[535] I.e. in relation to the quadrivium. "Non legant in festivis diebus, nisi Philosophos et rhetoricas et quadrivalia et barbarismum et ethicam, si placet." Suter, _Die Mathematik auf den Universitaeten des Mittelalters_, Zuerich, 1887, p. 56. Roger Bacon gives a still more gloomy view of Oxford in his time in his _Opus minus_, in the _Rerum Britannicarum medii aevi scriptores_, London, 1859, Vol. I, p. 327. For a picture of Cambridge at this time consult F. W. Newman, _The English Universities, translated from the German of V. A. Huber_, London, 1843, Vol. I, p. 61; W. W. R. Ball, _History of Mathematics at Cambridge_, 1889; S. Guenther, _Geschichte des mathematischen Unterrichts im deutschen Mittelalter bis zum Jahre 1525_, Berlin, 1887, being Vol. III of _Monumenta Germaniae paedagogica_. [536] On the commercial activity of the period, it is known that bills of exchange passed between Messina and Constantinople in 1161, and that a bank was founded at Venice in 1170, the Bank of San Marco being established in the following year. The activity of Pisa was very manifest at this time. Heyd, loc. cit., Vol. II, p. 5; V. Casagrandi, _Storia e cronologia_, 3d ed., Milan, 1901, p. 56. [537] J. A. Symonds, loc. cit., Vol. II, p. 127. [538] I. Taylor, _The Alphabet_, London, 1883, Vol. II, p. 263. [539] Cited by Unger's History, p. 15. The Arabic numerals appear in a Regensburg chronicle of 1167 and in Silesia in 1340. See Schmidt's _Encyclopaedie der Erziehung_, Vol. VI, p. 726; A. Kuckuk, "Die Rechenkunst im sechzehnten Jahrhundert," _Festschrift zur dritten Saecularfeier des Berlinischen Gymnasiums zum grauen Kloster_, Berlin, 1874, p. 4. [540] The text is given in Halliwell, _Rara Mathematica_, London, 1839. [541] Seven are given in Ashmole's _Catalogue of Manuscripts in the Oxford Library_, 1845. [542] Maximilian Curtze, _Petri Philomeni de Dacia in Algorismum Vulgarem Johannis de Sacrobosco commentarius, una cum Algorismo ipso_, Copenhagen, 1897; L. C. Karpinski, "Jordanus Nemorarius and John of Halifax," _American Mathematical Monthly_, Vol. XVII, pp. 108-113. [543] J. Aschbach, _Geschichte der Wiener Universitaet im ersten Jahrhunderte ihres Bestehens_, Wien, 1865, p. 93. [544] Curtze, loc. cit., gives the text. [545] Curtze, loc. cit., found some forty-five copies of the _Algorismus_ in three libraries of Munich, Venice, and Erfurt (Amploniana). Examination of two manuscripts from the Plimpton collection and the Columbia library shows such marked divergence from each other and from the text published by Curtze that the conclusion seems legitimate that these were students' lecture notes. The shorthand character of the writing further confirms this view, as it shows that they were written largely for the personal use of the writers. [546] "Quidam philosophus edidit nomine Algus, unde et Algorismus nuncupatur." [Curtze, loc. cit., p. 1.]