Ethics, part 2 | Page 9

III. A body in motion or at rest must be determined to motion
or rest by another body, which other body has been determined to
motion or rest by a third body, and that third again by a fourth, and so
on to infinity.
>>>>>Proof--Bodies are individual things (II., Def. i.), which (Lemma
i.) are distinguished one from the other in respect to motion and rest;
thus (I. xxviii.) each must necessarily be determined to motion or rest
by another individual thing, namely (II. vi.) by another body, which
other body is also (Ax. i.) in motion or at rest. And this body again can
only have been set in motion or caused to rest by being determined by a
third body to motion or rest. This third body again by a fourth, and so

on to infinity. Q.E.D.
<<<< motion, until it is determined to a state of rest by some other body; and
a body at rest remains so, until it is determined to a state of motion by
some other body. This is indeed self-evident. For when I suppose, for
instance, that a given body, A, is at rest, and do not take into
consideration other bodies in motion, I cannot affirm anything
concerning the body A, except that it is at rest. If it afterwards comes to
pass that A is in motion, this cannot have resulted from its having been
at rest, for no other consequence could have been involved than its
remaining at rest. If, on the other hand, A be given in motion, we shall,
so long as we only consider A, be unable to affirm anything concerning
it, except that it is in motion. If A is subsequently found to be at rest,
this rest cannot be the result of A's previous motion, for such motion
can only have led to continued motion; the state of rest therefore must
have resulted from something, which was not in A, namely, from an
external cause determining A to a state of rest.
-----Axiom I--All modes, wherein one body is affected by another body,
follow simultaneously from the nature of the body affected and the
body affecting; so that one and the same body may be moved in
different modes, according to the difference in the nature of the bodies
moving it; on the other hand, different bodies may be moved in
different modes by one and the same body.
-----Axiom II--When a body in motion impinges on another body at
rest, which it is unable to move, it recoils, in order to continue its
motion, and the angle made by the line of motion in the recoil and the
plane of the body at rest, whereon the moving body has impinged, will
be equal to the angle formed by the line of motion of incidence and the
same plane.
So far we have been speaking only of the most simple bodies, which
are only distinguished one from the other by motion and rest, quickness
and slowness. We now pass on to compound bodies.
Definition--When any given bodies of the same or different magnitude
are compelled by other bodies to remain in contact, or if they be moved
at the same or different rates of speed, so that their mutual movements
should preserve among themselves a certain fixed relation, we say that
such bodies are 'in union,' and that together they compose one body or

individual, which is distinguished from other bodies by the fact of this
union.
-----Axiom III--In proportion as the parts of an individual, or a
compound body, are in contact over a greater or less superficies, they
will with greater or less difficulty admit of being moved from their
position; consequently the individual will, with greater or less difficulty,
be brought to assume another form. Those bodies, whose parts are in
contact over large superficies, are called 'hard;' those, whose parts are
in contact over small superficies, are called 'soft;' those, whose parts are
in motion among one another, are called 'fluid.'
Lemma IV. If from a body or individual, compounded of several bodies,
certain bodies be separated, and if, at the same time, an equal number
of other bodies of the same nature take their place, the individual will
preserve its nature as before, without any change in its actuality
(forma).
>>>>>Proof--Bodies (Lemma i.) are not distinguished in respect of
substance: 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