The Works of Euclid, Vol. 1

of the Data of Euclid, which are certainly the only works of this forever-celebrated geometer that remain to us. For this reason, I collated manuscript 190 with the Oxford edition, and I wrote the variants in the margin of the printed work.

This task completed, I examined the marginal variants attentively, and with the help of the other manuscripts, I adopted or rejected, for the Paris edition, this or that variant. Manuscript 190 was always given preference, whenever I had no motive to prefer one reading to another.

The Greek text being thus established, I translated it into Latin, and I made to the French translation the changes required by the variants I had adopted.

My Latin translation corresponds word for word to the Greek text, unless some particular rule forced me to do otherwise. One will sometimes find Hellenisms in my translation, or at least certain expressions that seem to depart slightly from the genius of the Latin language. I could have avoided them; but my translation would have been less faithful.

I had submitted my system of translation to persons well-versed in the Greek and Latin languages. M. Delambre, perpetual secretary of the class of physical and mathematical sciences of the Imperial Institute of France and treasurer of the Imperial University, had the kindness to examine it with care, and to aid me with his wise advice. Here is the letter he did me the honor of writing to me on this subject:

Sir, I have read with pleasure the first six sheets of your Euclid in three languages. Your commissioners had expressed the wish to see appear a Greek edition of the text of Euclid, purged of all the errors that the manuscripts have led you to rectify, and enriched with all the additions that they have provided you: you are going to fulfill their wish, and that of all the learned.

I greatly approve of the decision you have taken to render the Latin version as literal as the genius of the two languages permits. The Greeks had two means of indicating oblique cases, the ending and the article; when one of these two resources failed them, as often happens in geometry, the article sufficed to remove all uncertainty.