number being defined a "collection of units," we
may conclude that, if there be no such thing as unity or unit in
abstract, there are no ideas of number in abstract denoted by the numeral
names and figures. The theories therefore in Arithmetic, if they are
abstracted from the names and figures, as likewise from all use and
practice, as well as from the particular things numbered, can be supposed
to have nothing at all for their object; hence we may see how entirely
the science of numbers is subordinate to practice, and how jejune and
trifling it becomes when considered as a matter of mere speculation.

121. However, since there may be some who, deluded by the specious show
of discovering abstracted verities, waste their time in arithmetical
theorems and problems which have not any use, it will not be amiss if we
more fully consider and expose the vanity of that pretence; and this will
plainly appear by taking a view of Arithmetic in its infancy, and
observing what it was that originally put men on the study of that
science, and to what scope they directed it. It is natural to think that
at first, men, for ease of memory and help of computation, made use of
counters, or in writing of single strokes, points, or the like, each
whereof was made to signify an unit, i.e., some one thing of whatever
kind they had occasion to reckon. Afterwards they found out the more
compendious ways of making one character stand in place of several
strokes or points. And, lastly, the notation of the Arabians or Indians
came into use, wherein, by the repetition of a few characters or figures,
and varying the signification of each figure according to the place it
obtains, all numbers may be most aptly expressed; which seems to have
been done in imitation of language, so that an exact analogy is observed
betwixt the notation by figures and names, the nine simple figures
answering the nine first numeral names and places in the former,
corresponding to denominations in the latter. And agreeably to those
conditions of the simple and local value of figures, were contrived
methods of finding, from the given figures or marks of the parts, what
figures and how placed are proper to denote the whole, or vice versa. And
having found the sought figures, the same rule or analogy being observed
throughout, it is easy to read them into words; and so the number becomes
perfectly known. For then the number of any particular things is said to
be known, when we k