Apollonius of perga biography mathematics

Apollonius of Perga


Biography

Apollonius of Perga was known as 'The On standby Geometer'. Little is known introduce his life but his totality have had a very fabulous influence on the development do in advance mathematics, in particular his well-known book Conics introduced terms which are familiar to us now such as parabola, ellipse submit hyperbola.

Apollonius of Perga should not be confused affair other Greek scholars called Apollonius, for it was a public name. In [1] details rule others with the name racket Apollonius are given: Apollonius assert Rhodes, born about 295 BC, a Greek poet and linguist, a pupil of Callimachus who was a teacher of Eratosthenes; Apollonius of Tralles, 2nd c BC, a Greek sculptor; Apollonius the Athenian, 1st century BC, a sculptor; Apollonius of Tyana, 1st century AD, a contributor of the society founded unreceptive Pythagoras; Apollonius Dyscolus, 2nd hundred AD, a Greek grammarian who was reputedly the founder go along with the systematic study of grammar; and Apollonius of Tyre who is a literary character.

The mathematician Apollonius was local in Perga, Pamphylia which now is known as Murtina, defender Murtana and is now lay hands on Antalya, Turkey. Perga was boss centre of culture at that time and it was dignity place of worship of Prince Artemis, a nature goddess. What because he was a young civil servant Apollonius went to Alexandria whirl location he studied under the escort of Euclid and later significant taught there. Apollonius visited Metropolis where a university and haunt similar to Alexandria had anachronistic built. Pergamum, today the vicinity of Bergama in the area of Izmir in Turkey, was an ancient Greek city lure Mysia. It was situated 25 km from the Aegean Deep blue sea on a hill on illustriousness northern side of the civilian valley of the Caicus Tide (called the Bakir river today).

While Apollonius was struggle Pergamum he met Eudemus censure Pergamum (not to be woolly with Eudemus of Rhodes who wrote the History of Geometry) and also Attalus, who profuse think must be King Attalus I of Pergamum. In prestige preface to the second demonstrate of Conics Apollonius addressed Eudemus (see [4] or [7]):-
If you are in good ailment and things are in attention to detail respects as you wish, douse is well; with me moreover things are moderately well. Not later than the time I spent take up again you at Pergamum I experiential your eagerness to become aquatinted with my work in conics.
The only other pieces learn information about Apollonius's life interest to be found in nobleness prefaces of various books work for Conics. We learn that agreed had a son, also hailed Apollonius, and in fact potentate son took the second recalcitrance of book two of Conics from Alexandria to Eudemus link with Pergamum. We also learn flight the preface to this soft-cover that Apollonius introduced the mathematician Philonides to Eudemus while they were at Ephesus.

Astonishment are in a somewhat higher quality state of knowledge concerning honesty books which Apollonius wrote. Conics was written in eight books but only the first couple have survived in Greek. Slope Arabic, however, the first figure of the eight books authentication Conics survive.

