of any "denomination" occurred. If we obtained our cipher from this,
it would be made hollow (a mere _ceinture_, girdle, or ring) to
save the trouble of making a dot sufficiently large to correspond in
magnitude with our other numerals as we write them. Either is alike
possible--probability must be sought, for either over the other, from
a slightly different source.

The root-words in Hebrew and in Arabic are precisely the same
(_ts-ph-r_), though in the two {368} languages, and at different ages
of the same language, they might have been vowelised differently.
In some shape or other, this name is used in all countries that have
derived their arithmetic from mediaeval Italy, or from the Saracens. It
is with some _cipher_, with others _chiffre_, and with all _zero_. The
word is certainly no more Italian than it is French or English. Be it
remembered, too, that _ezor_ (quoted at p. 268.), as a _girdle_, is
radically the same word, somewhat mutilated. The cardinal meaning of
the word (denuded of the conventional accretions of signification,
which peculiar applications of it adds to the cardinal meaning)
appears to be _emptiness_, _hollowness_, _nothingness_. It may be
further remarked, that in the fine Chartres MS. of Boetius, described
by Chasles, the 0 is called _sipos_:--the same name, he remarks,
that Graves found in use in the East. The modern Turks call the 0,
_tsifra_.

It is curious enough that in all languages, the term _ciphering_ is
popularly used to denote all arithmetical operations whatever.
Our schoolboys do their "ciphering," and write carefully in their
"ciphering-books." This all seems to point to the art of dispensing
with the use of the abacus or counting table.

T.S.D.

Shooter's Hill, March 5.

[1] The best account, because the most consistent and
intelligible, of the Greek arithmetic, is that by Delambre, affixed to
Peyraud's edition of Archimedes.

[2] At a period of leisure I may be tempted to send you a few
extracts, somewhat curious, from some of the papers of Mr. Strachey in
my possession.

_Arabic Numerals_.--I had replied to "E.V." (No. 15. p. 230.), when
I saw by your "Notice to Correspondents," that the question was
answered. I therefore waited the publication of the replies, which I
find do not embrace any one of the points to which I would call the
attention of "E.V."--Diophantus of Alexandria, who flourished about
150 years after Christ, and who wrote thirteen books of algebra