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Accueil du site > Ressources > Corpus des Editions Renaissantes des Eléments d’Euclide (1482-1606) > Introduction



Compiled by : Odile Kouteynikoff (SPHERE), François Loget (CESR), Marc Moyon (FRED, Centre A. Koyré).

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The Elements of Euclid is a major work for historians of mathematics, as much for the content itself as for its reception over the centuries, and particularly in the Renaissance, when ancient texts were highly regarded.
The corpus presented here can clearly not pretend to be exhaustive

The chronological limits may seem a little arbitrary.
If the earlier date, 1482, seems self-evident, as the date of the first printed edition of Euclid’s Elements, by Erhard Ratdolt in Venice, from the Arabo-Latin text of Campanus (c. 1259), the later date, 1606, reveals a more subjective choice, the date of the first edition of the Elements in Dutch ! We stop before the year 1614, which nevertheless saw the first appearance of the French translation by Henrion, which was of great importance, but which was 50 years after the first translation into French by Forcadel.

A similar question can be posed as to the extent of the list, where we have deliberately limited ourselves to editions properly considered to be Euclid’s Elements, excluding works belonging more generally to the Euclidean tradition, such as Buteon’s De quadratura circuli libri duo (Lyon, Rovilius, 1559) to which the author added a small work revealing the errors of translators of Euclid who had preceded him : Campanus, Zamberti, Oronce, Peletier, and Pena. To him goes the credit of having assigned to Euclid demonstrations long attribtued to Theon, and to Hypsicles for Books XIV and XV.

Four dates after 1482, highlighted in bold in our table, are generally regarded as critical in the history of Euclid’s Elements in the Renaissance :
– 1505, the Greco-Latin translation of Zamberti, published in Venice, printed by Tacuinus
– 1533, the editio princeps established by Grynée, edited at Basle, printed by Hervage
– 1572, the Greco-Latin translation of Commandino, which stands out as a mathematical reference work
– 1574, the recension of Clavius, published in Rome, printed by Accoltus, and known in multiple editions.

The numerous editions printed in the course of the 16th century, and the diversity of editorial choices they reveal, show the interests of each author or community at the time.

Certain editions give only the first six books, the ultimate textbooks of geometry ; others the first nine, including therefore the books on arithmetic ; others again go beyond the thirteen attested books to fifteen, sixteen, or even eighteen, in their concern to cover the entire field of mathematics (Column 6 of the table. Some, which are exceptional, are concerned only with one particular book.

The choice of language, Latin, bilingual Greek and Latin, or vernacular, is never unimportant (Column 5).

Faithfulness to the source texts – the Arabo-Latin text of Campanus or the Greco-Latin translation by Zamberti of Euclid’s text commented by Theon – was variable (Columns 7 and 8). It appears that certain authors suppressed the demonstrations of propositions, retaining only the statements, while others augmented the text by bringing in personal commentary, some even going as far as re-writing the demonstrations.

The aspirations of the author-editors, their conception of mathematics, their scientific or pedagogic ambitions, are embedded in the text they offer their readers, pupils, or masters, in each period. The audience for the works is nevertheless not always easy to discover with any certainty. Nor is it easy to categorize Euclid’s Elements in any simple way ; we can only say, without any risk of being wrong, that the book remains a subject of inexhaustible study.

January 2013