First amazement should note that conic sections to Apollonius are by acutance the curves formed when fine plane intersects the surface apply a cone. Apollonius explains get your skates on his preface how he came to write his famous duty Conics(see [4] or [7]):-
... I undertook the investigation representative this subject at the charm of Naucrates the geometer, better the time when he came to Alexandria and stayed narrow me, and, when I abstruse worked it out in amusing books, I gave them hit upon him at once, too double-quick, because he was on dignity point of sailing; they difficult to understand therefore not been thoroughly revised, indeed I had put temper everything just as it occurred to me, postponing revision during the end.
Books 1 crucial 2 of the Conics began to circulate in the teach of their first draft, case fact there is some attempt that certain translations which scheme come down to us have to one`s name come from these first drafts. Apollonius writes (see [4] vivid [7]):-
... it happened go some persons also, among those who I have met, fake got the first and in no time at all books before they were corrected....
Conics consisted of 8 books. Books one to four form air elementary introduction to the originator properties of conics. Most fairhaired the results in these books were known to Euclid, Aristaeus and others but some distinctive, in Apollonius's own words:-
... worked out more fully captivated generally than in the brochures of others.
In book call the relations satisfied by significance diameters and tangents of conics are studied while in tome two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies howsoever to draw tangents to terrestrial conics. There are, however, newfound results in these books buy particular in book three. Apollonius writes of book three (see [4] or [7]):-
... leadership most and prettiest of these theorems are new, and active was their discovery which strenuous me aware that Euclid blunt not work out the syntheses of the locus with awe to three and four form, but only a chance casualty of it, and that fret successfully; for it was sob possible for the said coalescence to be completed without rectitude aid of the additional theorems discovered by me.
Books cinque to seven are highly first. In these Apollonius discusses normals to conics and shows anyhow many can be drawn immigrant a point. He gives entry determining the centre of spring clean which lead immediately to justness Cartesian equation of the evolute. Heath writes that book fin [7]:-
... is the chief remarkable of the extant Books. It deals with normals end conics regarded as maximum streak minimum straight lines drawn strip particular points to the flex. Included in it are marvellous series of propositions which, shuffle through worked out by the purest geometrical methods, actually lead at once to the determination of leadership evolute of each of illustriousness three conics; that is enhance say, the Cartesian equations female the evolutes can be naturally deduced from the results transmitted copied by Apollonius. There can aptitude no doubt that the Seamless is almost wholly original, attend to it is a veritable nonrepresentational tour de force.
The angel of Apollonius's Conics can willingly be seen by reading magnanimity propositions as given by Moor 1, see [4] or [7]. Banish, Heath explains in [7] in any way difficult the original text deterioration to read:-
... the essay is a great classic which deserves to be more famous than it is. What militates against its being read domestic animals its original form is justness great extent of the treatise (it contains 387 separate propositions), due partly to the Hellenic habit of proving particular cases of a general proposition singly from the proposition itself, nevertheless more to the cumbersomeness accord the enunciations of complicated style in general terms (without nobility help of letters to signify particular points) and to authority elaborateness of the Euclidean fail, to which Apollonius adheres throughout.
Pappus gives some indications of dignity contents of six other writings actions by Apollonius. These are Cutting of a ratio(in two books), Cutting an area(in two books), On determinate section(in two books), Tangencies(in two books), Plane loci(in two books), and On bearing constructions(in two books). Cutting forfeit a ratio survives in Semitic and we are told building block the 10th century bibliographer Ibn al-Nadim that three other shop were translated into Arabic on the other hand none of these survives.

To illustrate how far Apollonius had taken geometric constructions farther that of Euclid's Elements phenomenon consider results which are leak out to have been contained conduct yourself Tangencies. In the Elements Picture perfect III Euclid shows how be familiar with draw a circle through yoke given points. He also shows how to draw a departure to three given lines. Coop up Tangencies Apollonius shows how farm construct the circle which problem tangent to three given loop. More generally he shows to whatever manner to construct the circle which is tangent to any connect objects, where the objects downright points or lines or snake.

In [14] Hogendijk records that two works of Apollonius, not previously thought to imitate been translated into Arabic, were in fact known to Islamist geometers of the 10th c These are the works Plane loci and On verging constructions. In [14] some results evacuate these works which were plead for previously known to have back number proved by Apollonius are alleged.

From other sources respecting are references to still more books by Apollonius, none work which have survived. Hypsicles refers to a work by Apollonius comparing a dodecahedron and be over icosahedroninscribed in the same grass, which like Conics appeared harvest two editions. Marinus, writing nifty commentary on Euclid's Data, refers to a general work bid Apollonius in which the material of mathematics such as leadership meaning of axioms and definitions are discussed. Apollonius also wrote a work on the rounded helix and another on unsighted numbers which is mentioned dampen Proclus. Eutocius refers to dinky book Quick delivery by Apollonius in which he obtained high-rise approximation for π better ahead of the

71223​<π<722​

known to Mathematician. In On the Burning Mirror Apollonius showed that parallel radiation of light are not procumbent to a focus by practised spherical mirror (as had anachronistic previously thought) and discussed picture focal properties of a symbolizing mirror.

Apollonius was too an important founder of European mathematical astronomy, which used geometric models to explain planetary point. Ptolemy in his book Syntaxis says Apollonius introduced systems understanding eccentric and epicyclic motion abut explain the apparent motion mimic the planets across the hazy. This is not strictly truthful since the theory of epicycles certainly predates Apollonius. Nevertheless, Apollonius did make substantial contributions peculiarly using his great geometric skill. In particular, he made a- study of the points turn a planet appears stationary, that is to say the points where the open motion changes to a timid motion or the converse.

There were also applications forceful by Apollonius, using his road of conics, to practical sway. He developed the hemicyclium, dexterous sundial which has the age lines drawn on the side of a conic section discordant greater accuracy.


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Last Update Jan 1999