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zweidimensionale Geometrie - traduction vers Anglais
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![A disproof of Euclidean geometry as a description of physical space. In a 1919 test of the general theory of relativity, stars (marked with short horizontal lines) were photographed during a solar [[eclipse]]. The rays of starlight were bent by the Sun's gravity on their way to Earth. This is interpreted as evidence in favor of Einstein's prediction that gravity would cause deviations from Euclidean geometry.](https://commons.wikimedia.org/wiki/Special:FilePath/1919 eclipse negative.jpg?width=200 "A disproof of Euclidean geometry as a description of physical space. In a 1919 test of the general theory of relativity, stars (marked with short horizontal lines) were photographed during a solar [[eclipse]]. The rays of starlight were bent by the Sun's gravity on their way to Earth. This is interpreted as evidence in favor of Einstein's prediction that gravity would cause deviations from Euclidean geometry.")
![invariant]]s and studying them is the essence of geometry.](https://commons.wikimedia.org/wiki/Special:FilePath/Congruentie.svg?width=200 "invariant]]s and studying them is the essence of geometry.")
![René Descartes. Portrait after [[Frans Hals]], 1648.](https://commons.wikimedia.org/wiki/Special:FilePath/Frans Hals - Portret van René Descartes.jpg?width=200 "René Descartes. Portrait after [[Frans Hals]], 1648.")
![Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized [[compass and straightedge]].](https://commons.wikimedia.org/wiki/Special:FilePath/Squaring the circle.svg?width=200 "Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized [[compass and straightedge]].")
![The ''[[pons asinorum]]'' or ''bridge of asses theorem'' states that in an isosceles triangle, α = β and γ = δ.](https://commons.wikimedia.org/wiki/Special:FilePath/pons_asinorum_dzmanto.png?width=200 "The ''[[pons asinorum]]'' or ''bridge of asses theorem'' states that in an isosceles triangle, α = β and γ = δ.")
![The ''[[Pythagorean theorem]]'' states that the sum of the areas of the two squares on the legs (''a'' and ''b'') of a right triangle equals the area of the square on the hypotenuse (''c'').](https://commons.wikimedia.org/wiki/Special:FilePath/Pythagorean.svg?width=200 "The ''[[Pythagorean theorem]]'' states that the sum of the areas of the two squares on the legs (''a'' and ''b'') of a right triangle equals the area of the square on the hypotenuse (''c'').")
![''[[Thales' theorem]]'' states that if AC is a diameter, then the angle at B is a right angle.](https://commons.wikimedia.org/wiki/Special:FilePath/Thales' Theorem Simple.svg?width=200 "''[[Thales' theorem]]'' states that if AC is a diameter, then the angle at B is a right angle.")
![level]]](https://commons.wikimedia.org/wiki/Special:FilePath/us land survey officer.jpg?width=200 "level]]")
![orange]]s.](https://commons.wikimedia.org/wiki/Special:FilePath/Ambersweet oranges.jpg?width=200 "orange]]s.")
Définition
Wikipédia
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La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes. In the Discourse, he presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique (Optics) and Les Météores (Meteorology), were published with the Discourse to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience).
The work was the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking. It also contributed to the mathematical ideas of Leibniz and Newton and was thus important in the development of calculus.
