It would, without doubt, seem odd to a
mathematician to go about to convince him the diagrams he saw upon paper
were not the figures, or even the likeness of the figures, which make the
subject of the demonstration. The contrary being held an unquestionable
truth, not only by mathematicians, but also by those who apply themselves
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.
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