Page x

copies’ original: "transumpta". This text has never been printed, and though comparatively many manuscripts are known, they differ widely from each other. His translation dates from the end of the first quarter of the twelfth century. Abridgments containing only the enunciations: the formal statements of mathematical theorems or propositions are the form of his translation more usually met with. The Digby manuscript 174, folio 99, from the prologue of which the remark quoted above is taken, contains demonstrations: the step-by-step logical proofs of a theorem only with the diagrams. The enunciations are usually represented by their first few words.

But no general statement as to this version can be made until a list of the manuscripts has been drawn up, and at least their chief variants studied. A text which has been copied and recopied for over a century and a quarter for use by students, especially towards the end of the twelfth century when Gerard of Cremona translated the version of Euclid edited by Thabit ben Qurra, must inevitably have suffered considerable change. In the third quarter of the thirteenth century another version of Euclid by Campanus of Novara appeared, and this version became the standard text up to and long after the end of the Middle Ages.

It has often been said that Campanus took over the work of Adelard without acknowledgment, but if this late twelfth-century Digby text represents the original of Adelard at all accurately, there is little verbal correspondence between the versions to justify the accusation, as far as my limited examination allows me to form an opinion. Weissenhorn in his study The Translations of Euclid (Abhandlungen z. G. d. Mathematik, Vol. 3) has dealt with some aspects of this question. What is noteworthy is that in one case where Bacon declares that he will give a better illustration than that in Euclid’s text (p. 125):

"But I will demonstrate the eighth for one of the ten reasons stated, namely so that the horrible cruelty of the proofs which reigns in this book may be seen, and so that such damnable waste of time might be avoided." original: "Octavam autem demonstrabo propter unam causam decem dictarum, scilicet ut videatur crudelitas demonstracionum horribilis que in hoc libro regnat, ut hujusmodi dampnabilis consumpcio temporis evitetur"

This demonstration (pp. 128, 129, line 22) of Book V, proposition 8, is to be found at length in the same words in the version of Campanus, and most of Bacon’s other demonstrations of the fifth book are likewise incorporated by him. I have already remarked on the great similarity of parts