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Euclid's Elements

The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates and mathematical proofs of the propositions; the books cover plane and solid Euclidean geometry, elementary number theory, incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics, it has proven instrumental in the development of logic and modern science, its logical rigor was not surpassed until the 19th century. Euclid's Elements has been referred to as the most successful and influential textbook written, it was one of the earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482, with the number reaching well over one thousand. For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students.

Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read. Geometry emerged as an indispensable part of the standard education of the English gentleman in the eighteenth century; the standard textbook for this purpose was none other than Euclid's The Elements. Scholars believe that the Elements is a compilation of propositions based on books by earlier Greek mathematicians. Proclus, a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the Elements: "Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors". Pythagoras was the source for most of books I and II, Hippocrates of Chios for book III, Eudoxus of Cnidus for book V, while books IV, VI, XI, XII came from other Pythagorean or Athenian mathematicians.

The Elements may have been based on an earlier textbook by Hippocrates of Chios, who may have originated the use of letters to refer to figures. In the fourth century AD, Theon of Alexandria produced an edition of Euclid, so used that it became the only surviving source until François Peyrard's 1808 discovery at the Vatican of a manuscript not derived from Theon's; this manuscript, the Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions. Papyrus Oxyrhynchus 29 is a tiny fragment of an older manuscript, but only contains the statement of one proposition. 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; the Arabs received the Elements from the Byzantines around 760. 800. The Byzantine scholar Arethas commissioned the copying of one of the extant Greek manuscripts of Euclid in the late ninth century. Although known in Byzantium, the Elements was lost to Western Europe until about 1120, when the English monk Adelard of Bath translated it into Latin from an Arabic translation.

The first printed edition appeared in 1482, since it has been translated into many languages and published in about a thousand different editions. Theon's Greek edition was recovered in 1533. In 1570, John Dee provided a respected "Mathematical Preface", along with copious notes and supplementary material, to the first English edition by Henry Billingsley. Copies of the Greek text still exist, some of which can be found in the Vatican Library and the Bodleian Library in Oxford; the manuscripts available are of variable quality, invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text. Ancient texts which refer to the Elements itself, to other mathematical theories that were current at the time it was written, are important in this process; such analyses are conducted by J. L. Heiberg and Sir Thomas Little Heath in their editions of the text. Of importance are the scholia, or annotations to the text; these additions, which distinguished themselves from the main text accumulated over time as opinions varied upon what was worthy of explanation or further study.

The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, Sir Isaac Newton were all influenced by the Elements, applied their knowledge of it to their work. Mathematicians and philosophers, such as Thomas Hobbes, Baruch Spinoza, Alfred North Whitehead, Bertrand Russell, have attempted to create their own foundational "Elements" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced; the austere beauty of Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly system of perfection and certainty. Abraham Lincoln kept a copy of Euclid in his saddlebag, studied it late at ni

JNR Class ED76

The Class ED76 is a Bo-2-Bo wheel arrangement AC electric locomotive type operated on passenger and freight services in Japan since 1965 by Japanese National Railways, by Hokkaido Railway Company, Kyushu Railway Company and Japan Freight Railway Company. As of 1 April 2016, just 10 locomotives remained in service, all operated by JR Freight. ED76-0 ED76-500 ED76-1000 94 class ED76-0 locomotives were built from 1965 to 1976 and numbered ED76 1 to ED76 94; as of 1 April 2016, the remaining fleet consists of two locomotives, ED76 81 and ED76 83, operated by JR Freight. 22 class ED76-500 locomotives were built from 1968 for use in Hokkaido, numbered ED76 501 to ED76 522. These locomotives included larger water and fuel tanks for the train heating steam generator and had accordingly longer bodies, they were intended to be used in pairs, featured cab gangway doors. ED76 514 was modified for used in the Seikan Tunnel and renumbered ED76 551. All ED76-500s except for the unique ED76 551 were withdrawn by 1994.

ED76 551 was withdrawn in 2001. 23 class ED76-1000 locomotives were built from 1970 to 1979 for express freight use and numbered ED76 1001 to ED76 1023. As of 1 April 2016, the remaining fleet consists of eight locomotives, operated by JR Freight; the following examples have been preserved. ED76 1: Kyushu Railway Heritage Museum, ED76 91: Hita Tenryosui no Sato, Oita ED76 505: Mikasa Railway Village, Hokkaido ED76 509: Otaru Transport Museum, Hokkaido ED76 1006: JR Freight Moji Depot The ED76 classification for this locomotive type is explained below. E: Electric locomotive D: Four driving axles 7x: AC locomotive with maximum speed exceeding 85 km/h

Xavier Beauvois

Xavier Beauvois is a French actor, film director and screenwriter. His film Don't Forget You're Going to Die was entered into the 1995 Cannes Film Festival where it won the Jury Prize, his film Of Gods and Men received the Grand Prix and the Prize of the Ecumenical Jury at the 2010 Cannes Film Festival. The film was selected as France's submission for the Academy Award for Best Foreign Language Film at the 83rd Academy Awards, but it did not make the final shortlist, his 2014 film La Rançon de la gloire was selected to compete for the Golden Lion at the 71st Venice International Film Festival. He is married to film editor Marie-Julie Maille, they have two sons, born in August 1992, Antoine, born May 1996. Xavier Beauvois on IMDb