Previously Unpublished Works, Fascicle 16

doubtful; on the other hand, we have to remember the large sums paid by Bacon in collecting manuscripts over many years, and that they were in existence either as early manuscripts or as translations from the Arabic at his time.

Boethius moulded, if he did not dominate, the scientific thought of the early Middle Ages until the complete victory of the Aristotelian physics. His system of numerical proportions and means original: "medietates" was ultimately designed to assist in the comprehension of the Platonic conceptions in the latter part of the Timaeus and of the Republic: in short, of "God as the arithmetician," to use modern scientific slang. Early in the thirteenth century Jordanus Nemorariensis undertook to recast his theory of Arithmetic in ten books, each containing a number of definite propositions. His work was edited by J. le Fèvre of Étaples (Faber Stapulensis) and printed at Paris in 1514 by Stephanus with notes and a useful table of correspondence with the text of Boethius, which has eliminated the need of giving detailed references to the quotations from Jordanus by Bacon. Le Fèvre in another connection has rendered service to medieval students by printing the text of an undescribed version from the Greek of the Topics and Sophistical Refutations in the Logic of Aristotle original: "Topica and Sophistici Elenchi in Logica Aristotelis", Lyons, 1509.

Bacon has followed Boethius very closely: not always in the main order of his argument, for example, he puts geometric progression before arithmetical, but in close agreement with his thought. Indeed, he sometimes elaborates his details, as in the ratios of two numbers, which he distinguishes very minutely in accordance with his own principle that unless a thing has a name and a definition it cannot be the subject of reasoning. Bacon evidently hoped that by his methods he would throw light on the mysteries of the Christian faith (p. 144-145) as Boethius had hoped to solve the Platonic riddles. The Abacus of Gerbert (and of Bacon) was that attributed to Boethius (illustrated by Friedlein) but no doubt of much later introduction.

The text of Euclid used by Bacon was that "composed by Euclid in Arabic and translated into Latin by Adelard of Bath" original: "ab Euclide in arabico composita et ab Adhelardo Bathoniensi in latinum"