e of this
hypothesis. The first ideas of number must necessarily then have been
derived from like or equal magnitudes as seen chiefly in organic
objects; and as the like magnitudes most frequently observed magnitudes
of extension, it follows that geometry and arithmetic had a
simultaneous origin.

Not only are the first distinct ideas of number co-ordinate with ideas
of likeness and equality, but the first efforts at numeration displayed
the same relationship. On reading the accounts of various savage tribes,
we find that the method of counting by the fingers, still followed by
many children, is the aboriginal method. Neglecting the several cases in
which the ability to enumerate does not reach even to the number of
fingers on one hand, there are many cases in which it does not extend
beyond ten--the limit of the simple finger notation. The fact that in so
many instances, remote, and seemingly unrelated nations, have adopted
_ten_ as their basic number; together with the fact that in the
remaining instances the basic number is either _five_ (the fingers of
one hand) or _twenty_ (the fingers and toes); almost of themselves show
that the fingers were the original units of numeration. The still
surviving use of the word _digit_, as the general name for a figure in
arithmetic, is significant; and it is even said that our word _ten_
(Sax. _tyn_; Dutch, _tien_; German, _zehn_) means in its primitive
expanded form _two hands_. So that originally, to say there were ten
things, was to say there were two hands of them.

From all which evidence it is tolerably clear that the earliest mode of
conveying the idea of any number of things, was by holding up as many
fingers as there were things; that is--using a symbol which was _equal_,
in respect of multiplicity, to the group symbolised. For which inference
there is, indeed, strong confirmation in the recent statement that our
own soldiers are even now spontaneously adopting this device in their
dealings with the Turks. And here it should be remarked that in this
recombination of the notion of equality with that of multiplicity, by
which the first steps in numeration are effected, we may see one of the
earliest of those inosculations between the diverging branches of
science, which are afterwards of perpetual occurrence.

Indeed, as this observation suggests, it will be well, before tracing
the mode in which exact science finally emerges from the merely
approximate judgments of the