ETHICS(II, P13) 503
Axiom 2: When a moving body collides with a body at rest and is unable to cause it to
move, it is reflected so as to continue its motion, and the angle between the line of
motion of the reflection and the plane of the body at rest with which it has collided is
equal to the angle between the line of incidence of motion and the said plane.
So far we have been discussing the simplest bodies, those which are distinguished
from one another solely by motion-and-rest, quickness and slowness. Now let us
advance to composite bodies.
Definition: When a number of bodies of the same or different magnitude form
close contact with one another through the pressure of other bodies upon them, or if
they are moving at the same or different rates of speed so as to preserve an unvarying
relation of movement among themselves, these bodies are said to be united with one
another and all together to form one body or individual thing, which is distinguished
from other things through this union of bodies.
Axiom 3: The degree of difficulty with which the parts of an individual thing or com-
posite body can be made to change their position and consequently the degree of diffi-
culty with which the individual takes on different shapes is proportional to the extent of
the surface areas along which they are in close contact. Hence bodies whose parts main-
tain close contact along large areas of their surfaces I term hard; those whose parts
maintain contact along small surface areas I term soft; while those whose parts are in a
state of motion among themselves I term liquid.
Lemma 4:If from a body, or an individual thing composed of a number of bodies, cer-
tain bodies are separated, and at the same time a like number of other bodies of the
same nature take their place, the individual thing will retain its nature as before, with-
out any change in its form[forma].
Proof: Bodies are not distinguished in respect of substance (Lemma 1). That which
constitutes the form of the individual thing consists in a union of bodies (preceding
definition). But this union, by hypothesis, is retained in spite of the continuous change of
component bodies. Therefore, the individual thing will retain its own nature as before,
both in respect of substance and of mode.
Lemma 5:If the parts of an individual thing become greater or smaller, but so propor-
tionately that they all preserve the same mutual relation of motion-and-rest as before,
the individual thing will likewise retain its own nature as before without any change in
its form.
Proof: The reasoning is the same as in the preceding Lemma.
Lemma 6:If certain bodies composing an individual thing are made to change the exist-
ing direction of their motion, but in such a way that they can continue their motion and
keep the same mutual relation as before, the individual thing will likewise preserve its
own nature without any change of form.