Pythagoras c. This manuscript, the Heiberg manuscript, is from a Byzantine workshop around and is the basis of modern editions. Although known to, for instance, Cicero , no record exists of the text having been translated into Latin prior to Boethius in the fifth or sixth century. Mentioned in T. Private collection Hector Zenil. In , John Dee provided a widely respected "Mathematical Preface", along with copious notes and supplementary material, to the first English edition by Henry Billingsley.

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He was likely born c. He is mentioned by name, though rarely, by other Greek mathematicians from Archimedes c. This biography is generally believed to be fictitious.

Proclus believes that Euclid is not much younger than these, and that he must have lived during the time of Ptolemy I c. Although the apparent citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before Archimedes wrote his.

However, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The diagram accompanies Book II, Proposition 5. Most of the copies say they are "from the edition of Theon " or the "lectures of Theon", [18] while the text considered to be primary, held by the Vatican, mentions no author.

Proclus provides the only reference ascribing the Elements to Euclid. Although best known for its geometric results, the Elements also includes number theory.

The geometrical system described in the Elements was long known simply as geometry , and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries discovered in the 19th century. More recent scholarship suggests a date of 75— AD. Heath reads: [20] If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.

Construction of a dodecahedron by placing faces on the edges of a cube. In addition to the Elements, at least five works of Euclid have survived to the present day.

They follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a first-century AD work by Heron of Alexandria.

Catoptrics , which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal.

Lost works Other works are credibly attributed to Euclid, but have been lost. Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning. Surface Loci concerned either loci sets of points on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.

Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions.

These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

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## Table of Contents

He was likely born c. He is mentioned by name, though rarely, by other Greek mathematicians from Archimedes c. This biography is generally believed to be fictitious. Proclus believes that Euclid is not much younger than these, and that he must have lived during the time of Ptolemy I c. Although the apparent citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before Archimedes wrote his.

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## Elemente (Euklid)

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## Elementen van Euclides

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