stance: that which constitutes the actuality (formam) of an
individual consists (by the last Def.) in a union of bodies; but
this union, although there is a continual change of bodies, will
(by our hypothesis) be maintained; the individual, therefore,
will retain its nature as before, both in respect of substance
and in respect of mode. Q.E.D.

LEMMA V. If the parts composing an individual become greater
or less, but in such proportion, that they all preserve the same
mutual relations of motion and rest, the individual will still
preserve its original nature, and its actuality will not be
changed.

Proof.--The same as for the last Lemma.

LEMMA VI. If certain bodies composing an individual be
compelled to change the motion, which they have in one direction,
for motion in another direction, but in such a manner, that they
be able to continue their motions and their mutual communication
in the same relations as before, the individual will retain its
own nature without any change of its actuality.

Proof.--This proposition is self--evident, for the individual
is supposed to retain all that, which, in its definition, we
spoke of as its actual being.

LEMMA VII. Furthermore, the individual thus composed
preserves its nature, whether it be, as a whole, in motion or at
rest, whether it be moved in this or that direction; so long as
each part retains its motion, and preserves its communication
with other parts as before.

Proof.--This proposition is evident from the definition of an
individual prefixed to Lemma iv.

Note.--We thus see, how a composite individual may be affected
in many different ways, and preserve its nature notwithstanding.
Thus far we have conceived an individual as composed of bodies
only distinguished one from the other in respect of motion and
rest, speed and slowness; that is, of bodies of the most simple
character. If, however, we now conceive another individual
composed of several individuals of diverse natures, we shall find
that the number of ways in which it can be affected, without
losing its nature, will be greatly multiplied. Each of its parts
would consist of several bodies, and therefore (by Lemma vi.)
each part would admit, without change to its nature, of quicker
or slower motion, and would consequently be able to transmit its
motions more quickly or more slowly to the remaining parts. If
we further conceive a third kind of individuals composed of
individuals of this second