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.