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A Cross-Disciplinary Study of Euclid’s Elements

This project studies the historical impact of this internationally important work.

The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570.

About the project

Euclid’s Elements were written in Alexandria about 300 B.C. and became almost at once the standard work on mathematics, or rather geometry, which at the time was the basic language of mathematical computation. But the importance of the work did not end in Antiquity, since this work became the basic text-book for the the whole European tradition of mathematics, and also physics, being kept as such even until the end of the 19th century, when it was succeeded by various paraphrases of the work, more in tune with modern mathematical methods, as one has assumed.

However, also aspects of modern mathematics were inspired by the work: The lack of proof of the parallel postulate gave birth to non-euclidean geometrical theories. Thus, existing as a textbook for more than 2000 years, it is definitely one of the most read, translated and commented on work in European history – only superceded by the Bible – as a schoolbook and the basic manual of mathematical disciplines.

And, indeed, not only European traditions of science have been influenced by the Elements. It was, to wit, translated into Arabic about 800 A.D., influencing profoundly also this tradition and its thinking on problems of natural science. And the prestige of Arabic natural science in the 10th to the 15th centuries is evidenced by the fact that the Elements was translated into Latin a number of times from its Arabic version – not only form the Greek.

However, the multilingualism of the Elements goes even further. Not only was it translated into the various European national languages from the Renaissance on, it was translated into Chinese from one of its Latin versions by the Italian missionary Mattheo Ricci in the beginning of the 17th century, and from its Arabicversion into Sanskrit quite in the beginning of the 18th century.

Objectives

On this background we have undertaken an interdisciplinary project to study the historical impact of this internationally important work, to understand better the global diffusion of its mathematical ideas, based on the methods of comparative philology, involving all the language areas mentioned above. We wish to understand better its semantical content as being transformed by its numerous translations, and the new terminologies created in this process, as well as its practical use in physics, architecture and other crafts and fields of knowledge.

Our project will also take into account the great significance the Elements have had for pedagogical methods throughout history, and thus create an informed background on which to discuss the place of geometry even inmodern schools.

The Elements have also served as a model on which argumentative consistency is to be developed, and have as such influenced philosophical thought in Antiquity and throughout history. Thus its social impact may be traced even in legal argumentative practices. Euclid’s work thus deserves such an interdisciplinary study.

However, to produce an analytic, historical and comparative version, including the texts in its most important languages as well as the geometrical images from these traditions, must remain the basis of the study: Thus we have initiated such a version in our Bibiliotheca Polyglotta. This multilingual version will constitute a basis for our extended study, but the dynamic internet application will also serve as a means of publication also of the various analyses during our study.

Cooperation

KULTRANS, Uniersity of Oslo

Max Planck Institute for the History of Science, Berlin

Published May 15, 2017 12:47 PM - Last modified May 15, 2017 2:51 PM