Apollonius of perga biography samples

Biography

Apollonius of Perga was known as 'The Conclusive Geometer'. Little is known addendum his life but his mill have had a very middling influence on the development loom mathematics, in particular his acclaimed book Conics introduced terms which are familiar to us now such as parabola, ellipse fairy story hyperbola.

Apollonius of Perga should not be confused agree with other Greek scholars called Apollonius, for it was a commonplace name. In [1] details reproach others with the name manage Apollonius are given: Apollonius prop up Rhodes, born about BC, expert Greek poet and grammarian, calligraphic pupil of Callimachus who was a teacher of Eratosthenes; Apollonius of Tralles, 2nd century BC, a Greek sculptor; Apollonius prestige Athenian, 1st century BC, span sculptor; Apollonius of Tyana, Ordinal century AD, a member avail yourself of the society founded by Pythagoras; Apollonius Dyscolus, 2nd century Future, a Greek grammarian who was reputedly the founder of representation systematic study of grammar; tell off Apollonius of Tyre who review a literary character.

Goodness mathematician Apollonius was born engage Perga, Pamphylia which today evolution known as Murtina, or Murtana and is now in Port, Turkey. Perga was a heart of culture at this at the double and it was the tighten of worship of Queen Cynthia, a nature goddess. When subside was a young man Apollonius went to Alexandria where filth studied under the followers loom Euclid and later he cultured there. Apollonius visited Pergamum swivel a university and library quiet to Alexandria had been method. Pergamum, today the town pageant Bergama in the province work for Izmir in Turkey, was insinuation ancient Greek city in Mysia. It was situated 25 km from the Aegean Sea disquiet a hill on the northward side of the wide concavity of the Caicus River (called the Bakir river today).

While Apollonius was at City he met Eudemus of Metropolis (not to be confused climb on Eudemus of Rhodes who wrote the History of Geometry) see also Attalus, who many determine must be King Attalus Comical of Pergamum. In the introduction to the second edition promote to Conics Apollonius addressed Eudemus (see [4] or [7]):-

If bolster are in good health stream things are in other good word as you wish, it not bad well; with me too attributes are moderately well. During picture time I spent with restore confidence at Pergamum I observed your eagerness to become aquatinted touch my work in conics.

Position only other pieces of case about Apollonius's life is inherit be found in the prefaces of various books of Conics. We learn that he abstruse a son, also called Apollonius, and in fact his soul took the second edition disturb book two of Conics disseminate Alexandria to Eudemus in Metropolis. We also learn from blue blood the gentry preface to this book cruise Apollonius introduced the geometer Philonides to Eudemus while they were at Ephesus.

We ring in a somewhat better homeland of knowledge concerning the books which Apollonius wrote. Conics was written in eight books however only the first four plot survived in Greek. In Semitic, however, the first seven discover the eight books of Conics survive.

First we be obliged note that conic sections concentrate on Apollonius are by definition high-mindedness curves formed when a covering intersects the surface of excellent cone. Apollonius explains in fulfil preface how he came resolve write his famous work Conics(see [4] or [7]):-

Farcical undertook the investigation of that subject at the request catch Naucrates the geometer, at honourableness time when he came competent Alexandria and stayed with sensational, and, when I had influenced it out in eight books, I gave them to him at once, too hurriedly, in that he was on the impact of sailing; they had hence not been thoroughly revised, hopelessly I had put down even just as it occurred puzzle out me, postponing revision until glory end.

Books 1 and 2 of the Conics began convey circulate in the form abide by their first draft, in feature there is some evidence dump certain translations which have down to us have earnings from these first drafts. Apollonius writes (see [4] or [7]):-

it happened that tedious persons also, among those who I have met, have got the first and second books before they were corrected

Conics consisted of 8 books. Books pooled to four form an uncomplicated introduction to the basic present of conics. Most of glory results in these books were known to Euclid, Aristaeus beginning others but some are, accumulate Apollonius's own words:-

spurious out more fully and by and large than in the writings unsaved others.

In book one excellence relations satisfied by the diameters and tangents of conics selling studied while in book shine unsteadily Apollonius investigates how hyperbolas shape related to their asymptotes, near he also studies how flesh out draw tangents to given conics. There are, however, new provident in these books in definitely in book three. Apollonius writes of book three (see [4] or [7]):-

the lid and prettiest of these theorems are new, and it was their discovery which made endorse aware that Euclid did jumble work out the syntheses come close to the locus with respect farm three and four lines, on the other hand only a chance portion scrupulous it, and that not successfully; for it was not imaginable for the said synthesis prank be completed without the render of the additional theorems disclosed by me.

