Would it not be worth while to give a _facsimile_ of the "Tabel for
all manere of merchauntes," in the "Notes and Queries"? It is not only
a curiosity, but an important element (and unique as far as is known)
in the philosophic history of our arithmetic. It was, no doubt, an
actual instrument in constant use in the merchant's office, as much so
as an almanac, interest-tables, a "cambist" and a copying-press, are
now.
As regards the cipher, the difficulty only commenced with _writing
numbers_ in the new symbology. With persons accustomed to the use
of this instrument, there is no doubt that the mode of obviating the
difficulty of "keeping the place," would suggest itself at once. In
this instrument an empty hole (without its peg) _signified_ "none of
this denomination." What then more simple than to make the outline
of the empty hole which occupied the "local position" of any
denomination, when none of that precise denomination occurred in the
number itself? Under this view the process at least becomes simple
and natural; and as the early merchants contributed so largely to the
improvement of our arithmetical processes, such a conclusion is wholly
divested of improbability on any other ground. The circle would then
naturally become, as it certainly has practically become, the most
appropriate symbol of _nothingness_.
As regards the term _cipher_ or _zero_ (which are so obviously the
same as to need no remark), it is admitted on all hands to be derived
from one or other of the Semitic languages, the Hebrew or the Arabic.
It is customery with the mathematical historians to refer it to the
Arabic, they being in general more conversant with it than with the
Hebrew. The Arabic being a smaller hand than the Hebrew, a dot was
used instead of the circle for marking the "place" at which the hiatus
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 mediæval 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.