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The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
The Thirteen Books of Euclid's Elements: vol. 1, vol. 2, vol. 3; The Thirteen Books of Euclid's Elements - Second Edition Revised with Additions: Vol. 1-3; PDF files of many of Heath's works, including those on Diophantus, Apollonius, etc. Excerpts from MacTutor. Heath: Everyman's Library Euclid Introduction
The Elements does not exclusively discuss geometry as is sometimes believed. [37] It is traditionally divided into three topics: plane geometry (books 1–6), basic number theory (books 7–10) and solid geometry (books 11–13)—though book 5 (on proportions) and 10 (on irrational lines) do not exactly fit this scheme.
Oliver Byrne (/ b ɜːr n /; 31 July 1810 – 9 December 1880) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering.He is best known for his 'coloured' book of Euclid's Elements.
The two first subsections, are proofs of the generalized version of Euclid's lemma, namely that: if n divides ab and is coprime with a then it divides b. The original Euclid's lemma follows immediately, since, if n is prime then it divides a or does not divide a in which case it is coprime with a so per the generalized version it divides b.
The Elements consists of thirteen books dealing with geometry (including the geometry of three-dimensional objects such as polyhedra), number theory, and the theory of proportions. It was essentially a compilation of all mathematics known to the Greeks up until Euclid's time.
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The Thirteen Books of Euclid's Elements Vol. 1. p. 29. It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus; Helmig, Christoph; Steel, Carlos (2011). "Proclus". In Zalta, Edward N. (ed.).
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