[360] a, h, i, are from the Friedlein ed.; the original in the manuscript from which a is taken contains a zero symbol, as do all of the six plates given by Friedlein. b-e from the Boncompagni _Bulletino_, Vol. X, p. 596; f ibid., Vol. XV, p. 186; g _Memorie della classe di sci., Reale Acc. dei Lincei_, An. CCLXXIV (1876-1877), April, 1877. A twelfth-century arithmetician, possibly John of Luna (Hispalensis, of Seville, c. 1150), speaks of the great diversity of these forms even in his day, saying: "Est autem in aliquibus figuram istarum apud multos diuersitas. Quidam enim septimam hanc figuram representant [Symbol] alii autem sic [Symbol], uel sic [Symbol]. Quidam vero quartam sic [Symbol]." [Boncompagni, _Trattati_, Vol. II, p. 28.] [361] Loc. cit., p. 59. [362] Ibid., p. 101. [363] Loc. cit., p. 396. [364] Khosr[=u] I, who began to reign in 531 A.D. See W. S. W Vaux, _Persia, _London, 1875, p. 169; Th. Noeldeke, _Aufsaetze zur persichen Geschichte_, Leipzig, 1887, p. 113, and his article in the ninth edition of the _Encyclopaedia Britannica_. [365] Colebrooke, _Essays_, Vol. II, p. 504, on the authority of Ibn al-Adam[=i], astronomer, in a work published by his continuator Al-Q[=a]sim in 920 A.D.; Al-B[=i]r[=u]n[=i], _India, _Vol. II, p. 15. [366] H. Suter, _Die Mathematiker_ etc., pp. 4-5, states that Al-Faz[=a]r[=i] died between 796 and 806. [367] Suter, loc. cit., p. 63. [368] Suter, loc. cit., p. 74. [369] Suter, _Das Mathematiker-Verzeichniss im Fihrist_. The references to Suter, unless otherwise stated, are to his later work _Die Mathematiker und Astronomen der Araber_ etc. [370] Suter, _Fihrist_, p. 37, no date. [371] Suter, _Fihrist_, p. 38, no date. [372] Possibly late tenth, since he refers to one arithmetical work which is entitled _Book of the Cyphers_ in his _Chronology_, English ed., p. 132. Suter, _Die Mathematiker_ etc., pp. 98-100, does not mention this work; see the _Nachtraege und Berichtigungen_, pp. 170-172. [373] Suter, pp. 96-97. [374] Suter, p. 111. [375] Suter, p. 124. As the name shows, he came from the West. [376] Suter, p. 138. [377] Hankel, _Zur Geschichte der Mathematik_, p. 256, refers to him as writing on the Hindu art of reckoning; Suter, p. 162. [378] [Greek: Psephophoria kat' Indous], Greek ed., C. I. Gerhardt, Halle, 1865; and German translation, _Das Rechenbuch des Maximus Planudes_, H. Waeschke, Halle, 1878. [379] "Sur une donnee historique relative a l'emploi des chiffres indiens par les Arabes," Tortolini's _Annali di scienze mat. e fis._, 1855. [380] Suter, p. 80. [381] Suter, p. 68. [382] Sprenger also calls attention to this fact, in the _Zeitschrift d. deutschen morgenlaend. Gesellschaft_, Vol. XLV, p. 367. [383] Libri, _Histoire des mathematiques_, Vol. I, p. 147. [384] "Dictant la paix a l'empereur de Constantinople, l'Arabe victorieux demandait des manuscrits et des savans." [Libri, loc. cit., p. 108.] [385] Persian _bagadata_, "God-given."