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Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
This is a list of axioms as that term is understood in mathematics. In epistemology , the word axiom is understood differently; see axiom and self-evidence . Individual axioms are almost always part of a larger axiomatic system .
Euclid introduced certain axioms, or postulates, expressing primary or self-evident properties of points, lines, and planes. [39] He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid's approach to geometry was its rigor, and it has come to be known as axiomatic or synthetic geometry ...
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Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these. Although many of Euclid's results had been stated by earlier mathematicians, [7] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. [8]
== Description == Euclid's ''Elements'' (Ancient Greek) Compiled for anyone who would want to read the Euclid's work in Greek, especially in order to provide them a printer-friendly copy of the wor: 09:37, 16 April 2007: No thumbnail: 0 × 0 (1.84 MB) Mingshey~commonswiki: 이전 버전으로 되돌렸습니다. 09:35, 16 April 2007: No thumbnail
Euclid gave the definition of parallel lines in Book I, Definition 23 [2] just before the five postulates. [3] Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. The postulate was long considered to be obvious or inevitable, but proofs were elusive.
Historically, Euclid's parallel postulate has turned out to be independent of the other axioms. Simply discarding it gives absolute geometry , while negating it yields hyperbolic geometry . Other consistent axiom sets can yield other geometries, such as projective , elliptic , spherical or affine geometry.