The history of the Arabic numerals, as they are generally called, is so
mixed up with that of the use of the decimal scale, that they form, in
fact, but a single inquiry. The mere history of the bare forms of
symbols has, doubtless, its use: but then it is only in the character of
_matériel_ for a philosophical discussion of the question--a discussion
into which the natural progress of the human mind and the urgency of
social wants must enter largely.
It might at first sight appear, from the cognate character of the Hebrew
and Arabic languages, that the idea of using a single symbol for each
number, might originate with either--with one as likely as with the
other. But on reflection it will readily appear that the question rather
resolves itself into one respecting the "hand-cursive" of the Jews and
Saracens, than into one respecting the constitution of the languages. Of
the Jewish we know nothing, or next to nothing, at the period in
question; whilst the Arabic is as well known as even our own present
style of calligraphy. It deserves to be more carefully inquired into
than has yet been done, whether the invention of contracting the written
compound symbols of the digital numbers into single symbols did not
really originate amongst the Jews rather than the Saracens; and even
whether the Arabs themselves did not obtain them from the "Jew
merchants" of the earlier ages of our era. One thing is tolerably
certain:--that the Jew merchant would, as a matter of precaution, keep
all his accounts in some secret notation, or in cipher. Whether this
should be a modified form of the Hebrew notation, or of the Latin, must
in a great degree depend upon the amount of literary acquirement common
amongst that people at the time.
Assuming that the Jews, as a literate people, were upon a par with their
Christian contemporaries, and that their knowledge was mainly confined
to mere commercial notation, an anonymous writer has shown how the
modifications of form could be naturally made, in vol. ii. of the _Bath
and Bristol Magazine_, pp. 393-412.; the motto being _valent quanti
valet_, as well as the title professing it to be wholly "conjectural."
Some of the speculations in it may, however, deserve further
considerations than they have yet received.[1]
The contraction of the compound symbols for the first nine digits into
single "figures," enabled the computer to dispense with the manual
labour of the _abacus_, whilst in his graphic notation he retained its
essential principle of _place_. It seems to be almost invariably
forgotten by writers on {280} the subject, what, without _this
principle_, no improvement in mere notation would have been of material
use in arithmetic; and on the other hand that the main difference
between the arithmetic of the _abacus_ and the arithmetic of the
_slate_, consists in the inevitable consequences of the denotation of
the single digits by single symbols.
The _abacus_, however, in its ordinary form, is essentially a decimal
instrument: but its form was also varied for commercial purposes,
perhaps in different ways. I never heard of the existence of one in any
collection: but there is preserved in the British Museum a picture of
one. This was printed by Mr. Halliwell in his _Rara Mathematica_--not a
fac-simile, but a rule and type representation of it, ciphers being used
by him for the circles in the original. Mr. Halliwell gives it without
note or remark; and evidently had not divined its meaning. This was
done, however, soon after in a review of Mr. Halliwell's book in the
_Philosophical Magazine_. I am not able at this moment to refer to
either, so as to give exact dates: but is was somewhere from 1838 to
1840.
Perhaps, however, I am giving "E.V." information that may be irrelevant
to his purpose; though it may of some use to another class of inquirers.
I proceed, therefore, to one or two notices that seem to have a more
direct bearing on his object:
1. Chasles' _Aperçu Historique sur l'Origine et le Développement de
Méthodes en Géométrie_; passim, but especially in note xii.: 4to.,
Bruxelles, 1837.
2. Chasles' several notices in _Comptes Rendus des Séances de l'Acad.
des Sciences._ All subsequent to the "Aperçu."
His _Catalogue des Manuscrits de la Bibliothèque de Ville de Chartres_
should also be consulted, if accessible to "E.V." Copies of it, however,
are very rare in the country, as it was privately printed and never
published. If, however, your correspondent have any serious inquiry in
view which should render his consultation of it desirable, I can put it
in his power to do so personally through you.