si deus
uoluerit." [Boncompagni, _Trattati d'Aritmetica_, Rome, 1857.] Discussed
by F. Woepcke, _Sur l'introduction de l'arithmetique indienne en Occident_,
Rome, 1859.

[13] Thus in a commentary by `Al[=i] ibn Ab[=i] Bekr ibn al-Jam[=a]l
al-An[s.][=a]r[=i

[14] See also Woepcke, _Propagation_, p. 505. The origin is discussed at
much length by G. R. Kaye, "Notes on Indian Mathematics.--Arithmetical
Notation," _Journ. and Proc. of the Asiatic Soc. of Bengal_, Vol. III,
1907, p. 489.

[15] _Alberuni's India_, Arabic version, London, 1887; English translation,
ibid., 1888.

[16] _Chronology of Ancient Nations_, London, 1879. Arabic and English
versions, by C. E. Sachau.

[17] _India_, Vol. I, chap. xvi.

[18] The Hindu name for the symbols of the decimal place system.

[19] Sachau's English edition of the _Chronology_, p. 64.

[20] _Litterature arabe_, Cl. Huart, Paris, 1902.

[21] Huart, _History of Arabic Literature_, English ed., New York, 1903, p.
182 seq.

[22] Al-Mas`[=u]d[=i]'s _Meadows of Gold_, translated in part by Aloys
Sprenger, London, 1841; _Les prairies d'or_, trad. par C. Barbier de
Meynard et Pavet de Courteille, Vols. I to IX, Paris, 1861-1877.

[23] _Les prairies d'or_, Vol. VIII, p. 289 seq.

[24] _Essays_, Vol. II, p. 428.

[25] Loc. cit., p. 504.

[26] _Materiaux pour servir a l'histoire comparee des sciences
mathematiques chez les Grecs et les Orientaux_, 2 vols., Paris, 1845-1849,
pp. 438-439.

[27] He made an exception, however, in favor of the numerals, loc. cit.,
Vol. II, p. 503.

[28] _Bibliotheca Arabico-Hispana Escurialensis_, Madrid, 1760-1770, pp.
426-427.

[29] The author, Ibn al-Qif[t.][=i], flourished A.D. 1198 [Colebrooke, loc.
cit., note Vol. II, p. 510].

[30] "Liber Artis Logisticae a Mohamado Ben Musa _Alkhuarezmita_ exornatus,
qui ceteros omnes brevitate methodi ac facilitate praestat, Indorum que in
praeclarissimis inventis ingenium & acumen ostendit." [Casiri, loc. cit.,
p. 427.]

[31] Macoudi, _Le livre de l'avertissement et de la revision_. Translation
by B. Carra de Vaux, Paris, 1896.

[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 refe