ndependently from the senses, imagination, and impressions of
bodies.

Moreover, although I would not frankly acknowledge that I have a
clear idea of unity, which is the foundation of all numbers, because
they are but repetitions or collections of units: I must at least
be forced to own that I know a great many numbers with their
proprieties and relations. I know, for instance, how much make
900,000,000 joined with 800,000,000 of another sum. I make no
mistake in it; and I should, with certainty, immediately rectify any
man that should. Nevertheless, neither my senses nor my imagination
were ever able to represent to me distinctly all those millions put
together. Nor would the image they should represent to me be more
like seventeen hundred millions than a far inferior number.
Therefore, how came I by so distinct an idea of numbers, which I
never could either feel or imagine? These ideas, independent upon
bodies, can neither be corporeal nor admitted in a corporeal
subject. They discover to me the nature of my soul, which admits
what is incorporeal and receives it within itself in an incorporeal
manner. Now, how came I by so incorporeal an idea of bodies
themselves? I cannot by my own nature carry it within me, since
what in me knows bodies is incorporeal; and since it knows them,
without receiving that knowledge through the canal of corporeal
organs, such as the senses and imagination. What thinks in me must
be, as it were, a nothing of corporeal nature. How was I able to
know beings that have by nature no relation with my thinking being?
Certainly a being superior to those two natures, so very different,
and which comprehends them both in its infinity, must have joined
them in my soul, and given me an idea of a nature entirely different
from that which thinks in me.

SECT. LXII. The Idea of the Unity proves that there are Immaterial
Substances; and that there is a Being Perfectly One, who is God.

As for units, some perhaps will say that I do not know them by the
bodies, but only by the spirits; and, therefore, that my mind being
one, and truly known to me, it is by it, and not by the bodies, I
have the idea of unity. But to this I answer.

It will, at least, follow from thence that I know substances that
have no manner of extension or divisibility, and which are present.
Here are already beings purely incorporeal, in the number of which I
ought to place my soul. Now, who is it that has united