Euclid's Elements

Euclid's Elements (Greek Στοιχεία) is a mathematical and geometric treatise, consisting of 13 books, written by the Greek mathematician Euclid around 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems) and proofs thereof. Euclid's books are in the fields of Euclidean geometry, as well as the ancient Greek version of number theory. The Elements is one of the oldest extant axiomatic deductive treatments of geometry, and has proved instrumental in the development of logic and modern science.

History

Elements was written in approximately 300 BC by Euclid, an ancient Greek mathematician who probably studied under the pupils of Plato. Although most of the theorems had been developed earlier, Elements was so impressive and comprehensive that the Greeks had no use for the older books, and little is known about earlier geometers today.

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It was translated later into Arabic after being gifted to the Arabs by Byzantium and from those secondary translations into Latin. The first printed edition appeared in 1482, and since then it has been translated into many languages and published in about a thousand different editions. Copies of the Greek text also exist, e.g. in the Vatican Library and the Bodlean library in Oxford. However, the manuscripts available are of very variable quality and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been drawn about the contents of the original text (copies of which are no longer available). Texts which refer to the Elements itself and mathematical theories which were current at the time it was written are also important in this process. Such analyses are conducted by J.L. Heiberg and Sir Thomas L. Heath in their translations of the text.

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1482 - Vatican Library

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Also of importance are the scholia, or footnotes to the text. These additions, which often distinguished themselves from the main text (depending on the manuscript), gradually accumulated over time as opinions varied upon what was worthy of explanation or elucidation. Some of these are useful and add to the text, but many are not.

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It is strongly suspected that book XIII was added to the others at a later date.

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Some idea of the importance of Elements to science can be gained by comparing the scientific achievements of technologically advanced nations such as China and Japan before Westernization with Europe. It is believed that the European tradition of rationalism (derived from Euclid and others) was fundamental to its advancement past these nations.

Related Topics:
China - Japan

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