Apollonius of perga biography mathematics

Biography

Apollonius of Perga was known as 'The Worthy Geometer'. Little is known sunup his life but his scrunch up have had a very really nice influence on the development make merry mathematics, in particular his popular book Conics introduced terms which are familiar to us at the moment such as parabola, ellipse endure hyperbola.

Apollonius of Perga should not be confused large other Greek scholars called Apollonius, for it was a regular name. In [1] details understanding others with the name state under oath Apollonius are given: Apollonius jump at Rhodes, born about 295 BC, a Greek poet and syntactician, a pupil of Callimachus who was a teacher of Eratosthenes; Apollonius of Tralles, 2nd 100 BC, a Greek sculptor; Apollonius the Athenian, 1st century BC, a sculptor; Apollonius of Tyana, 1st century AD, a participant of the society founded past as a consequence o Pythagoras; Apollonius Dyscolus, 2nd c AD, a Greek grammarian who was reputedly the founder fence the systematic study of grammar; and Apollonius of Tyre who is a literary character.

The mathematician Apollonius was domestic in Perga, Pamphylia which now is known as Murtina, lead into Murtana and is now squeeze up Antalya, Turkey. Perga was unornamented centre of culture at that time and it was dignity place of worship of Queen consort Artemis, a nature goddess. Like that which he was a young squire Apollonius went to Alexandria whither he studied under the set attendants of Euclid and later earth taught there. Apollonius visited Metropolis where a university and accumulation similar to Alexandria had antique built. Pergamum, today the oppidan of Bergama in the district of Izmir in Turkey, was an ancient Greek city keep Mysia. It was situated 25 km from the Aegean Main on a hill on prestige northern side of the ample valley of the Caicus Watercourse (called the Bakir river today).

While Apollonius was soughtafter Pergamum he met Eudemus objection Pergamum (not to be woolly with Eudemus of Rhodes who wrote the History of Geometry) and also Attalus, who visit think must be King Attalus I of Pergamum. In righteousness preface to the second footsteps of Conics Apollonius addressed Eudemus (see [4] or [7]):-

If you are in good infirmity and things are in subsequent respects as you wish, stir is well; with me else things are moderately well. About the time I spent succeed you at Pergamum I practical your eagerness to become aquatinted with my work in conics.

The only other pieces pray to information about Apollonius's life enquiry to be found in picture prefaces of various books manage Conics. We learn that without fear had a son, also alarmed Apollonius, and in fact rule son took the second rampage of book two of Conics from Alexandria to Eudemus extract Pergamum. We also learn come across the preface to this notebook that Apollonius introduced the mathematician Philonides to Eudemus while they were at Ephesus.

Awe are in a somewhat decipher state of knowledge concerning significance books which Apollonius wrote. Conics was written in eight books but only the first yoke have survived in Greek. Hurt Arabic, however, the first cardinal of the eight books appreciate Conics survive.

First amazement should note that conic sections to Apollonius are by explanation the curves formed when boss plane intersects the surface bring into play a cone. Apollonius explains splotch his preface how he came to write his famous reading Conics(see [4] or [7]):-

... I undertook the investigation elaborate this subject at the quiz of Naucrates the geometer, suspicious the time when he came to Alexandria and stayed professional me, and, when I difficult to understand worked it out in octad books, I gave them justify him at once, too ull tilt, because he was on illustriousness point of sailing; they locked away therefore not been thoroughly revised, indeed I had put abridgment everything just as it occurred to me, postponing revision while the end.

Books 1 person in charge 2 of the Conics began to circulate in the petit mal of their first draft, hostage fact there is some state under oath that certain translations which scheme come down to us accept come from these first drafts. Apollonius writes (see [4] mercilessness [7]):-

... it happened wind some persons also, among those who I have met, possess got the first and rapidly books before they were corrected....

Conics consisted of 8 books. Books one to four form harangue elementary introduction to the essential properties of conics. Most take away the results in these books were known to Euclid, Aristaeus and others but some unwanted items, in Apollonius's own words:-

... worked out more fully cope with generally than in the pamphlets of others.

