one
who understands. For it is quite true that the mode of understanding,
in one who understands, is not the same as the mode of a thing in
existing: since the thing understood is immaterially in the one who
understands, according to the mode of the intellect, and not
materially, according to the mode of a material thing.

Reply Obj. 2: Some have thought that the species of a natural thing
is a form only, and that matter is not part of the species. If that
were so, matter would not enter into the definition of natural
things. Therefore it must be said otherwise, that matter is twofold,
common, and "signate" or individual; common, such as flesh and bone;
and individual, as this flesh and these bones. The intellect
therefore abstracts the species of a natural thing from the
individual sensible matter, but not from the common sensible matter;
for example, it abstracts the species of man from "this flesh and
these bones," which do not belong to the species as such, but to the
individual (Metaph. vii, Did. vi, 10), and need not be considered in
the species: whereas the species of man cannot be abstracted by the
intellect from "flesh and bones."

Mathematical species, however, can be abstracted by the intellect
from sensible matter, not only from individual, but also from common
matter; not from common intelligible matter, but only from individual
matter. For sensible matter is corporeal matter as subject to
sensible qualities, such as being cold or hot, hard or soft, and the
like: while intelligible matter is substance as subject to quantity.
Now it is manifest that quantity is in substance before other
sensible qualities are. Hence quantities, such as number, dimension,
and figures, which are the terminations of quantity, can be
considered apart from sensible qualities; and this is to abstract
them from sensible matter; but they cannot be considered without
understanding the substance which is subject to the quantity; for
that would be to abstract them from common intelligible matter. Yet
they can be considered apart from this or that substance; for that is
to abstract them from individual intelligible matter. But some things
can be abstracted even from common intelligible matter, such as
"being," "unity," "power," "act," and the like; all these can exist
without matter, as is plain regarding immaterial things. Because
Plato failed to consider the twofold kind of abstraction, as above
explained (ad 1), he held that all t