[Boncompagni Buttetino, XV, p. 132.] Turchill (twelfth century) gives the names Igin, andras, hormis, arbas, quimas, caletis, zenis, temenias, celentis, saying: "Has autem figuras, ut donnus [dominus] Gvillelmus Rx testatur, a pytagoricis habemus, nomina uero ab arabibus." (Who the William R. was is not known. Boncompagni Bulletino XV, p. 136.) Radulph of Laon (d. 1131) asserted that they were Chaldean (Propagation, p. 48 n.). A discussion of the whole question is also given in E. C. Bayley, loc. cit. Huet, writing in 1679, asserted that they were of Semitic origin, as did Nesselmann in spite of his despair over ormis, calctis, and celentis; see Woepcke, Propagation, p. 48. The names were used as late as the fifteenth century, without the zero, but with the superscript dot for 10's, two dots for 100's, etc., as among the early Arabs. Gerhardt mentions having seen a fourteenth or fifteenth century manuscript in the Bibliotheca Amploniana with the names "Ingnin, andras, armis, arbas, quinas, calctis, zencis, zemenias, zcelentis," and the statement "Si unum punctum super ingnin ponitur, X significat.... Si duo puncta super ... figuras superponunter, fiet decuplim illius quod cum uno puncto significabatur," in Monatsberichte der K. P. Akad. d. Wiss., Berlin, 1867, p. 40.
[471] A chart of ten numerals in 200 tongues, by Rev. R. Patrick, London, 1812.
[472] "Numeratio figuralis est cuiusuis numeri per notas, et figuras numerates descriptio." [Clichtoveus, edition of c. 1507, fol. C ii, v.] "Aristoteles enim uoces rerum σύμβολα uocat: id translatum, sonat notas." [Noviomagus, De Numeris Libri II, cap. vi.] "Alphabetum decem notarum." [Schonerus, notes to Ramus, 1586, p. 3 seq.] Richer says: "novem numero notas omnem numerum significantes." [Bubnov, loc. cit., p. 381.]
[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 hæ notulæ, 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. Blassière'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 Köbel, 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 für 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.