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A Treatise Concerning the Principles of Human Knowledge by George Berkeley
page 92 of 112 (82%)
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 know the name of figures (with their due arrangement)
that according to the standing analogy belong to them. For, these signs
being known, we can by the operations of arithmetic know the signs of any
part of the particular sums signified by them; and, thus computing in
signs (because of the connexion established betwixt them and the distinct
multitudes of things whereof one is taken for an unit), we may be able
rightly to sum up, divide, and proportion the things themselves that we
intend to number.

122. In Arithmetic, therefore, we regard not the things, but the signs,
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