r, showed
(_Algebra der Griechen_, 1842, p. 138), that Ptolemy merely used [Greek: o]
for [Greek: ouden], with no notion of zero. See also G. Fazzari, "Dell'
origine delle parole zero e cifra," _Ateneo_, Anno I, No. 11, reprinted at
Naples in 1903, where the use of the point and the small cross for zero is
also mentioned. Th. H. Martin, _Les signes numeraux_ etc., reprint p. 30,
and J. Brandis, _Das Muenz-, Mass- und Gewichtswesen in Vorderasien bis auf
Alexander den Grossen_, Berlin, 1866, p. 10, also discuss this usage of
[Greek: o], without the notion of place value, by the Greeks.

[201] _Al-Batt[=a]n[=i] sive Albatenii opus astronomicum_. Ad fidem codicis
escurialensis arabice editum, latine versum, adnotationibus instructum a
Carolo Alphonso Nallino, 1899-1907. Publicazioni del R. Osservatorio di
Brera in Milano, No. XL.

[202] Loc. cit., Vol. II, p. 271.

[203] C. Henry, "Prologus N. Ocreati in Helceph ad Adelardum Batensem
magistrum suum," _Abhandlungen zur Geschichte der Mathematik_, Vol. III,
1880.

[204] Max. Curtze, "Ueber eine Algorismus-Schrift des XII. Jahrhunderts,"
_Abhandlungen zur Geschichte der Mathematik_, Vol. VIII, 1898, pp. 1-27;
Alfred Nagl, "Ueber eine Algorismus-Schrift des XII. Jahrhunderts und ueber
die Verbreitung der indisch-arabischen Rechenkunst und Zahlzeichen im
christl. Abendlande," _Zeitschrift fuer Mathematik und Physik, Hist.-lit.
Abth._, Vol. XXXIV, pp. 129-146 and 161-170, with one plate.

[205] "Byzantinische Analekten," _Abhandlungen zur Geschichte der
Mathematik_, Vol. IX, pp. 161-189.

[206] [symbol] or [symbol] for 0. [symbol] also used for 5. [symbols] for
13. [Heiberg, loc. cit.]

[207] Gerhardt, _Etudes historiques sur l'arithmetique de position_,
Berlin, 1856, p. 12; J. Bowring, _The Decimal System in Numbers, Coins, &
Accounts_, London, 1854, p. 33.

[208] Karabacek, _Wiener Zeitschrift fuer die Kunde des Morgenlandes_, Vol.
XI, p. 13; _Fuehrer durch die Papyrus-Ausstellung Erzherzog Rainer_, Vienna,
1894, p. 216.

[209] In the library of G. A. Plimpton, Esq.

[210] Cantor, _Geschichte_, Vol. I (3), p. 674; Y. Mikami, "A Remark on the
Chinese Mathematics in Cantor's Geschichte der Mathematik," _Archiv der
Mathematik und Physik_, Vol. XV (3), pp. 68-70.

[211] Of course the earlier historians made innumerable guesses as to the
origin of the word _cipher_. E.g. Matthew Hostus, _De numeratione
emendata_, Antwerp, 1582, p. 10, says: "Siphra vox Hebraeam origine