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Linea 1: [[Fasciculus:Sanzio_01_Euclid.jpg\|thumb\|Pars [[Raphael Sanctius Urbinas\|Raphaëlis]] ''[[Schola Atheniensis (Raphael)\|Schola Atheniensis]]'', in quo depingitur mathematicus Graecus, fortasse [[Euclides]] aut [[Archimedes]], qui [[circinus\|circino]] constructionem geometricam facit]] '''Geometria Euclidea''' est systema [[mathematica\|mathematicum]], quod [[Euclides]] [[Alexandria\|Alexandrinus]] in libro suo de [[geometria]], [[Elementa (Euclides)\|Elementis]], descripsit. Modus Euclidis consistit in ponendis axiomatibus, ex quibus multa [[theorema]]ta concludit. Conclusiones Euclidis, quamquam partim a prioribus mathematicis expositae, ab Euclide primum in uno amplo systemate logico ordinatae sunt. ''Elementa'' incipiunt geometriâ [[planum\|plani]], quae systema axiomatica, inductio in [[demonstratio mathematica\|demonstrationes mathematicas]], etiamnunc in [[schola\|ludis]] docetur. Deinde procedit ad [[geometria solida\|geometriam solidam]] trium [[dimensio]]num. Magna pars ''Elementorum'' continet propositiones, lingua geometrica explicatas, quae hodie partes [[algebra]]e et [[theoria numerorum\|theoriae numerorum]] habentur. <!-- <!--Although many of Euclid's results had been stated by earlier mathematicians,<ref>Eves, vol. 1., p. 19</ref> Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.<ref>Eves (1963), vol. 1, p. 10</ref> The ''Elements'' begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of [[Demonstratio mathematica\|formal proof]]. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called [[algebra]] and [[Theoria numerorum\|number theory]], explained in geometrical language.<ref>Eves, p. 19</ref> For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of [[Albertus Einstein\|Albert Einstein]]'s theory of [[Relativitas generalis\|general relativity]] is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the [[Gravitas (physica)\|gravitational field]] is weak.<ref>Misner, Thorne, and Wheeler (1973), p. 47</ref>

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