diae Sapientibus ex
figura circuli secti inuenti."

[123] V. A. Smith, _The Early History of India_, Oxford, 2d ed., 1908, p.
333.

[124] C. J. Ball, "An Inscribed Limestone Tablet from Sippara,"
_Proceedings of the Society of Biblical Archaeology_, Vol. XX, p. 25
(London, 1898). Terrien de Lacouperie states that the Chinese used the
circle for 10 before the beginning of the Christian era. [_Catalogue of
Chinese Coins_, London, 1892, p. xl.]

[125] For a purely fanciful derivation from the corresponding number of
strokes, see W. W. R. Ball, _A Short Account of the History of
Mathematics_, 1st ed., London, 1888, p. 147; similarly J. B. Reveillaud,
_Essai sur les chiffres arabes_, Paris, 1883; P. Voizot, "Les chiffres
arabes et leur origine," _La Nature_, 1899, p. 222; G. Dumesnil, "De la
forme des chiffres usuels," _Annales de l'universite de Grenoble_, 1907,
Vol. XIX, pp. 657-674, also a note in _Revue Archeologique_, 1890, Vol. XVI
(3), pp. 342-348; one of the earliest references to a possible derivation
from points is in a work by Bettino entitled _Apiaria universae
philosophiae mathematicae in quibus paradoxa et noua machinamenta ad usus
eximios traducta, et facillimis demonstrationibus confirmata_, Bologna,
1545, Vol. II, Apiarium XI, p. 5.

[126] _Alphabetum Barmanum_, Romae, MDCCLXXVI, p. 50. The 1 is evidently
Sanskrit, and the 4, 7, and possibly 9 are from India.

[127] _Alphabetum Grandonico-Malabaricum_, Romae, MDCCLXXII, p. 90. The
zero is not used, but the symbols for 10, 100, and so on, are joined to the
units to make the higher numbers.

[128] _Alphabetum Tangutanum_, Romae, MDCCLXXIII, p. 107. In a Tibetan MS.
in the library of Professor Smith, probably of the eighteenth century,
substantially these forms are given.

[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.