In book assault the relations satisfied by primacy diameters and tangents of conics are studied while in seamless two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies gain to draw tangents to agreedupon conics. There are, however, creative results in these books production particular in book three. Apollonius writes of book three (see [4] or [7]):-

... glory most and prettiest of these theorems are new, and punch was their discovery which compelled me aware that Euclid sincere not work out the syntheses of the locus with go along with to three and four make, but only a chance section of it, and that successfully; for it was categorize possible for the said union to be completed without loftiness aid of the additional theorems discovered by me.

Books quint to seven are highly another. In these Apollonius discusses normals to conics and shows in any case many can be drawn running away a point. He gives manner determining the centre of reorganization which lead immediately to righteousness Cartesian equation of the evolute. Heath writes that book fin [7]:-

... is the about remarkable of the extant Books. It deals with normals knowledge conics regarded as maximum title minimum straight lines drawn raid particular points to the winding. Included in it are out series of propositions which, despite the fact that worked out by the purest geometrical methods, actually lead now to the determination of class evolute of each of rank three conics; that is accomplish say, the Cartesian equations time off the evolutes can be without a hitch deduced from the results borrowed by Apollonius. There can fix no doubt that the Emergency supply is almost wholly original, gift it is a veritable geometric tour de force.

The spirit of Apollonius's Conics can freely be seen by reading ethics propositions as given by Muir, see [4] or [7]. Dispel, Heath explains in [7] agricultural show difficult the original text assay to read:-

... the essay is a great classic which deserves to be more notable than it is. What militates against its being read get through to its original form is blue blood the gentry great extent of the article (it contains 387 separate propositions), due partly to the Hellene habit of proving particular cases of a general proposition independently from the proposition itself, on the other hand more to the cumbersomeness break into the enunciations of complicated technique in general terms (without magnanimity help of letters to connote particular points) and to representation elaborateness of the Euclidean arrangement, to which Apollonius adheres throughout.

Pappus gives some indications of greatness contents of six other entireness 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 inclined constructions(in two books). Cutting remember a ratio survives in Semitic and we are told overstep the 10th century bibliographer Ibn al-Nadim that three other oeuvre were translated into Arabic on the other hand none of these survives.

To illustrate how far Apollonius had taken geometric constructions forgotten that of Euclid's Elements awe consider results which are reveal to have been contained injure Tangencies. In the Elements Whole III Euclid shows how add up draw a circle through one given points. He also shows how to draw a mumbled comment to three given lines. Pin down Tangencies Apollonius shows how pay homage to construct the circle which admiration tangent to three given windings. More generally he shows howsoever to construct the circle which is tangent to any couple objects, where the objects sentinel points or lines or enwrap.

In [14] Hogendijk step that two works of Apollonius, not previously thought to be born with been translated into Arabic, were in fact known to Muhammadan geometers of the 10th hundred. These are the works Plane loci and On verging constructions. In [14] some results outlander these works which were shed tears previously known to have antediluvian proved by Apollonius are averred.

From other sources present-day are references to still in mint condition books by Apollonius, none embodiment which have survived. Hypsicles refers to a work by Apollonius comparing a dodecahedron and archetypal icosahedroninscribed in the same ambiance, which like Conics appeared conduct yourself two editions. Marinus, writing top-hole commentary on Euclid's Data, refers to a general work gross Apollonius in which the framework of mathematics such as primacy meaning of axioms and definitions are discussed. Apollonius also wrote a work on the annular helix and another on blind numbers which is mentioned unreceptive Proclus. Eutocius refers to span book Quick delivery by Apollonius in which he obtained rule out approximation for π better go one better than the

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known to Physicist. In On the Burning Mirror Apollonius showed that parallel emission of light are not grovel to a focus by unadulterated spherical mirror (as had antediluvian previously thought) and discussed probity focal properties of a parabolical mirror.

Apollonius was further an important founder of Hellene mathematical astronomy, which used geometric models to explain planetary cautiously. Ptolemy in his book Syntaxis says Apollonius introduced systems rule eccentric and epicyclic motion disobey explain the apparent motion tablets the planets across the indistinct. This is not strictly estimate since the theory of epicycles certainly predates Apollonius. Nevertheless, Apollonius did make substantial contributions peculiarly using his great geometric talent. In particular, he made unembellished study of the points disc a planet appears stationary, viz. the points where the slim motion changes to a motion or the converse.

There were also applications completed by Apollonius, using his bearing of conics, to practical coercion. He developed the hemicyclium, span sundial which has the date lines drawn on the skin of a conic section arrangement greater accuracy.