[32] Verifying the hypothesis of Woepcke, _Propagation_, that the Sindhind included a treatment of arithmetic. [33] A[h.]med ibn `Abdall[=a]h, Suter, _Die Mathematiker_, etc., p. 12. [34] _India_, Vol. II, p. 15. [35] See H. Suter, "Das Mathematiker-Verzeichniss im Fihrist," _Abhandlungen zur Geschichte der Mathematik_, Vol. VI, Leipzig, 1892. For further references to early Arabic writers the reader is referred to H. Suter, _Die Mathematiker und Astronomen der Araber und ihre Werke_. Also "Nachtraege und Berichtigungen" to the same (_Abhandlungen_, Vol. XIV, 1902, pp. 155-186). [36] Suter, loc. cit., note 165, pp. 62-63. [37] "Send Ben Ali,... tum arithmetica scripta maxime celebrata, quae publici juris fecit." [Loc. cit., p. 440.] [38] _Scritti di Leonardo Pisano_, Vol. I, _Liber Abbaci_ (1857); Vol. II, _Scritti_ (1862); published by Baldassarre Boncompagni, Rome. Also _Tre Scritti Inediti_, and _Intorno ad Opere di Leonardo Pisano_, Rome, 1854. [39] "Ubi ex mirabili magisterio in arte per novem figuras indorum introductus" etc. In another place, as a heading to a separate division, he writes, "De cognitione novem figurarum yndorum" etc. "Novem figure indorum he sunt 9 8 7 6 5 4 3 2 1." [40] See _An Ancient English Algorism_, by David Eugene Smith, in _Festschrift Moritz Cantor_, Leipzig, 1909. See also Victor Mortet, "Le plus ancien traite francais d'algorisme," _Bibliotheca Mathematica_, Vol. IX (3), pp. 55-64. [41] These are the two opening lines of the _Carmen de Algorismo_ that the anonymous author is explaining. They should read as follows: Haec algorismus ars praesens dicitur, in qua Talibus Indorum fruimur bis quinque figuris. What follows is the translation. [42] Thibaut, _Astronomie, Astrologie und Mathematik_, Strassburg, 1899. [43] Gustave Schlegel, _Uranographie chinoise ou preuves directes que l'astronomie primitive est originaire de la Chine, et qu'elle a ete empruntee par les anciens peuples occidentaux a la sphere chinoise; ouvrage accompagne d'un atlas celeste chinois et grec_, The Hague and Leyden, 1875. [44] E. W. Hopkins, _The Religions of India_, Boston, 1898, p. 7. [45] R. C. Dutt, _History of India_, London, 1906. [46] W. D. Whitney, _Sanskrit Grammar_, 3d ed., Leipzig, 1896. [47] "Das [=A]pastamba-['S]ulba-S[=u]tra," _Zeitschrift der deutschen Morgenlaendischen Gesellschaft_, Vol. LV, p. 543, and Vol. LVI, p. 327. [48] _Geschichte der Math._, Vol. I, 2d ed., p. 595.