ry natural body has
a greater or smaller determinate quantity. Hence it is impossible for
a natural body to be infinite. The same appears from movement; because
every natural body has some natural movement; whereas an infinite body
could not have any natural movement; neither direct, because nothing
moves naturally by a direct movement unless it is out of its place;
and this could not happen to an infinite body, for it would occupy
every place, and thus every place would be indifferently its own
place. Neither could it move circularly; forasmuch as circular motion
requires that one part of the body is necessarily transferred to a
place occupied by another part, and this could not happen as regards
an infinite circular body: for if two lines be drawn from the centre,
the farther they extend from the centre, the farther they are from
each other; therefore, if a body were infinite, the lines would be
infinitely distant from each other; and thus one could never occupy
the place belonging to any other.

The same applies to a mathematical body. For if we imagine a
mathematical body actually existing, we must imagine it under some
form, because nothing is actual except by its form; hence, since the
form of quantity as such is figure, such a body must have some figure,
and so would be finite; for figure is confined by a term or boundary.

Reply Obj. 1: A geometrician does not need to assume a line
actually infinite, but takes some actually finite line, from which he
subtracts whatever he finds necessary; which line he calls infinite.

Reply Obj. 2: Although the infinite is not against the nature
of magnitude in general, still it is against the nature of any species
of it; thus, for instance, it is against the nature of a bicubical or
tricubical magnitude, whether circular or triangular, and so on. Now
what is not possible in any species cannot exist in the genus; hence
there cannot be any infinite magnitude, since no species of magnitude
is infinite.

Reply Obj. 3: The infinite in quantity, as was shown above,
belongs to matter. Now by division of the whole we approach to matter,
forasmuch as parts have the aspect of matter; but by addition we
approach to the whole which has the aspect of a form. Therefore the
infinite is not in the addition of magnitude, but only in division.

Reply Obj. 4: Movement and time are whole, not actually but
successively; hence they have potentiality mixed with actuality. But
magnitude is an a