[365] Ep. 167 (in Migne, Ep. 174).

[366] Richer, Hist. iii. 47, 48.

[367] Several of his compositions are extant.

[368] Richer, Hist. iii. 48-53.

[369] Richer, Hist. iii. cap. 55-65.

[370] See post, Chapter XXXV. If one should hesitate to find a phase of the veritable Gerbert in Richer’s report of the disputation with Otric, one may turn to Gerbert’s own philosophic or logical Libellus—de rationali et ratione uti (Migne 139, col. 159-168). It is addressed to Otto II., and the opening paragraph recalls to the emperor the disputation which we have been following. The Libellus is naturally more coherent than the disputation, in which Otric’s questions seem intended rather to trip his adversary than to lead a topic on to its proper end. It is devoted, however, to a problem exactly analogous to the point taken by Otric, that the term rational was not as broad as the term mortal. For the Libellus discusses whether the use of reason (ratione uti) can be predicated of the rational being (rationale). The concept of the predicate should be the broader one, but here it might seem less broad, since all reasonable beings do not exercise reason. The discussion closely resembles the dispute in the character of the intellectual interests disclosed, and its arguments are not more original than those employed against Otric. Disputation and Libellus alike represent necessary endeavours of the mind, which has reached a certain stage of tuition and development, to adjust itself with problems of logical order and method.

[371] Post, Chapter XV.

[372] Cf. Sackür, Die Cluniacenser, ii. 330 sqq.; Pfister. Études sur le règne de Robert le Pieux, p. 2 sqq. (the latter takes an extreme view).

[373] Aimoin’s Vita Abbonis, cap. 7 (Migne, Pat. Lat. 139, col. 393). The same volume contains most of Abbo’s extant writings, and those of Aimoin. On Abbo see Sackür, Die Cluniacenser, ii. 345 sqq.

An incredibly large number of students are said to have attended Abbo’s lectures. His studies and teaching lay mainly in astronomy, mathematics, chronology, and grammar. The pupil Aimoin cultivated history and biography, compiling a History of the Francs and a History of the miracles of St. Benedict, the latter a theme worthy of the tenth century. One leaves it with a sigh of relief, so barren was it save for its feat of gestation in giving birth to Gerbert.