? It is so very distinct that I cannot seriously doubt of
it; and so, immediately, without the least hesitation, I rectify any
man that does not follow it in computation. If a man says seventeen
and three make twenty-two, I presently tell him seventeen and three
make but twenty; and he is immediately convinced by his own light,
and acquiesces in my correction. The same Master who speaks within
me to correct him speaks at the same time within him to bid him
acquiesce. These are not two masters that have agreed to make us
agree. It is something indivisible, eternal, immutable, that speaks
at the same time with an invincible persuasion in us both. Once
more, how come I by so just a notion of numbers? All numbers are
but repeated units. Every number is but a compound, or a repetition
of units. The number of two, for instance, is but two units; the
number of four is reducible to one repeated four times. Therefore
we cannot conceive any number without conceiving unity, which is the
essential foundation of any possible number; nor can we conceive any
repetition of units without conceiving unity itself, which is its
basis.

But which way can I know any real unit? I never saw, nor so much as
imagined any by the report of my senses. Let me take, for instance,
the most subtle atom; it must have a figure, length, breadth, and
depth, a top and a bottom, a left and a right side; and again the
top is not the bottom, nor one side the other. Therefore this atom
is not truly one, for it consists of parts. Now a compound is a
real number, and a multitude of beings. It is not a real unit, but
a collection of beings, one of which is not the other. I therefore
never learnt by my eyes, my ears, my hands, nor even by my
imagination, that there is in nature any real unity; on the
contrary, neither my senses nor my imagination ever presented to me
anything but what is a compound, a real number or a multitude. All
unity continually escapes me; it flies me as it were by a kind of
enchantment. Since I look for it in so many divisions of an atom, I
certainly have a distinct idea of it; and it is only by its simple
and clear idea that I arrive, by the repetition of it, at the
knowledge of so many other numbers. But since it escapes me in all
the divisions of the bodies of nature, it clearly follows that I
never came by the knowledge of it, through the canal of my senses
and imagination. Here therefore is an idea which is in me
i