the circle of Apollonius and the Apollonian problem are named.

In astronomy was Apollonius in the epicycle theory and showed its connection to the eccentric theory. He explained so that the decline in planetary motion and the movement of the moon. His theories were addressed among others by Hipparchus and Ptolemy and developed. He should have also developed an improved sundial with hour lines on conic sections.

Long books V to VIII of the conic sections were considered lost ( and various mathematicians of the 17th century made efforts to reconstruction, as Franciscus Maurolicus ) to place in the Laurentian Library in Florence an Arabic manuscript ( Thabit ibn Qurra of translation ) with the -lost books V to VII was, which was published by Giovanni Alfonso Borelli and Abraham Ecchellensis 1661 in Florence as a translation. Book VIII is lost.

Book 1 to 4 treat as an introduction to elementary theory of conic sections, and the material was largely already known, Euclid ( as Apollonius himself writes ), but book 3 also contains new results. From Book 1 and 2, it seems to have given prior versions, was circulated to Apollonius, on which some of the surviving manuscripts are based. Book 5-7 contain completely new, otherwise unknown originary material of Apollonius, for example, to normal at conics in book 5, which anticipate the later construction of the evolute of conics. In the representation Apollonius follows the style of Euclid's Elements.

Pappus of Alexandria mentions the titles of other works of Apollonius. Of these, only excerpts in Pappus, Proclus and others have survived, apart from an Arabic manuscript of De rationis sectione from the 10th century ( more Arabic Manuscripts should have existed according to Ibn al - Nadim, but are not preserved). Pappus mentions De spatii sectione ( section of a surface ), De sectione determinata, De Tactionibus ( About touches, Apollo African problem), De Inclinationibus ( inclinations ), De locis Planis ( level loci ), each in two books. Claudius Ptolemy gave two theorems from a lost astronomical book by Apollonius.

More books by Apollonius are only known title after: Hypsicles mentions a work in which Apollonius comparing a sphere inscribed dodecahedron and icosahedron, Marinos mentioned in a Euclid - comment a general work of Apollonius on the foundations of mathematics (meaning of axioms, definitions and others), according to Proclus, he wrote a book about irrational numbers, and on the helix on a cylinder. He is said to have written a book on burning mirrors and have given after Eutocius in a book a better approximation as Archimedes.

From Eutocius comes a commentary on the first four books of conics.