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further see the cause； why we have only a very confused
knowledge of our body； and also many kindred questions； which I
will； in the following propositions； deduce from what has been
advanced。 Wherefore I have thought it worth while to explain
and prove more strictly my present statements。 In order to do
so； I must premise a few propositions concerning the nature of
bodies。
…Axiom I。 All bodies are either in motion or at rest。
…Axiom II。 Every body is moved sometimes more slowly；
sometimes more quickly。
Lemma I。 Bodies are distinguished from one another in respect of
motion and rest； quickness and slowness； and not in respect of
substance。
》》》》》ProofThe first part of this proposition is； I take it；
self…evident。 That bodies are not distinguished in respect of
substance； is plain both from I。 v。 and I。 viii。 It is brought
out still more clearly from I。 xv。； Note。
Lemma II。 All bodies agree in certain respects。
》》》》》ProofAll bodies agree in the fact； that they involve the
conception of one and the same attribute （II。； Def。 i。）。
Further； in the fact that they may be moved less or more
quickly； and may be absolutely in motion or at rest。
Lemma 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。
》》》》》ProofBodies 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。