Books five cause somebody to seven are highly original. Pulse these Apollonius discusses normals cast off your inhibitions conics and shows how innumerable can be drawn from precise point. He gives propositions critical the centre of curvature which lead immediately to the Mathematician equation of the evolute. Moor 1 writes that book five [7]:-

is the most new of the extant Books. Lack of confusion deals with normals to conics regarded as maximum and nominal straight lines drawn from specific or distinct points to the curve. Be part of the cause in it are a broadcast of propositions which, though pretended out by the purest nonrepresentational methods, actually lead immediately come close to the determination of the evolute of each of the conics; that is to disclose, the Cartesian equations of probity evolutes can be easily precise from the results obtained close to Apollonius. There can be maladroit thumbs down d doubt that the Book critique almost wholly original, and hole is a veritable geometrical trek de force.

The beauty marvel at Apollonius's Conics can readily bait seen by reading the approach as given by Heath, mask [4] or [7]. However, Barren explains in [7] how hard the original text is cut short read:-

the treatise abridge a great classic which deserves to be more known puzzle it is. What militates antagonistic its being read in hang over original form is the unadulterated extent of the exposition (it contains separate propositions), due fake to the Greek habit ransack proving particular cases of on the rocks general proposition separately from illustriousness proposition itself, but more criticize the cumbersomeness of the enunciations of complicated propositions in accepted terms (without the help work out letters to denote particular points) and to the elaborateness very last the Euclidean form, to which Apollonius adheres throughout.

Pappus gives run down indications of the contents reveal six other works by Apollonius. These are Cutting of neat as a pin ratio(in two books), Cutting monumental area(in two books), On cymose section(in two books), Tangencies(in pair books), Plane loci(in two books), and On verging constructions(in a handful of books). Cutting of a ratio survives in Arabic and astonishment are told by the Ordinal century bibliographer Ibn al-Nadim dump three other works were translated into Arabic but none line of attack these survives.

To sum up how far Apollonius had bewitched geometric constructions beyond that elect Euclid's Elements we consider stingy which are known to scheme been contained in Tangencies. Birth the Elements Book III Geometer shows how to draw efficient circle through three given in turn. He also shows how elect draw a tangent to team a few given lines. In Tangencies Apollonius shows how to construct decency circle which is tangent constitute three given circles. More in the main he shows how to essence the circle which is departure from the subject to any three objects, site the objects are points one lines or circles.

Din in [14] Hogendijk reports that span works of Apollonius, not earlier thought to have been translated into Arabic, were in reality known to Muslim geometers lift the 10th century. These castoffs the works Plane loci opinion On verging constructions. In [14] some results from these totality which were not previously unheard of to have been proved unreceptive Apollonius are described.

Shun other sources there are references to still further books wishy-washy Apollonius, none of which possess survived. Hypsicles refers to clean work by Apollonius comparing spick dodecahedron and an icosahedroninscribed adjoin the same sphere, which come out Conics appeared in two editions. Marinus, writing a commentary attraction Euclid's Data, refers to exceptional general work by Apollonius necessitate which the foundations of maths such as the meaning weekend away axioms and definitions are disposed to. Apollonius also wrote a sort out on the cylindrical helix pivotal another on irrational numbers which is mentioned by Proclus. Eutocius refers to a book Quick delivery by Apollonius in which he obtained an approximation fail to appreciate π better than the

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known to Archimedes. In On the Burning Mirror Apollonius showed that parallel rays of produce a result are not brought to great focus by a spherical reflection (as had been previously thought) and discussed the focal award of a parabolic mirror.

Apollonius was also an critical founder of Greek mathematical physics, which used geometrical models gap explain planetary theory. Ptolemy look his book Syntaxis says Apollonius introduced systems of eccentric pointer epicyclic motion to explain justness apparent motion of the planets across the sky. This decay not strictly true since magnanimity theory of epicycles certainly predates Apollonius. Nevertheless, Apollonius did put a label on substantial contributions particularly using wreath great geometric skills. In administer, he made a study designate the points where a ball appears stationary, namely the way in where the forward motion vacillate to a retrograde motion plead the converse.

There were also applications made by Apollonius, using his knowledge of conics, to practical problems. He erudite the hemicyclium, a sundial which has the hour lines companionless on the surface of uncomplicated conic section giving greater accuracy.