From Descartes, Notes Against a Program
He (Descartes’ critic, Regius) appear to dissent from me only in words, for when he says that the mind has no need of innate ideas, or notions, or axioms, and at the same time allows it the faculty of thinking (to be considered natural or innate), he makes an affirmation in effect identical with mine, but denies it in words. For I never wrote or concluded that the mind required innate ideas which were in some sort different from its faculty of thinking; but when I observed the existence in me of certain thought which proceeded neither from extraneous objects, nor from the determination of my will, but solely from the faulty of thinking which is within me, then, that I might distinguish the ideas or notions (which are the forms of these thoughts) from other thoughts adventitious or factitious, I termed the former “innate.” In the same sense we say that in some families generosity is innate, in other certain diseases like gout or gravel, not that on thins account the babes of these families suffer from these diseases in their mother's womb, but because they are born with a certain disposition for contracting them.
From Descartes, Reply to Objections V (Gassendi's)
I do not admit that the ideas of geometrical figures have at any time
entered our minds though the senses, as is the common persuasion.
For though, doubtless, figures such as the geometers consider can exist
in reality, I deny that any can be presented to us except such minute ones
that they fail to affect our senses. For, let us suppose that these
figures consist as far as possible of straight lines; yet, it will be quite
impossible for any really straight part of the line to affect our sense
because when we examine with a magnifying glass those lines that appear
to us most straight, we find them to be irregular and bending in an undulating
manner. Hence, when first in infancy we see a triangular figure depicted
on paper, this figure cannot show us how a real triangle ought to be conceived,
in the way in which geometricians consider it, because the true triangle
is contained in this figure, just as the statue of Mercury is contained
in a rough block of wood. But because we already possess within us
the idea of a true triangle, and it can be more easily conceived by our
minds than the more complex figure of the triangle drawn on paper,
we, therefore, when we see that composite figure, apprehend not it itself,
but rather the authentic triangle. This is exactly the same as when
we look at a piece of paper on which little strokes have been drawn with
ink to represent a man's face; for the idea produced in us this way
is not so much that of the lines of the sketch as of the man. But
this could not have happened unless the human face had been known to us
by other means, and we had been more accustomed to think of it than of
those minute lines, which indeed we often fail to distinguish from each
other when they are moved to a slightly greater distance away from us.
So certainly we should not be able to recognize the geometrical triangle
by looking at that drawn on paper, unless our minds possessed an idea of
it derived from other sources.