[223] "Decima vero o dicitur teca, circulus, vel cyfra vel figura nichili." [Maximilian Curtze, _Petri Philomeni de Dacia in Algorismum Vulgarem Johannis de Sacrobosco commentarius, una cum Algorismo ipso_, Copenhagen, 1897, p. 2.] Curtze cites five manuscripts (fourteenth and fifteenth centuries) of Dacia's commentary in the libraries at Erfurt, Leipzig, and Salzburg, in addition to those given by Enestroem, _Oefversigt af Kongl. Vetenskaps-Akademiens Foerhandlingar_, 1885, pp. 15-27, 65-70; 1886, pp. 57-60. [224] Curtze, loc. cit., p. VI. [225] _Rara Mathematica_, London, 1841, chap, i, "Joannis de Sacro-Bosco Tractatus de Arte Numerandi." [226] Smith, _Rara Arithmetica_, Boston, 1909. [227] In the 1484 edition, Borghi uses the form "cefiro: ouero nulla:" while in the 1488 edition he uses "zefiro: ouero nulla," and in the 1540 edition, f. 3, appears "Chiamata zero, ouero nulla." Woepcke asserted that it first appeared in Calandri (1491) in this sentence: "Sono dieci le figure con le quali ciascuno numero si puo significare: delle quali n'e una che si chiama zero: et per se sola nulla significa." (f. 4). [See _Propagation_, p. 522.] [228] Boncompagni _Bulletino_, Vol. XVI, pp. 673-685. [229] Leo Jordan, loc. cit. In the _Catalogue of MSS., Bibl. de l'Arsenal_, Vol. III, pp. 154-156, this work is No. 2904 (184 S.A.F.), Bibl. Nat., and is also called _Petit traicte de algorisme_. [230] Texada (1546) says that there are "nueue letros yvn zero o cifra" (f. 3). [231] Savonne (1563, 1751 ed., f. 1): "Vne ansi formee (o) qui s'appelle nulle, & entre marchans zero," showing the influence of Italian names on French mercantile customs. Trenchant (Lyons, 1566, 1578 ed., p. 12) also says: "La derniere qui s'apele nulle, ou zero;" but Champenois, his contemporary, writing in Paris in 1577 (although the work was not published until 1578), uses "cipher," the Italian influence showing itself less in this center of university culture than in the commercial atmosphere of Lyons. [232] Thus Radulph of Laon (c. 1100): "Inscribitur in ultimo ordine et figura [symbol] sipos nomine, quae, licet numerum nullum signitet, tantum ad alia quaedam utilis, ut insequentibus declarabitur." ["Der Arithmetische Tractat des Radulph von Laon," _Abhandlungen zur Geschichte der Mathematik_, Vol. V, p. 97, from a manuscript of the thirteenth century.] Chasles (_Comptes rendus_, t. 16, 1843, pp. 1393, 1408) calls attention to the fact that Radulph did not know how to use the zero, and he doubts if the sipos was really identical with it. Radulph says: "... figuram, cui sipos nomen est [symbol] in motum rotulae formatam nullius numeri significatione inscribi solere praediximus," and thereafter uses _rotula_. He uses the sipos simply as a kind of marker on the abacus.