[530] Now part of Algiers.
[531] E. Reclus, Africa, New York, 1893, Vol. II, p. 253.
[532] "Sed hoc totum et algorismum atque arcus pictagore quasi errorem computavi respectu modi indorum." Woepcke, Propagation etc., regards this as referring to two different systems, but the expression may very well mean algorism as performed upon the Pythagorean arcs (or table).
[533] "Book of the Abacus," this term then being used, and long afterwards in Italy, to mean merely the arithmetic of computation.
[534] "Incipit liber Abaci a Leonardo filio Bonacci compositus anno 1202 et correctus ab eodem anno 1228." Three MSS. of the thirteenth century are known, viz. at Milan, at Siena, and in the Vatican library. The work was first printed by Boncompagni in 1857.
[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 Universitäten des Mittelalters, Zürich, 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. Günther, 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 Encyclopädie der Erziehung, Vol. VI, p. 726; A. Kuckuk, "Die Rechenkunst im sechzehnten Jahrhundert," Festschrift zur dritten Säcularfeier des Berlinischen Gymnasiums zum grauen Kloster, Berlin, 1874, p. 4.