Nor does the objection hold good that possibly this idea
of a triangle has reached my mind through the medium of my
senses, since I have sometimes seen bodies triangular in
shape; because I can form in my mind an infinitude of other
figures regarding which we cannot have the least conception of
their ever having been objects of sense, and I can
nevertheless demonstrate various properties pertaining to
their nature as well as to that of the triangle, and these
must certainly all be true since I conceive them clearly.
Hence they are something, and not pure negation; for it is
perfectly clear that all that is true is something, and I have
already fully demonstrated that all that I know clearly is
true. And even although I had not demonstrated this, the
nature of my mind is such that I could not prevent myself from
holding them to be true so long as I conceive them clearly;
and I recollect that even when I was still strongly attached
to the objects of sense, I counted as the most certain those
truths which I conceived clearly as regards figures, numbers,
and the other matters which pertain to arithmetic and
geometry, and, in general, to pure and abstract mathematics.
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