[244] It appears in the Polish arithmetic of Klos (1538) as cyfra. "The Ciphra 0 augmenteth places, but of himselfe signifieth not," Digges, 1579, p. 1. Hodder (10th ed., 1672, p. 2) uses only this word (cypher or cipher), and the same is true of the first native American arithmetic, written by Isaac Greenwood (1729, p. 1). Petrus de Dacia derives cyfra from circumference. "Vocatur etiam cyfra, quasi circumfacta vel circumferenda, quod idem est, quod circulus non habito respectu ad centrum." [Loc. cit., p. 26.]
[245] Opera mathematica, 1695, Oxford, Vol. I, chap. ix, Mathesis universalis, "De figuris numeralibus," pp. 46-49; Vol. II, Algebra, p. 10.
[246] Martin, Origine de notre système de numération écrite, note 149, p. 36 of reprint, spells τσίφρα from Maximus Planudes, citing Wallis as an authority. This is an error, for Wallis gives the correct form as above.
Alexander von Humboldt, "Über die bei verschiedenen Völkern üblichen Systeme von Zahlzeichen und über den Ursprung des Stellenwerthes in den indischen Zahlen," Crelle's Journal für reine und angewandte Mathematik, Vol. IV, 1829, called attention to the work ἀριθμοὶ Ἰνδικοί of the monk Neophytos, supposed to be of the fourteenth century. In this work the forms τζύφρα and τζύμφρα appear. See also Boeckh, De abaco Graecorum, Berlin, 1841, and Tannery, "Le Scholie du moine Néophytos," Revue Archéologique, 1885, pp. 99-102. Jordan, loc. cit., gives from twelfth and thirteenth century manuscripts the forms cifra, ciffre, chifras, and cifrus. Du Cange, Glossarium mediae et infimae Latinitatis, Paris, 1842, gives also chilerae. Dasypodius, Institutiones Mathematicae, Strassburg, 1593-1596, adds the forms zyphra and syphra. Boissière, L'art d'arythmetique contenant toute dimention, tres-singulier et commode, tant pour l'art militaire que autres calculations, Paris, 1554: "Puis y en a vn autre dict zero lequel ne designe nulle quantité par soy, ains seulement les loges vuides."
[247] Propagation, pp. 27, 234, 442. Treutlein, "Das Rechnen im 16. Jahrhundert," Abhandlungen zur Geschichte der Mathematik, Vol. I, p. 5, favors the same view. It is combated by many writers, e.g. A. C. Burnell, loc. cit., p. 59. Long before Woepcke, I. F. and G. I. Weidler, De characteribus numerorum vulgaribus et eorum aetatibus, Wittenberg, 1727, asserted the possibility of their introduction into Greece by Pythagoras or one of his followers: "Potuerunt autem ex oriente, uel ex phoenicia, ad graecos traduci, uel Pythagorae, uel eius discipulorum auxilio, cum aliquis eo, proficiendi in literis causa, iter faceret, et hoc quoque inuentum addisceret."
[248] E.g., they adopted the Greek numerals in use in Damascus and Syria, and the Coptic in Egypt. Theophanes (758-818 A.D.), Chronographia, Scriptores Historiae Byzantinae, Vol. XXXIX, Bonnae, 1839, p. 575, relates that in 699 A.D. the caliph Walīd forbade the use of the Greek language in the bookkeeping of the treasury of the caliphate, but permitted the use of the Greek alphabetic numerals, since the Arabs had no convenient number notation: καὶ ἐκώλυσε γράφεσθαι Ἑλληνιστὶ τοὺς δημοσίους τῶν λογοθεσίων κώδικας, ἀλλ' Ἀραβίοις αὐτὰ παρασημαίνεσθαι, χωρὶς τῶν ψήφων, ἐπειδὴ ἀδύνατον τῇ ἐκείνων γλώσσῃ μονάδα ἢ δυάδα ἢ τριάδα ἢ ὀκτὼ ἥμισυ ἢ τρία γράφεσθαι· διὸ καὶ ἕως σήμερόν εἰσιν σὺν αὐτοῖς νοτάριοι Χριστιανοί. The importance of this contemporaneous document was pointed out by Martin, loc. cit. Karabacek, "Die Involutio im arabischen Schriftwesen," Vol. CXXXV of Sitzungsberichte d. phil.-hist. Classe d. k. Akad. d. Wiss., Vienna, 1896, p. 25, gives an Arabic date of 868 A.D. in Greek letters.
[249] The Origin and History of Our Numerals (in Russian), Kiev, 1908; The Independence of European Arithmetic (in Russian), Kiev.
[250] Woepcke, loc. cit., pp. 462, 262.
[251] Woepcke, loc. cit., p. 240. Ḥisāb-al-Ġobār, by an anonymous author, probably Abū Sahl Dunash ibn Tamim, is given by Steinschneider, "Die Mathematik bei den Juden," Bibliotheca Mathematica, 1896, p. 26.
[252] Steinschneider in the Abhandlungen, Vol. III, p. 110.