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 it to my body?  This soul of mine is not an infinite being; it has not been always, and it thinks within certain bounds.  Now, again, who makes it know bodies so different from it?  Who gives it so great a command over a certain body; and who gives reciprocally to that body so great a command over the soul?  Moreover, which way do I know whether this thinking soul is really one, or whether it has parts?  I do not see this soul.  Now, will anybody say that it is in so invisible, and so impenetrable, a thing that I clearly see what unity is?  I am so far from learning by my soul what the being One is, that, on the contrary, it is by the clear idea I have already of unity that I examine whether my soul be one or divisible.