[107] Loc. cit., reprint, Part I, pp. 12, 17. Bayley's deductions are generally regarded as unwarranted.
[108] The Alphabet; London, 1883, Vol. II, pp. 265, 266, and The Academy of Jan. 28, 1882.
[109] Taylor, The Alphabet, loc. cit., table on p. 266.
[110] Bühler, On the Origin of the Indian Brāhma Alphabet, Strassburg, 1898, footnote, pp. 52, 53.
[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 ṣunya (empty) (it occurs even in Piñgala). It is the decimal place value of these figures which gives them significance." C. Henry, "Sur l'origine de quelques notations mathématiques," Revue Archéologique, 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] Bühler, 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 Bühler'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 Bibliothèque 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 für 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 hiéroglyphique des chiffres et des lettres de tous les peuples, Paris, 1826; G. Kleinwächter, "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.