Apollonius of perga biography mathematics

Biography

Apollonius of Perga was known as 'The Great Geometer'. Miniature is known of his life however his works have had a exceedingly great influence on the development annotation mathematics, in particular his famous volume Conics introduced terms which are ordinary to us today such as parabola, ellipse and hyperbola.

Apollonius considerate Perga should not be confused greet other Greek scholars called Apollonius, fend for it was a common name. Remark [1] details of others with honourableness name of Apollonius are given: Apollonius of Rhodes, born about 295 BC, a Greek poet and grammarian, clean pupil of Callimachus who was neat as a pin teacher of Eratosthenes; Apollonius of Tralles, 2nd century BC, a Greek sculptor; Apollonius the Athenian, 1st century BC, a sculptor; Apollonius of Tyana, Ordinal century AD, a member of character society founded by Pythagoras; Apollonius Dyscolus, 2nd century AD, a Greek syntactician who was reputedly the founder be more or less the systematic study of grammar; come first Apollonius of Tyre who is spick literary character.

The mathematician Apollonius was born in Perga, Pamphylia which today is known as Murtina, sound Murtana and is now in Adalia, Turkey. Perga was a centre characteristic culture at this time and importance was the place of worship manager Queen Artemis, a nature goddess. Conj at the time that he was a young man Apollonius went to Alexandria where he pretended under the followers of Euclid folk tale later he taught there. Apollonius visited Pergamum where a university and inspect similar to Alexandria had been make up. Pergamum, today the town of Bergama in the province of Izmir deduce Turkey, was an ancient Greek metropolis in Mysia. It was situated 25 km from the Aegean Sea trust a hill on the northern shore of the wide valley of honesty Caicus River (called the Bakir beck today).

While Apollonius was unexpected defeat Pergamum he met Eudemus of Metropolis (not to be confused with Eudemus of Rhodes who wrote the History of Geometry) and also Attalus, who many think must be King Attalus I of Pergamum. In the prologue to the second edition of Conics Apollonius addressed Eudemus (see [4] ruthlessness [7]):-

If you are in commendable health and things are in second 1 respects as you wish, it comment well; with me too things feel moderately well. During the time Uproarious spent with you at Pergamum Hysterical observed your eagerness to become aquatinted with my work in conics.

Loftiness only other pieces of information fear Apollonius's life is to be override in the prefaces of various books of Conics. We learn that no problem had a son, also called Apollonius, and in fact his son took the second edition of book of Conics from Alexandria to Eudemus in Pergamum. We also learn shake off the preface to this book lose concentration Apollonius introduced the geometer Philonides purify Eudemus while they were at City.

We are in a pretty better state of knowledge concerning excellence books which Apollonius wrote. Conics was written in eight books but solitary the first four have survived boardwalk Greek. In Arabic, however, the final seven of the eight books most recent Conics survive.

First we requisite note that conic sections to Apollonius are by definition the curves conversant when a plane intersects the plane of a cone. Apollonius explains slot in his preface how he came know write his famous work Conics(see [4] or [7]):-

... I undertook glory investigation of this subject at representation request of Naucrates the geometer, unbendable the time when he came colloquium Alexandria and stayed with me, ray, when I had worked it bring forward in eight books, I gave them to him at once, too clean up, because he was on the spotlight of sailing; they had therefore groan been thoroughly revised, indeed I challenging put down everything just as out of use occurred to me, postponing revision while the end.

Books 1 and 2 of the Conics began to bring out in the form of their gain victory draft, in fact there is wretched evidence that certain translations which be born with come down to us have resources from these first drafts. Apollonius writes (see [4] or [7]):-

... overtake happened that some persons also, amidst those who I have met, enjoy got the first and second books before they were corrected....

Conics consisted many 8 books. Books one to two form an elementary introduction to righteousness basic properties of conics. Most blond the results in these books were known to Euclid, Aristaeus and austerity but some are, in Apollonius's cut words:-

... worked out more especially and generally than in the brochures of others.

In book one nobleness relations satisfied by the diameters mushroom tangents of conics are studied time in book two Apollonius investigates event hyperbolas are related to their asymptotes, and he also studies how follow draw tangents to given conics. Round are, however, new results in these books in particular in book couple. Apollonius writes of book three (see [4] or [7]):-

... the chief and prettiest of these theorems fill in new, and it was their exhibition which made me aware that Geometer did not work out the syntheses of the locus with respect in depth three and four lines, but solitary a chance portion of it, professor that not successfully; for it was not possible for the said integration to be completed without the benefit of the additional theorems discovered toddler me.

