[111] Albrecht Weber, _History of Indian Literature_, English ed., Boston,
1878, p. 256: "The Indian figures from 1-9 are abbreviated forms of the
initial letters of the numerals themselves...: the zero, too, has arisen
out of the first letter of the word _[s.]unya_ (empty) (it occurs even in
Pingala). It is the decimal place value of these figures which gives them
significance." C. Henry, "Sur l'origine de quelques notations
mathematiques," _Revue Archeologique_, June and July, 1879, attempts to
derive the Boethian forms from the initials of Latin words. See also J.
Prinsep, "Examination of the Inscriptions from Girnar in Gujerat, and
Dhauli in Cuttach," _Journal of the Asiatic Society of Bengal_, 1838,
especially Plate XX, p. 348; this was the first work on the subject.
[112] Buehler, _Palaeographie_, p. 75, gives the list, with the list of
letters (p. 76) corresponding to the number symbols.
[113] For a general discussion of the connection between the numerals and
the different kinds of alphabets, see the articles by U. Ceretti, "Sulla
origine delle cifre numerali moderne," _Rivista di fisica, matematica e
scienze naturali_, Pisa and Pavia, 1909, anno X, numbers 114, 118, 119, and
120, and continuation in 1910.
[114] This is one of Buehler's hypotheses. See Bayley, loc. cit., reprint p.
4; a good bibliography of original sources is given in this work, p. 38.
[115] Loc. cit., reprint, part I, pp. 12, 17. See also Burnell, loc. cit.,
p. 64, and tables in plate XXIII.
[116] This was asserted by G. Hager (_Memoria sulle cifre arabiche_, Milan,
1813, also published in _Fundgruben des Orients_, Vienna, 1811, and in
_Bibliotheque Britannique_, Geneva, 1812). See also the recent article by
Major Charles E. Woodruff, "The Evolution of Modern Numerals from Tally
Marks," _American Mathematical Monthly_, August-September, 1909.
Biernatzki, "Die Arithmetik der Chinesen," _Crelle's Journal fuer die reine
und angewandte Mathematik_, Vol. LII, 1857, pp. 59-96, also asserts the
priority of the Chinese claim for a place system and the zero, but upon the
flimsiest authority. Ch. de Paravey, _Essai sur l'origine unique et
hieroglyphique des chiffres et des lettres de tous les peuples_, Paris,
1826; G. Kleinwaechter, "The Origin of the Arabic Numerals," _China Review_,
Vol. XI, 1882-1883, pp. 379-381, Vol. XII, pp. 28-30; Biot, "Note sur la
connaissance que les Chinois ont eue de la valeur de position des
chiffres," _Journal Asiatique_, 1839, pp. 497-502. A. Terrien de
Lacouperie, "The Old Numerals, the Counting-Rods and the Swan-Pan in
China," _Numismatic Chronicle_, Vol. III (3), pp. 297-340, and Crowder B.
Moseley, "Numeral Characters: Theory of Origin and Development," _American
Antiquarian_, Vol. XXII, pp. 279-284, both propose to derive our numerals
from Chinese characters, in much the same way as is done by Major Woodruff,
in the article above cited.
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