et infimae
Latinitatis_, Paris, 1842, gives also _chilerae_. Dasypodius,
_Institutiones Mathematicae_, Strassburg, 1593-1596, adds the forms
_zyphra_ and _syphra_. Boissiere, _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 quantite 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 Wal[=i]d 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: [Greek: kai ekoluse graphesthai Hellenisti tous demosious ton
logothesion kodikas, all' Arabiois auta parasemainesthai, choris ton
psephon, epeide adunaton tei ekeinon glossei monada e duada e triada e okto
hemisu e tria graphesthai; dio kai heos semeron eisin sun autois notarioi
Christianoi.] 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. _[H.]is[=a]b-al-[.G]ob[=a]r_, by an
anonymous author, probably Ab[=u] Sahl Dunash ibn Tamim, is given by
Steinschne