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Proposition II of Book II was entirely corrupted in the three manuscripts, in the editions of Basel and Oxford, and in the translations of Zamberti and Commandino. I have restored this demonstration in its entirety.
The reading on page 516 is my own. The manuscripts, the Basel edition, and the translations of Zamberti and Commandino presented no reasonable meaning, and the correction by Gregory did not appear successful to me.
The variant of the first line of page 531 is very remarkable. There was τῆς AB instead of τῆς; which caused Hypsicles to state an impossibility, and this error is found in all three manuscripts, in the editions of Basel and Oxford, and in the translations of Zamberti and Commandino.
My Euclid being finished, I am going to have the Works of Apollonius sent to the press immediately, which will be accompanied by the Lemmas of Pappus, the Commentaries of Eutocius, and the two books on the Cylinder and the Cone by Serenus. (See the Preface of the second volume.)
This third and final volume of the Works of Euclid would have appeared last October, were it not for the deplorable end of my eldest daughter, who, after having been the charm of my life for twenty-eight years, expired in my arms on Friday, September 19, unable, or rather unwilling, to survive her only daughter, who had died almost suddenly on her mother's breast on the Friday of the preceding week, in the third year of her age.
My soul broken by grief, and not expecting to be able to survive such cruel losses, arriving one after the other, I had requested M. Delambre, perpetual secretary of the Academy of Sciences, to be so kind, in the event of an occurrence, as to oversee the printing of the remainder of my work. Thus, thanks to this illustrious scholar, even my own death would have brought no delay to the complete publication of the Works of Euclid, which the public would have been enjoying for a long time, were it not for the calumnies and the ceaselessly recurring persecutions to which I have been subjected for sixteen full years.