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...point out that an alternative approach is possible which does not rely on Euclid's axioms. This approach, which is more advanced in that it needs some know ...nd cos do not depend, for example, on the acceptance or rejection of the [[Euclid's parallel axiom]]. The functions sin and cos can be defined algebraically,

Euclid showed that every number of the form

vocabularies NUMBERS, RELAT_2, RCOMP_1, SPPOL_1, SUBSET_1, EUCLID, TOPREAL1, MATRIX_1, RLTOPSP1, EUCLID, TOPREAL1, GOBOARD1, GOBOARD5, TOPREAL4,

...ellenistic mathematician [[Euclid]] details [[geometric]]al algebra in ''[[Euclid's Elements|Elements]]''.]]--> ...[Rhind Mathematical Papyrus]]'', ''[[Sulba Sutras]]'', [[Euclid's Elements|Euclid's ''Elements'']], and ''[[The Nine Chapters on the Mathematical Art]]''. T

...dopted the plan of using algebraic signs instead of words, and "Playfair’s Euclid" became well known in most mathematical schools. In 1797 he suffered a seve

...many primes, but one of the oldest and most familiar proofs goes back go [[Euclid]]. Euclid proved that for any finite set of prime numbers, there is always another pr

[[Euclid]] (Εύκλείδες, c. 300 BCE) was a Greek mathematician who worked in

* Farndon, John et al. ''The Great Scientists: From Euclid to Stephen Hawking'', Metro Books, New York (2007) pp. 80-83.

...oportion'''. The earliest existing description is found in the Elements of Euclid (Book 5, definition 3): ''A straight line is said to have been cut in extre

...ts name, the Pythagorean comma was first described in the West by [[pseudo-Euclid]] in ''Divisions of the Canon'' (c. 300 [[Common Era|BCE]]). Chinese mathem

...'' are two [[real number]]s specifying a [[point (geometry)|point]] in a [[Euclid|Euclidean]] plane (a 2-dimensional Euclidean point space, an [[affine space

which, via Euclid algorithm, leads to:

...ael Underwood|Michael Underwood]] created a [[free particle]] and proved [[Euclid's lemma]].

...many primes, but one of the oldest and most familiar proofs goes back go [[Euclid]]. Euclid proved that for any finite set of prime numbers, there is always another pr

...36461 Publisher's description:]</u></b>&nbsp;Herophilus, a contemporary of Euclid, practiced medicine in Alexandria in the third century B.C., and seems to h

...d years of development was written down by [[Euclid]] in ''[[The Elements (Euclid)|The Elements]]''. ...n, who made important contributions to geometry, reflected in Book VIII of Euclid's Elements.

...reasoning by which Apollonius tied the shape of certain conic sections to Euclid's concept of deficient areas.

...reasoning by which Apollonius tied the shape of certain conic sections to Euclid's concept of deficient areas.

...1957 ed.), p. 36-40) discusses the table in detail and mentions in passing Euclid's method in modern notation (Neugebauer, op. cit., p. 39)</ref> the triples Euclid IX 21--34

...are the stuff of legend. Among the lasting achievements of the Library are Euclid's geometry, along with Greek translation of the Old Testament (although it