The Works of Euclid, Vol. 1

I subscribed to it before it was sent to the press, before it had been purged of all errors. By means of the errata placed at the end of the last volume, errors may be corrected if I happen to discover any while reading the printed work with great attention.

Mr. , of Smyrna, a man commendable for his exceptional learning and a most diligent corrector, voluntarily read many proofs. Mr. , who has long cultivated the Greek, Latin, and French languages, used the utmost care and diligence so that my edition might be a credit to the French presses; while reading the proofs, he compared the Latin and French versions with the Greek text very attentively, and appended annotations to the margin.

Among the variant readings of the first volume, certain ones are especially to be noted.

In all the Greek and Latin editions, postulates 4, 5, and 6 are placed among the common notions.

The demonstration of the seventh of the first book has two cases, and yet only one case is demonstrated in all the , without exception, and in the editions of and . The second case is when point Δ falls within the ABΓ, or point Γ within the ABΔ. In order for the second case to be demonstrated, it had to be shown beforehand that, when the equal sides of an are produced, the angles under the base are equal to one another; which, indeed, demonstrated in the fifth , and this solely for the sake of the seventh , since, apart from the seventh , this demonstration has no use in the remaining ; from this it follows manifestly, all the commentators of say, that the Greek text of the seventh is mutilated. All the commentators were in error. The figure was incomplete in all the and in all the editions. I drew the second figure; I produced the straight lines BΓ, BΔ, and the demonstration was completed, without a single word being changed in the Greek text.

The demonstration of the 24th of the third book has three cases. For, having placed A upon Γ, and point B upon Δ, it is necessary to demonstrate that the segment AEB is not