...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 w
...uably a pioneer in the study of [[number systems]]. (Book X of [[Euclid's Elements]] is described by [[Pappus of Alexandria|Pappus]] as being largely based on
35 KB (5,541 words) - 14:27, 13 December 2011
While there are elements of what in retrospect can be seen as number theory
greatest common divisor of two numbers ([[Euclid's Elements]], Prop. VII.2) and a proof
27 KB (4,334 words) - 14:37, 13 December 2011
...e sequence of natural numbers, possibly attributable to the Greeks. One of Euclid's theorems states: "There exist more than any given number of primes" . Also
and if for any collection of elements of the system $ A $
23 KB (3,482 words) - 08:03, 6 June 2020
...llows: Incidence, Order, Congruence, Parallelism, and Continuity. Euclid ''Elements'' treats these as follows:
::* Incidence is referred to (and therefore relied upon) in Euclid's 1st postulate that has to do with drawing a line between 2 points.
39 KB (6,093 words) - 19:21, 24 February 2016
arithmetic and the first book of Euclid's Elements to the calculus
14 KB (2,270 words) - 18:15, 13 August 2023
...itely many primes. Let $\pi(x)$ be the number of primes not exceeding $x$. Euclid's theorem can then be formulated as follows: $\pi(x)\to +\infty$ as $x\to\inf
|valign="top"|{{Ref|Vi}}||valign="top"| I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian)
27 KB (4,516 words) - 18:38, 18 October 2014
...the moment when the concept of convergence has been introduced on a set of elements.
...convergence of elements of a set can be applied to one and the same set of elements, depending on the problem under consideration. The concept of convergence p
22 KB (3,726 words) - 10:31, 2 September 2017
the first six books of Euclid's elements. He had even tried his hands on the
19 KB (3,099 words) - 16:34, 14 August 2023
...by a rectangle with sides representing the respective factors. In Euclid's Elements (3th century B.C.), quantities are denoted by two letters, the initial and
18 KB (2,697 words) - 13:11, 13 December 2013
...field|skew-field]] is an associative ring in which the set of all non-zero elements is a multiplicative group. A [[Field|field]] is a skew-field in which multi
...}} </TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Algebra: Algebraic structures. Linear algebra" , '''1''' ,
17 KB (2,478 words) - 16:09, 1 April 2020
mathematics. It would appear that he had read the "Elements'' of
13 KB (2,017 words) - 09:45, 15 August 2023
...les of 1-1 correspondences between the elements of an infinite set and the elements of a proper subset
...s, the elements of an infinite set could be put in 1-1 correspondence with elements of one of its proper subsets.
189 KB (29,059 words) - 14:31, 19 March 2023
...al structures" rather than as "intuitively given magnitudes inherited from Euclid's geometry."<ref>Boyer p. 605</ref>
For example, Cauchy's definition was constructed using only these three elements
91 KB (14,186 words) - 16:58, 23 November 2023