Down in Cieldauro; and from martyrdom
And exile came it here."—Paradiso, Canto X.
[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 Bæda (672-735) and Hrabanus Maurus (c. 776-856), it was only after Gerbert's time that the Boëtii 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 numéraux etc., reprint, p. 4.]
[287] The general idea goes back to Pythagoras, however.
[288] J. C. Scaliger in his Poëtice 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 Théodoric, les lettres reprendre une nouvelle vie en Italie, les écoles florissantes et les savans honorés. Et certes les ouvrages de Boëce, de Cassiodore, de Symmaque, surpassent de beaucoup toutes les productions du siècle précédent." [Histoire des mathématiques, 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 Sīnā, as pointed out by Wüstenfeld, Geschichte der arabischen Aerzte und Naturforscher, Göttingen, 1840. His full name is Abū ‛Alī al-Ḥosein ibn Sīnā. For notes on Avicenna's arithmetic, see Woepcke, Propagation, p. 502.
[290] On the early travel between the East and the West the following works may be consulted: A. Hillebrandt, Alt-Indien, containing "Chinesische Reisende in Indien," Breslau, 1899, p. 179; C. A. Skeel, Travel in the First Century after Christ, Cambridge, 1901, p. 142; M. Reinaud, "Relations politiques et commerciales de l'empire romain avec l'Asie orientale," in the Journal Asiatique, Mars-Avril, 1863, Vol. I (6), p. 93; Beazley, Dawn of Modern Geography, a History of Exploration and Geographical Science from the Conversion of the Roman Empire to A.D. 1420, London, 1897-1906, 3 vols.; Heyd, Geschichte des Levanthandels im Mittelalter, Stuttgart, 1897; J. Keane, The Evolution of Geography, London, 1899, p. 38; A. Cunningham, Corpus inscriptionum Indicarum, Calcutta, 1877, Vol. I; A. Neander, General History of the Christian Religion and Church, 5th American ed., Boston, 1855, Vol. III, p. 89; R. C. Dutt, A History of Civilization in Ancient India, Vol. II, Bk. V, chap, ii; E. C. Bayley, loc. cit., p. 28 et seq.; A. C. Burnell, loc. cit., p. 3; J. E. Tennent, Ceylon, London, 1859, Vol. I, p. 159; Geo. Turnour, Epitome of the History of Ceylon, London, n.d., preface; "Philalethes," History of Ceylon, London, 1816, chap, i; H. C. Sirr, Ceylon and the Cingalese, London, 1850, Vol. I, chap. ix. On the Hindu knowledge of the Nile see F. Wilford, Asiatick Researches, Vol. III, p. 295, Calcutta, 1792.
[291] G. Oppert, On the Ancient Commerce of India, Madras, 1879, p. 8.