[500] John is said to have died in 1157.

[501] For it says, "Incipit prologus in libro alghoarismi de practica arismetrice. Qui editus est a magistro Johanne yspalensi." It is published in full in the second part of Boncompagni's Trattati d'aritmetica.

[502] Possibly, indeed, the meaning of "libro alghoarismi" is not "to Al-Khowārazmī's book," but "to a book of algorism." John of Luna says of it: "Hoc idem est illud etiam quod ... alcorismus dicere videtur." [Trattati, p. 68.]

[503] For a résumé, see Cantor, Vol. I (3), pp. 800-803. As to the author, see Eneström in the Bibliotheca Mathematica, Vol. VI (3), p. 114, and Vol. IX (3), p. 2.

[504] Born at Cremona (although some have asserted at Carmona, in Andalusia) in 1114; died at Toledo in 1187. Cantor, loc. cit.; Boncompagni, Atti d. R. Accad. d. n. Lincei, 1851.

[505] See Abhandlungen zur Geschichte der Mathematik, Vol. XIV, p. 149; Bibliotheca Mathematica, Vol. IV (3), p. 206. Boncompagni had a fourteenth-century manuscript of his work, Gerardi Cremonensis artis metrice practice. See also T. L. Heath, The Thirteen Books of Euclid's Elements, 3 vols., Cambridge, 1908, Vol. I, pp. 92-94 ; A. A. Björnbo, "Gerhard von Cremonas Übersetzung von Alkwarizmis Algebra und von Euklids Elementen," Bibliotheca Mathematica, Vol. VI (3), pp. 239-248.

[506] Wallis, Algebra, 1685, p. 12 seq.

[507] Cantor, Geschichte, Vol. I (3), p. 906; A. A. Björnbo, "Al-Chwārizmī's trigonometriske Tavler," Festskrift til H. G. Zeuthen, Copenhagen, 1909, pp. 1-17.

[508] Heath, loc. cit., pp. 93-96.

[509] M. Steinschneider, Zeitschrift der deutschen morgenländischen Gesellschaft, Vol. XXV, 1871, p. 104, and Zeitschrift für Mathematik und Physik, Vol. XVI, 1871, pp. 392-393; M. Curtze, Centralblatt für Bibliothekswesen, 1899, p. 289; E. Wappler, Zur Geschichte der deutschen Algebra im 15. Jahrhundert, Programm, Zwickau, 1887; L. C. Karpinski, "Robert of Chester's Translation of the Algebra of Al-Khowārazmī," Bibliotheca Mathematica, Vol. XI (3), p. 125. He is also known as Robertus Retinensis, or Robert of Reading.