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.

[233] Rabbi ben Ezra (1092-1168) used both [Hebrew: GLGL], _galgal_ (the
Hebrew for _wheel_), and [Hebrew: SPR'], _sifra_. See M. Steinschneider,
"Die Mathematik bei den Juden," in _Bibliotheca Mathematica_, 1893, p. 69,
and Silberberg, _Das Buch der Zahl des R. Abraham ibn Esra_, Frankfurt a.
M., 1895, p. 96, note 23; in this work the Hebrew letters are used for
numerals with place value, having the zero.

[234] E.g., in the twelfth-century _Liber aligorismi_ (see Boncompagni's
_Trattati_, II, p. 28). So Ramus (_Libri II_, 1569 ed., p. 1) says:
"Circulus quae nota est ultima: nil per se significat." (See also the
Schonerus ed. of Ramus, 1586, p. 1.)

[235] "Und wirt das ringlein o. die Ziffer genant die nichts bedeut."
[Koebel's _Rechenbuch_, 1549 ed., f. 10, and other editions.]

[236] I.e. "circular figure," our word _notation_ having come from the
medieval _nota_. Thus Tzwivel (1507,