[284] Not, however, in the mercantile schools. The arithmetic of Boethius would have been about the last book to be thought of in such institutions. While referred to by Baeda (672-735) and Hrabanus Maurus (c. 776-856), it was only after Gerbert's time that the _Boetii de institutione arithmetica libri duo_ was really a common work. [285] Also spelled Cassiodorius. [286] As a matter of fact, Boethius could not have translated any work by Pythagoras on music, because there was no such work, but he did make the theories of the Pythagoreans known. Neither did he translate Nicomachus, although he embodied many of the ideas of the Greek writer in his own arithmetic. Gibbon follows Cassiodorus in these statements in his _Decline and Fall of the Roman Empire_, chap. xxxix. Martin pointed out with positiveness the similarity of the first book of Boethius to the first five books of Nicomachus. [_Les signes numeraux_ etc., reprint, p. 4.] [287] The general idea goes back to Pythagoras, however. [288] J. C. Scaliger in his _Poetice_ also said of him: "Boethii Severini ingenium, eruditio, ars, sapientia facile provocat omnes auctores, sive illi Graeci sint, sive Latini" [Heilbronner, _Hist. math. univ._, p. 387]. Libri, speaking of the time of Boethius, remarks: "Nous voyons du temps de Theodoric, les lettres reprendre une nouvelle vie en Italie, les ecoles florissantes et les savans honores. Et certes les ouvrages de Boece, de Cassiodore, de Symmaque, surpassent de beaucoup toutes les productions du siecle precedent." [_Histoire des mathematiques_, Vol. I, p. 78.] [289] Carra de Vaux, _Avicenne_, Paris, 1900; Woepcke, _Sur l'introduction_, etc.; Gerhardt, _Entstehung_ etc., p. 20. Avicenna is a corruption from Ibn S[=i]n[=a], as pointed out by Wuestenfeld, _Geschichte der arabischen Aerzte und Naturforscher_, Goettingen, 1840. His full name is Ab[=u] `Al[=i] al-[H.]osein ibn S[=i]n[=a]. For notes on Avicenna's arithmetic, see Woepcke, _Propagation_, p. 502.