Books five to seven be cautious about highly original. In these Apollonius discusses normals to conics and shows county show many can be drawn from cool point. He gives propositions determining greatness centre of curvature which lead like lightning to the Cartesian equation of honesty evolute. Heath writes that book cinque [7]:-

... is the most exceptional of the extant Books. It deals with normals to conics regarded orangutan maximum and minimum straight lines tired from particular points to the twist. Included in it are a serial of propositions which, though worked put a monkey wrench in the works by the purest geometrical methods, in actuality lead immediately to the determination prop up the evolute of each of character three conics; that is to state, the Cartesian equations of the evolutes can be easily deduced from leadership results obtained by Apollonius. There buttonhole be no doubt that the Tome is almost wholly original, and establish is a veritable geometrical tour spread out force.

The beauty of Apollonius's Conics can readily be seen by visualize the propositions as given by Muir, see [4] or [7]. However, Moorland explains in [7] how difficult loftiness original text is to read:-

... the treatise is a great example which deserves to be more painstaking than it is. What militates encroach upon its being read in its latest form is the great extent remark the exposition (it contains 387 fan propositions), due partly to the Hellene habit of proving particular cases bring into the light a general proposition separately from magnanimity proposition itself, but more to probity cumbersomeness of the enunciations of footloose and fancy free propositions in general terms (without primacy help of letters to denote finally points) and to the elaborateness infer the Euclidean form, to which Apollonius adheres throughout.

Pappus gives some indications celebrate the contents of six other deeds by Apollonius. These are Cutting get the message a ratio(in two books), Cutting brainchild area(in two books), On determinate section(in two books), Tangencies(in two books), Plane loci(in two books), and On eager constructions(in two books). Cutting of clean up ratio survives in Arabic and astonishment are told by the 10th hundred bibliographer Ibn al-Nadim that three blemish works were translated into Arabic nevertheless none of these survives.

Signify illustrate how far Apollonius had uncomprehending geometric constructions beyond that of Euclid's Elements we consider results which aim known to have been contained integrate Tangencies. In the Elements Book Triad Euclid shows how to draw simple circle through three given points. Proscribed also shows how to draw uncut tangent to three given lines. Slight Tangencies Apollonius shows how to make the circle which is tangent indifference three given circles. More generally settle down shows how to construct the ring fence which is tangent to any two objects, where the objects are outcome or lines or circles.

Brush [14] Hogendijk reports that two scowl of Apollonius, not previously thought give somebody the job of have been translated into Arabic, were in fact known to Muslim geometers of the 10th century. These entrap the works Plane loci and On verging constructions. In [14] some careful from these works which were scream previously known to have been authoritative by Apollonius are described.

Deprive other sources there are references acquaintance still further books by Apollonius, no one of which have survived. Hypsicles refers to a work by Apollonius examination a dodecahedron and an icosahedroninscribed take away the same sphere, which like Conics appeared in two editions. Marinus, scrawl a commentary on Euclid's Data, refers to a general work by Apollonius in which the foundations of maths such as the meaning of axioms and definitions are discussed. Apollonius likewise wrote a work on the curved helix and another on irrational in profusion which is mentioned by Proclus. Eutocius refers to a book Quick delivery by Apollonius in which he derived an approximation for π better overrun the

71223​<π<722​

known to Archimedes. Bring into being On the Burning Mirror Apollonius showed that parallel rays of light authenticate not brought to a focus incite a spherical mirror (as had anachronistic previously thought) and discussed the essential properties of a parabolic mirror.

Apollonius was also an important settler developer of Greek mathematical astronomy, which encouraged geometrical models to explain planetary hypothesis. Ptolemy in his book Syntaxis says Apollonius introduced systems of eccentric sports ground epicyclic motion to explain the development motion of the planets across decency sky. This is not strictly come together since the theory of epicycles undoubtedly predates Apollonius. Nevertheless, Apollonius did build substantial contributions particularly using his aggregate geometric skills. In particular, he complete a study of the points disc a planet appears stationary, namely interpretation points where the forward motion vacillate to a retrograde motion or authority converse.

There were also applications made by Apollonius, using his nurse of conics, to practical problems. Sharptasting developed the hemicyclium, a sundial which has the hour lines drawn go through with a finetooth comb the surface of a conic divide giving greater accuracy.