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Euclid's Elements
Euclid's ''Elements'' ( ''Stoicheia'') is a mathematical and geometric treatise consisting of 13 books written by the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems,〔Heath (1956) (vol. 1), p. 372〕 including the problem of finding the square root of a number.〔Heath (1956) (vol. 1), p. 409〕 The ''Elements'' is the second oldest extant Greek mathematical treatises after Autolycus' ''On the Moving Sphere'', and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science.
According to Proclus the term "element" was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' is in the Greek language the same as 'letter'. This suggests that theorems in the ''Elements'' should be seen as standing in the same relation to geometry as letters to language. Later commentators give a slightly different meaning to the term 'element', emphasizing how the propositions have progressed in small steps, and continued to build on previous propositions in a well-defined order.〔Heath (1956) (vol. 1), p. 114〕
Euclid's ''Elements'' has been referred to as the most successful〔Encyclopedia of Ancient Greece (2006) by Nigel Guy Wilson, page 278. Published by Routledge Taylor and Francis Group. Quote:"Euclid's Elements subsequently became the basis of all mathematical education, not only in the Romand and Byzantine periods, but right down to the mid-20th century, and it could be argued that it is the most successful textbook ever written."〕 and influential textbook ever written. Being first set in type in Venice in 1482, it is one of the very earliest mathematical works to be printed after the invention of the printing press and was estimated by Carl Benjamin Boyer to be second only to the Bible in the number of editions published,〔 with the number reaching well over one thousand.〔The Historical Roots of Elementary Mathematics by Lucas Nicolaas Hendrik Bunt, Phillip S. Jones, Jack D. Bedient (1988), page 142. Dover publications. Quote:"the ''Elements'' became known to Western Europe via the Arabs and the Moors. There the ''Elements'' became the foundation of mathematical education. More than 1000 editions of the ''Elements'' are known. In all probability it is, next to the ''Bible'', the most widely spread book in the civilization of the Western world."〕 For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's ''Elements'' was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.〔From the introduction by Amit Hagar to ''Euclid and His Modern Rivals'' by Lewis Carroll (2009, Barnes & Noble) pg. xxviii: Geometry emerged as an indispensable part of the standard education of the English gentleman in the eighteenth century; by the Victorian period it was also becoming an important part of the education of artisans, children at Board Schools, colonial subjects and, to a rather lesser degree, women. ... The standard textbook for this purpose was none other than Euclid's ''The Elements''. 〕
== History ==
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