[473] "Il y a dix Characteres, autrement Figures, Notes, ou Elements." [Peletier, edition of 1607, p. 13.] "Numerorum notas alij figuras, alij signa, alij characteres uocant." [Glareanus, 1545 edition, f. 9, r.] "Per figuras (quas zyphras uocant) assignationem, quales sunt hae notulae, 1. 2. 3. 4...." [Noviomagus, _De Numeris Libri II_, cap. vi.] Gemma Frisius also uses _elementa_ and Cardan uses _literae_. In the first arithmetic by an American (Greenwood, 1729) the author speaks of "a few Arabian _Charecters_ or Numeral Figures, called _Digits_" (p. 1), and as late as 1790, in the third edition of J. J. Blassiere's arithmetic (1st ed. 1769), the name _characters_ is still in use, both for "de Latynsche en de Arabische" (p. 4), as is also the term "Cyfferletters" (p. 6, n.). _Ziffer_, the modern German form of cipher, was commonly used to designate any of the nine figures, as by Boeschenstein and Riese, although others, like Koebel, used it only for the zero. So _zifre_ appears in the arithmetic by Borgo, 1550 ed. In a Munich codex of the twelfth century, attributed to Gerland, they are called _characters_ only: "Usque ad VIIII. enim porrigitur omnis numerus et qui supercrescit eisdem designator Karacteribus." [Boncompagni _Bulletino_, Vol. X. p. 607.] [474] The title of his work is _Prologus N. Ocreati in Helceph_ (Arabic _al-qeif_, investigation or memoir) _ad Adelardum Batensem magistrum suum_. The work was made known by C. Henry, in the _Zeitschrift fuer Mathematik und Physik_, Vol. XXV, p. 129, and in the _Abhandlungen zur Geschichte der Mathematik_, Vol. III; Weissenborn, _Gerbert_, p. 188. [475] The zero is indicated by a vacant column. [476] Leo Jordan, loc. cit., p. 170. "Chifre en augorisme" is the expression used, while a century later "giffre en argorisme" and "cyffres d'augorisme" are similarly used. [477] _The Works of Geoffrey Chaucer_, edited by W. W. Skeat, Vol. IV, Oxford, 1894, p. 92. [478] Loc. cit., Vol. III, pp. 179 and 180. [479] In Book II, chap, vii, of _The Testament of Love_, printed with Chaucer's Works, loc. cit., Vol. VII, London, 1897. [480] _Liber Abacci_, published in Olleris, _Oeuvres de Gerbert_, pp. 357-400. [481] G. R. Kaye, "The Use of the Abacus in Ancient India," _Journal and Proceedings of the Asiatic Society of Bengal_, 1908, pp. 293-297. [482] _Liber Abbaci_, by Leonardo Pisano, loc. cit., p. 1. [483] Friedlein, "Die Entwickelung des Rechnens mit Columnen," _Zeitschrift fuer Mathematik und Physik_, Vol. X, p. 247. [484] The divisor 6 or 16 being increased by the difference 4, to 10 or 20 respectively. [485] E.g. Cantor, Vol. I, p. 882.