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]

the same letter (_ka_) appearing in the successive consonant forms, _ka_,
_kha_, _ga_, _gha_, etc. See C. I. Gerhardt, _Ueber die Entstehung und
Ausbreitung des dekadischen Zahlensystems_, Programm, p. 17, Salzwedel,
1853, and _Etudes historiques sur l'arithmetique de position_, Programm, p.
24, Berlin, 1856; E. Jacquet, _Mode d'expression symbolique des nombres_,
loc. cit., p. 97; L. Rodet, "Sur la veritable signi