[129] Bayley, loc. cit., plate II. Similar forms to these here shown, and numerous other forms found in India, as well as those of other oriental countries, are given by A. P. Pihan, _Expose des signes de numeration usites chez les peuples orientaux anciens et modernes_, Paris, 1860. [130] Buehler, loc. cit., p. 80; J. F. Fleet, _Corpus inscriptionum Indicarum_, Vol. III, Calcutta, 1888. Lists of such words are given also by Al-B[=i]r[=u]n[=i] in his work _India_; by Burnell, loc. cit.; by E. Jacquet, "Mode d'expression symbolique des nombres employe par les Indiens, les Tibetains et les Javanais," _Journal Asiatique_, Vol. XVI, Paris, 1835. [131] This date is given by Fleet, loc. cit., Vol. III, p. 73, as the earliest epigraphical instance of this usage in India proper. [132] Weber, _Indische Studien_, Vol. VIII, p. 166 seq. [133] _Journal of the Royal Asiatic Society_, Vol. I (N.S.), p. 407. [134] VIII, 20, 21. [135] Th. H. Martin, _Les signes numeraux_ ..., Rome, 1864; Lassen, _Indische Alterthumskunde_, Vol. II, 2d ed., Leipzig and London, 1874, p. 1153. [136] But see Burnell, loc. cit., and Thibaut, _Astronomie, Astrologie und Mathematik_, p. 71. [137] A. Barth, "Inscriptions Sanscrites du Cambodge," in the _Notices et extraits des Mss. de la Bibliotheque nationale_, Vol. XXVII, Part I, pp. 1-180, 1885; see also numerous articles in _Journal Asiatique_, by Aymonier. [138] Buehler, loc. cit., p. 82. [139] Loc. cit., p. 79. [140] Buehler, loc. cit., p. 83. The Hindu astrologers still use an alphabetical system of numerals. [Burnell, loc. cit., p. 79.] [141] Well could Ramus say, "Quicunq; autem fuerit inventor decem notarum laudem magnam meruit." [142] Al-B[=i]r[=u]n[=i] gives lists. [143] _Propagation_, loc. cit., p. 443. [144] See the quotation from _The Light of Asia_ in Chapter II, p. 16. [145] The nine ciphers were called _a[.n]ka_. [146] "Zur Geschichte des indischen Ziffernsystems," _Zeitschrift fuer die Kunde des Morgenlandes_, Vol. IV, 1842, pp. 74-83. [147] It is found in the Bakh[s.][=a]l[=i] MS. of an elementary arithmetic which Hoernle placed, at first, about the beginning of our era, but the date is much in question. G. Thibaut, loc. cit., places it between 700 and 900 A.D.; Cantor places the body of the work about the third or fourth century A.D., _Geschichte der Mathematik_, Vol. I (3), p. 598. [148] For the opposite side of the case see G. R. Kaye, "Notes on Indian Mathematics, No. 2.--[=A]ryabha[t.]a," _Journ. and Proc. of the Asiatic Soc. of Bengal_, Vol. IV, 1908, pp. 111-141. [149] He used one of the alphabetic systems explained above. This ran up to 10^{18} and was not difficult, beginning as follows: [Illustration]