more particularly to the study of logic; I mean, who consider the nature
of science, certainty, and demonstration: it being by them assigned as
one reason of the extraordinary clearness and evidence of geometry that
in this science the reasonings are free from those inconveniences which
attend the use of arbitrary signs, the very ideas themselves being copied
out and exposed to view upon paper. But, by the bye, how well this agrees
with what they likewise assert of abstract ideas being the object of
geometrical demonstration I leave to be considered.

151. To come to a resolution in this point we need only observe what hath
been said in sect. 59, 60, 61, where it is shown that visible extensions
in themselves are little regarded, and have no settled determinable
greatness, and that men measure altogether, by the application of
tangible extension to tangible extension. All which makes it evident that
visible extension and figures are not the object of geometry.

152. It is therefore plain that visible figure are of the same use in
geometry that words are: and the one may as well be accounted the object
of that science as the other, neither of them being otherwise concerned
therein than as they represent or suggest to the mind the particular
tangible figures connected with them. There is indeed this difference
between the signification of tangible figures by visible figures, and of
ideas by words: that whereas the latter is variable and uncertain,
depending altogether on the arbitrary appointment of men, the former is
fixed and immutably the same in all times and places. A visible square,
for instance, suggests to the mind the same tangible figure in Europe
that it doth in America. Hence it is that the voice of the Author of'
Nature which speaks to our eyes, is not liable to that misinterpretation
and ambiguity that languages of human contrivance are unavoidably subject
to.