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[[Fasciculus:Sanzio_01_Euclid.jpg|thumb|278x278px|Detail fromPars [[Raphael Sanctius Urbinas|RaphaelRaphaëlis]]'s ''[[Schola Atheniensis (Raphael)|TheSchola School of AthensAtheniensis]]'', featuringin aquo Greekdepingitur mathematicianmathematicus – perhapsGraecus, representingfortasse [[Euclides|Euclid]] oraut [[Archimedes]] –, using aqui [[Circinuscircinus|compasscircino]] to draw aconstructionem geometricgeometricam construction.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.
'''Euclidean geometry''' is a mathematical system attributed to the [[Alexandria|Alexandrian]] Greek mathematician [[Euclides|Euclid]], which he described in his textbook on [[Geometria|geometry]]: the ''Elements''. Euclid's method consists in assuming a small set of intuitively appealing [[Axioma|axioms]], and deducing many other propositions ([[Theorema|theorems]]) from these. Although many of Euclid's results had been stated by earlier mathematicians,<ref>Eves, vol. 1., p.&nbsp;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.&nbsp;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.&nbsp;19</ref>
 
'''Euclidean geometry''' is a mathematical system attributed to the [[Alexandria|Alexandrian]] Greek mathematician [[Euclides|Euclid]], which he described in his textbook on [[Geometria|geometry]]: the ''Elements''. Euclid's method consists in assuming a small set of intuitively appealing [[Axioma|axioms]], and deducing many other propositions ([[Theorema|theorems]]) from these. <!--Although many of Euclid's results had been stated by earlier mathematicians,<ref>Eves, vol. 1., p.&nbsp;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.&nbsp;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.&nbsp;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.&nbsp;47</ref>
 
Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of [[Systema coordinatarum|coordinates]]. This is in contrast to [[Geometria analytica|analytic geometry]], which uses coordinates.-->
 
{{NexInt}}
== See also ==
* [[Geometria analytica|Analytic geometry]]
* [[Theorema Pythagorae|Pythagorean theorem]]
* Birkhoff's axioms
* Cartesian coordinate system
* Hilbert's axioms
* Incidence geometry
* List of interactive geometry software
* Metric space
* Non-Euclidean geometry
* Ordered geometry
* Parallel postulate
* Type theory
 
=== ClassicalNotae theorems ===
<references />
* Angle bisector theorem
* Butterfly theorem
* Ceva's theorem
* Heron's formula
* Menelaus' theorem
* Nine-point circle
* [[Theorema Pythagorae|Pythagorean theorem]]
 
== NotesBibliographia ==
{{Reflist|35em}}
 
== References ==
* {{Cite book|last=Ball|first=W.W. Rouse|author-link=W. W. Rouse Ball|authorlink=W. W. Rouse Ball|year=1960|title=A Short Account of the History of Mathematics|pages=50–62|edition=4th ed. [Reprint. Original publication: London: Macmillan & Co., 1908]|location=New York|publisher=Dover Publications|isbn=0-486-20630-0|ISBN=0-486-20630-0}}
* {{Cite book|last=Coxeter|first=H.S.M.|author-link=H.S.M. Coxeter|authorlink=H.S.M. Coxeter|year=1961|title=Introduction to Geometry|location=New York|publisher=Wiley}}
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* Alfred Tarski (1951) ''A Decision Method for Elementary Algebra and Geometry''. Univ. of California Press.
 
== ExternalNexus linksexterni ==
* {{springer|title=Euclidean geometry|id=p/e036350}}
* {{springer|title=Plane trigonometry|id=p/p072810}}
* [http://www-math.mit.edu/~kedlaya/geometryunbound Kiran Kedlaya, ''Geometry Unbound''] (a treatment using analytic geometry; PDF format, GFDL licensed)
 
[[Categoria:Geometria elementaria]]
[[Categoria:Geometria Euclideana]]