There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are " from the edition of Theon " or the " lectures of Theon ", while the text considered to be primary, held by the Vatican, mentions no author.

Tusi mentions explicitly that he re-writes the treatise " in Khayyám's own words " and quotes Khayyám, saying that " they are worth adding to Euclid's Elements ( first book ) after Proposition 28.

Elements of this effort were liberally scattered through Seasons 25 and 26 of the series, and occasionally included hints about the Doctor's past ; for example, in Silver Nemesis, when Ace and the Doctor discuss the creation of validium, the Doctor mentions that it was created by Omega and Rassilon.

Lee, in his book The Elements of Roman Law ( 4th ed., 1956 ), commented that this definition was " not quite satisfactory " as treasure was not confined to money, nor was there any abandonment of ownership.

Euclid ’ s algorithm appears as Proposition II in Book VII (" Elementary Number Theory ") of his Elements.

In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms.

Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, " Euclid replied there is no royal road to geometry.

The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.

In addition to the Elements, at least five works of Euclid have survived to the present day.

* Heath, Thomas L. ( 1908 ), " Euclid and the Traditions About Him ", in Euclid, Elements ( Thomas L. Heath, ed.

Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources.

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

Near the beginning of the first book of the Elements, Euclid gives five postulates ( axioms ) for plane geometry, stated in terms of constructions ( as translated by Thomas Heath ):

Euclid himself seems to have considered it as being qualitatively different from the others, as evidenced by the organization of the Elements: the first 28 propositions he presents are those that can be proved without it.

The very first geometric proof in the Elements, shown in the figure above, is that any line segment is part of a triangle ; Euclid constructs this in the usual way, by drawing circles around both endpoints and taking their intersection as the third vertex.

It is named after the Greek mathematician Euclid, who described it in Books VII and X of his Elements.

Euclid ( c. 325-265 BC ), of Alexandria, probably a student of one of Plato ’ s students, wrote a treatise in 13 books ( chapters ), titled The Elements of Geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as Euclidean geometry.

A proof from Euclid | Euclid's Euclid's Elements | Elements, widely considered the most influential textbook of all time.

It has customarily been translated as Five Elements probably because of the similarity of this doctrine to the Western system of four elements.

William Maccall, another Unitarian preacher, and probably an acquaintance of Smith, came somewhat later, although influenced by John Stuart Mill, Thomas Carlyle, and German Romanticism, to the same positive conclusions, in his 1847 work " Elements of Individualism ".

While Greek astronomy — thanks to Alexander's conquests — probably influenced Indian learning, to the point of introducing trigonometry, it seems to be the case that Indian mathematics is otherwise an indigenous tradition ; in particular, there is no evidence that Euclid's Elements reached India before the 18th century.

Campanus of Novara probably had access to Adelard's translation of Elements, and it is Campanus ' edition that was first published in Venice in 1482 after the invention of the printing press.

" This was variously interpreted over the years to mean the north side of the front of a fixed altar, the north end of a fixed altar ( i. e., facing south ), the north side of a free-standing altar ( presumably facing those intending to receive the Elements who would be sitting in the quire stalls opposite ), or at the north end of a free-standing altar placed lengthwise in the chancel, facing a congregation seated in the nave.

His work surrounding Euclid ’ s Elements, for example, was of great help in providing training that would help future scholars understand the relationships between demonstrative and geometrical proofs.

This would contain some of the group's most ambitious work yet, with the title track " Elements " on Elements, Pt.

Elements within the Soviet space industry convinced Leonid Brezhnev that the Shuttle was a single-orbit weapon that would be launched from Vandenberg, maneuver to avoid existing anti-ballistic missile sites, bomb Moscow in a first strike, and then land.

Elements of this would be dropped in the comic.

Elements that would form the basis of Christian socialism are found in the Old and New Testaments.

There he became Chaos, the Master of Evil, and sent the Four Fiends of the Elements ahead 2000 years into the future, where they would send him back in time.

Loomis died in 1959, but his final book, Eye of the Painter and Elements of Beauty, would be printed posthumously in 1961.

Elements of the Compilation of Final Fantasy VII would later expand upon his character, detailing the character's history before and after the events of the original game.

Elements crossing behind or before one another would pose additional problems.

Elements from some of these stories would appear in the Modesty Blaise comic strip which O ' Donnell wrote concurrent with his book series.

Elements of the German XIX Panzer Corps ( elements of 3rd Panzer Division and entire 2nd Motorised Infantry Division ) were advancing rapidly and Epler suspected that the Germans would advance on the towns of Brześć and Kobryń, as well as toward an important railway node located in the village of Żabinka.

For the first four years in New York Coleman spent a good deal of time playing in the streets and in tiny clubs with a band that he put together with trumpeter Graham Haynes, the group that would evolve into the ensemble Steve Coleman and Five Elements that would serve as the main ensemble for Coleman's activities.

Despite the achievements of Shen and Guo's work in trigonometry, another substantial work in Chinese trigonometry would not be published again until 1607, with the dual publication of Euclid's Elements by Chinese official and astronomer Xu Guangqi ( 1562 – 1633 ) and the Italian Jesuit Matteo Ricci ( 1552 – 1610 ).

Elements of the story would be incorporated into Dick's 1965 novel, The Three Stigmata of Palmer Eldritch.

Therefore the name would get a new meaning: " Unit for the Elimination and Neutralisation of Armed Elements ".

Professor Ein orders Bomberman to Tentacalls to defeat the Crush Bombers and the Hige Hige Bandits, and to get the Bomb Elements before they do, for if even one element falls into their hands, then the universe would be as Mujoe pleases.

In 1937 he painted the Judgement of Paris, which Hitler personally acquired some time later, hanging it in his residence at Munich-Hitler would later also hang Ziegler's The Four Elements at a residence in Munich.

Avery, also a lawyer, would often proclaim " I refer to Bacon "— meaning The Elements of the Common Laws of England, the noted law text written by Francis Bacon — when making a point.