Euclide

Euclide , in Greek old Εὐκλείδης Eukleidês (born towards -325, died towards -265 with Alexandria) is a Mathématicien of the ancient Greece, author of the Éléments , which are regarded as one of the texts founders of the modern Mathématiques.

Biography

One knows very few things relating to the life of Euclide, if not that it was a Greek mathematician who was perhaps born with Athens towards 325 before J.C. It left in Egypt to teach there mathematics under the reign of Ptolémée 1 {{er}}. He died towards 265 before J.C He worked with the Museum of Alexandria and founded the School of mathematics there. Surrounded by its disciples, it undertook many research tasks to it. It probably met Archimedes.

Euclide would have also taken part, like many mathematicians of its time, with the political life. It would have thus made adopt in Athens a provision stipulating that the texts of the laws, consigned hitherto in the local alphabet, should be republished in the alphabet known as of Millet which gave its preference to the direction left-right-hand side.

The freemasons regard Euclide as one of the founders of their organization, in way symbolic system (because it is chronologically improbable).

Writings

See also: Elements of Euclide

The Elements are a compilation of the geometrical knowledge and remained the core of mathematical teaching during nearly 2000 years. It may be that none the results contained in the Elements is of Euclide, but the organization of the matter and its talk are due for him.

The Elements are divided into thirteen books. Books 1 to 6, plane geometry, books 7 to 9, theory of the reports/ratios, book 10, the theory of irrational numbers of Eudoxe, and finally books 11 to 13 of solid geometry. The book ends in the study of the properties of the five regular polyhedrons and a demonstration of their existence. The Elements are remarkable by the clearness with which the theorems are stated and shown.

More than one thousand of handwritten editions of the Elements were published before the first version printed in 1482. The rigor is not there always at the level of the current guns, but the method consisting starting from Axiome S, of postulates and definitions, to deduce a maximum of properties from the objects considered, the whole in an organized unit, was new for the time. The Éléments last their success with their superiority of organization, logical systematization and but not of exhaustiveness (neither Conique, nor resolution by neusis or adjustment). The last research undertaken in epistemology of mathematics tends to prove that Euclide is not the only author of the " Éléments". He was probably surrounded by a college of disciples having taken part all in their development.

The Géométrie such as it is defined by Euclide in this text was regarded during centuries as the geometry and it was difficult to remove this supremacy to him; Nicolaï Ivanovitch Lobatchevsky was the first to officially test there as of 1826, followed János Bolyai, but the legend wants that it was not taken with serious until the death of Gauss, when one discovered among the drafts of this last which it had also imagined to him of the nonEuclidean geometries.

In the books of Euclide a result appears which one calls the postulate of Euclide and which states that by a point taken out of a line it passes one and only one parallel on this line . There are primarily three kinds of geometries: that which admits the postulate of Euclide and which one calls plane geometry or Euclidean geometry , that which admits the postulate which says that by a point taken out of a line it does not pass any parallel on this line and that one calls spherical geometry or geometry riemanienne and that which admits the postulate which says that by a point taken out of a line it passes an infinity of parallels on this line and that one calls geometry of Lobatchevsky . Riemann showed that a model of the spherical geometry is the geometry of the sphere where the lines are the meridian lines or large circles. Poincaré gave a model of the geometry of Lobatchevsky. Since these three geometries have models, it there no reason of as a priviligier one rather than the other. The Theory of relativity of Einstein carried a fatal blow to the geometry of Euclide by showing the curve of space . Indeed when space curve , it gives up its Euclidean aspect.

Euclide was also interested in the Arithmétique in book 7. It thus defined the division which one calls Euclidean Division and a algorithm to calculate the highest common factor of two numbers, known under the name of Algorithme of Euclide.

Euclide is also the author of the Données (94 theorems) and of optics and reflecting the . Its writings Surfaces , Porismes , the Conical S , the book of the Paradox S and the Elements of Music have all disappeared.

Euclide was perhaps not a mathematician of foreground, but the quality of the Elements in made the Master of mathematics of antiquity.

Introductio harmonica , where it treats music;
Optica, Catoptrica ;
De Divislonibus (of the division of the polygons) , disputed work and of which there remains only one Latin version;
Porismes , restored according to the analysis left by Pappus and published in 1860 with Paris by Michel Chasles.

Its complete Œuvres was given by David Gregory, Oxford, 1703, Greek-Latin, and was translated into French by François Peyrard, Paris, 1814 - 1818, 3 volumes in-4, with Greek text and Latin translation.

Contemporary bibliography

Euclide, the elements . Volume I, Books I-IV, plane Geometry; transl. of the text of Heiberg and comments by Bernard Vitrac; general introduction by Maurice Caveing. Paris: University presses of France, 1990. (Library of history of sciences). 531 p. ISBN 2-13-043240-9.

Euclide, the elements . Volume II, Books V to IX V-VI, Proportions and similarity; Books VII-IX, Arithmetic; transl. of the text of Heiberg and comments by Bernard Vitrac. Paris: University presses of France, 1994. (Library of history of sciences). 572p. ISBN 2-13-045568-9.

Euclide, the elements . Volume III, Delivers X, Grandeurs commensurable and incommensurable, classification of the irrational lines; transl. of the text of Heiberg and comments by Bernard Vitrac. Paris: University presses of France, 1998. (Library of history of sciences). 432 p. ISBN 2-13-049586-9.

Euclide, the elements . Volume IV, Delivers XI-XIII, Géométrie of the solids; transl. of the text of Heiberg and comments by Bernard Vitrac. Paris: University presses of France, 2001. (Library of history of sciences). 482 p. ISBN 2-13-051927-X.

See too

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