[187] From a letter to D. E. Smith, from G. F. Hill of the British Museum. See also his monograph "On the Early Use of Arabic Numerals in Europe," in _Archaeologia_, Vol. LXII (1910), p. 137. [188] R. Hoernle, "The Baksh[=a]l[=i] Manuscript," _Indian Antiquary_, Vol. XVII, pp. 33-48 and 275-279, 1888; Thibaut, _Astronomie, Astrologie und Mathematik_, p. 75; Hoernle, _Verhandlungen_, loc. cit., p. 132. [189] Bayley, loc. cit., Vol. XV, p. 29. Also Bendall, "On a System of Numerals used in South India," _Journal of the Royal Asiatic Society_, 1896, pp. 789-792. [190] V. A. Smith, _The Early History of India_, 2d ed., Oxford, 1908, p. 14. [191] Colebrooke, _Algebra, with Arithmetic and Mensuration, from the Sanskrit of Brahmegupta and Bhascara_, London, 1817, pp. 339-340. [192] Ibid., p. 138. [193] D. E. Smith, in the _Bibliotheca Mathematica_, Vol. IX (3), pp. 106-110. [194] As when we use three dots (...). [195] "The Hindus call the nought explicitly _['s][=u]nyabindu_ 'the dot marking a blank,' and about 500 A.D. they marked it by a simple dot, which latter is commonly used in inscriptions and MSS. in order to mark a blank, and which was later converted into a small circle." [Buehler, _On the Origin of the Indian Alphabet_, p. 53, note.] [196] Fazzari, _Dell' origine delle parole zero e cifra_, Naples, 1903. [197] E. Wappler, "Zur Geschichte der Mathematik im 15. Jahrhundert," in the _Zeitschrift fuer Mathematik und Physik_, Vol. XLV, _Hist.-lit. Abt._, p. 47. The manuscript is No. C. 80, in the Dresden library. [198] J. G. Praendel, _Algebra nebst ihrer literarischen Geschichte_, p. 572, Munich, 1795. [199] See the table, p. 23. Does the fact that the early European arithmetics, following the Arab custom, always put the 0 after the 9, suggest that the 0 was derived from the old Hindu symbol for 10? [200] Bayley, loc. cit., p. 48. From this fact Delambre (_Histoire de l'astronomie ancienne_) inferred that Ptolemy knew the zero, a theory accepted by Chasles, _Apercu historique sur l'origine et le developpement des methodes en geometrie_, 1875 ed., p. 476; Nesselmann, however, showed (_Algebra der Griechen_, 1842, p. 138), that Ptolemy merely used [Greek: o] for [Greek: ouden], with no notion of zero. See also G. Fazzari, "Dell' origine delle parole zero e cifra," _Ateneo_, Anno I, No. 11, reprinted at Naples in 1903, where the use of the point and the small cross for zero is also mentioned. Th. H. Martin, _Les signes numeraux_ etc., reprint p. 30, and J. Brandis, _Das Muenz-, Mass- und Gewichtswesen in Vorderasien bis auf Alexander den Grossen_, Berlin, 1866, p. 10, also discuss this usage of [Greek: o], without the notion of place value, by the Greeks. [201] _Al-Batt[=a]n[=i] sive Albatenii opus astronomicum_. Ad fidem codicis escurialensis arabice editum, latine versum, adnotationibus instructum a Carolo Alphonso Nallino, 1899-1907. Publicazioni del R. Osservatorio di Brera in Milano, No. XL. [202] Loc. cit., Vol. II, p. 271.