infinite number of parts is individually the same idea with that of an
infinite extension; that no finite extension is capable of containing an
infinite number of parts; and consequently that no finite extension is
infinitely divisible [Footnote 3.].

[Footnote 3. It has been objected to me, that infinite divisibility
supposes only an infinite number of PROPORTIONAL not of ALIQIOT parts,
and that an infinite number of proportional parts does not form an
infinite extension. But this distinction is entirely frivolous. Whether
these parts be calld ALIQUOT or PROPORTIONAL, they cannot be inferior to
those minute parts we conceive; and therefore cannot form a less extension
by their conjunction.]

I may subjoin another argument proposed by a noted author [Mons.
MALEZIEU], which seems to me very strong and beautiful. It is evident,
that existence in itself belongs only to unity, and is never applicable to
number, but on account of the unites, of which the number is composed.
Twenty men may be said to exist; but it is only because one, two, three,
four, &c. are existent, and if you deny the existence of the latter, that
of the former falls of course. It is therefore utterly absurd to suppose
any number to exist, and yet deny the existence of unites; and as
extension is always a number, according to the common sentiment of
metaphysicians, and never resolves itself into any unite or indivisible
quantity, it follows, that extension can never at all exist. It is in vain
to reply, that any determinate quantity of extension is an unite; but
such-a-one as admits of an infinite number of fractions, and is
inexhaustible in its sub-divisions. For by the same rule these twenty men
may be considered as a unit. The whole globe of the earth, nay the whole
universe, may be considered as a unit. That term of unity is merely a
fictitious denomination, which the mind may apply to any quantity of