Ancient Greek geometer and astronomer noted for his writings on conic sections. Russian Wikipedia. Apollonii Pergei Opera detail. Detalle de una obra de representanto a Apolonio de Perge Spanish. Swedish Wikipedia. Italian Wikipedia.

Author: | Tujind Kilabar |

Country: | Iran |

Language: | English (Spanish) |

Genre: | Personal Growth |

Published (Last): | 22 December 2005 |

Pages: | 135 |

PDF File Size: | 10.28 Mb |

ePub File Size: | 10.89 Mb |

ISBN: | 391-1-19400-683-4 |

Downloads: | 30692 |

Price: | Free* [*Free Regsitration Required] |

Uploader: | Zoloshakar |

His works had a very great influence on the development of mathematics and his famous book Conics introduced the terms parabola, ellipse and hyperbola.

View one larger picture. Little is known of his life but his works have had a very great influence on the development of mathematics, in particular his famous book Conics introduced terms which are familiar to us today such as parabola , ellipse and hyperbola.

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

Perga was a centre of culture at this time and it was the place of worship of Queen Artemis, a nature goddess. When he was a young man Apollonius went to Alexandria where he studied under the followers of Euclid and later he taught there. Apollonius visited Pergamum where a university and library similar to Alexandria had been built.

Pergamum, today the town of Bergama in the province of Izmir in Turkey, was an ancient Greek city in Mysia. It was situated 25 km from the Aegean Sea on a hill on the northern side of the wide valley of the Caicus River called the Bakir river today. In the preface to the second edition of Conics Apollonius addressed Eudemus see [ 4 ] or [ 7 ] :- If you are in good health and things are in other respects as you wish, it is well; with me too things are moderately well.

During the time I spent with you at Pergamum I observed your eagerness to become aquatinted with my work in conics. The only other pieces of information about Apollonius's life is to be found in the prefaces of various books of Conics. We learn that he had a son, also called Apollonius, and in fact his son took the second edition of book two of Conics from Alexandria to Eudemus in Pergamum. We also learn from the preface to this book that Apollonius introduced the geometer Philonides to Eudemus while they were at Ephesus.

We are in a somewhat better state of knowledge concerning the books which Apollonius wrote. Conics was written in eight books but only the first four have survived in Greek. In Arabic, however, the first seven of the eight books of Conics survive. First we should note that conic sections to Apollonius are by definition the curves formed when a plane intersects the surface of a cone.

Apollonius explains in his preface how he came to write his famous work Conics see [ 4 ] or [ 7 ] I undertook the investigation of this subject at the request of Naucrates the geometer, at the time when he came to Alexandria and stayed with me, and, when I had worked it out in eight books, I gave them to him at once, too hurriedly, because he was on the point of sailing; they had therefore not been thoroughly revised, indeed I had put down everything just as it occurred to me, postponing revision until the end.

Books 1 and 2 of the Conics began to circulate in the form of their first draft, in fact there is some evidence that certain translations which have come down to us have come from these first drafts. Apollonius writes see [ 4 ] or [ 7 ] Conics consisted of 8 books.

Books one to four form an elementary introduction to the basic properties of conics. Most of the results in these books were known to Euclid , Aristaeus and others but some are, in Apollonius's own words In book one the relations satisfied by the diameters and tangents of conics are studied while in book two Apollonius investigates how hyperbolas are related to their asymptotes , and he also studies how to draw tangents to given conics.

There are, however, new results in these books in particular in book three. Apollonius writes of book three see [ 4 ] or [ 7 ] Books five to seven are highly original.

In these Apollonius discusses normals to conics and shows how many can be drawn from a point. He gives propositions determining the centre of curvature which lead immediately to the Cartesian equation of the evolute.

Heath writes that book five [ 7 ] It deals with normals to conics regarded as maximum and minimum straight lines drawn from particular points to the curve. Included in it are a series of propositions which, though worked out by the purest geometrical methods, actually lead immediately to the determination of the evolute of each of the three conics; that is to say, the Cartesian equations of the evolutes can be easily deduced from the results obtained by Apollonius.

There can be no doubt that the Book is almost wholly original, and it is a veritable geometrical tour de force. The beauty of Apollonius's Conics can readily be seen by reading the propositions as given by Heath , see [ 4 ] or [ 7 ]. However, Heath explains in [ 7 ] how difficult the original text is to read What militates against its being read in its original form is the great extent of the exposition it contains separate propositions , due partly to the Greek habit of proving particular cases of a general proposition separately from the proposition itself, but more to the cumbersomeness of the enunciations of complicated propositions in general terms without the help of letters to denote particular points and to the elaborateness of the Euclidean form, to which Apollonius adheres throughout.

Pappus gives some indications of the contents of six other works 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 verging constructions in two books. Cutting of a ratio survives in Arabic and we are told by the 10 th century bibliographer Ibn al-Nadim that three other works were translated into Arabic but none of these survives.

To illustrate how far Apollonius had taken geometric constructions beyond that of Euclid 's Elements we consider results which are known to have been contained in Tangencies. He also shows how to draw a tangent to three given lines. In Tangencies Apollonius shows how to construct the circle which is tangent to three given circles. More generally he shows how to construct the circle which is tangent to any three objects, where the objects are points or lines or circles.

In [ 14 ] Hogendijk reports that two works of Apollonius, not previously thought to have been translated into Arabic, were in fact known to Muslim geometers of the 10 th century. These are the works Plane loci and On verging constructions. In [ 14 ] some results from these works which were not previously known to have been proved by Apollonius are described. From other sources there are references to still further books by Apollonius, none of which have survived.

Hypsicles refers to a work by Apollonius comparing a dodecahedron and an icosahedron inscribed in the same sphere, which like Conics appeared in two editions. Marinus , writing a commentary on Euclid 's Data , refers to a general work by Apollonius in which the foundations of mathematics such as the meaning of axioms and definitions are discussed.

Apollonius also wrote a work on the cylindrical helix and another on irrational numbers which is mentioned by Proclus. References show. Biography in Encyclopaedia Britannica. Oxford, Trudy Vyp. Nauka Od. Nauka N. A V Dorofeeva, Apollonius ca. Russian , Mat. Exact Sci. O Neugebauer, The equivalence of eccentric and epicyclic motion according to Apollonius, Scripta Math.

O Neugebauer, Apollonius' planetary theory, Comm. Pure Appl. B A Rozenfeld, Inversion with respect to the circle and inversion with respect to the ellipse, the hyperbola and the parabola in the 'Conic sections' of Apollonius Russian , Istor.

Storia Sci. Torino Cl. Additional Resources show. Honours show. Cross-references show.

CONDE DE GOBINEAU ENSAYO SOBRE LA DESIGUALDAD PDF

## Apollonius of Perga

.

CROW SRDT15 PDF

## Apollonii Pergaei Conicorum Lib. V, VI, VII paraphraste Abalphato ...

.