16,  Part  I.)  ;  therefore  to  some  object  which  needs
only  God's  concurrence  for  its  existence  (per  Prop.  12,
Part  I.),  that  is  (per  Def.  2),  to  substance.     Q.  E.  D.
PART  II


LEMMA  II.
IV e  clearly  and  distinctly  conceive  of  rarefaction
and  condensation.  We  would  not  concede,  however,
that  a  body  occupies  more  space  utider  rarefaction
than  under  condensation.
DEMONSTRATION.
We  can  have  a  clear  and  a  distinct  concept  of  these
because  we  can  conceive  that  the  parts  of  a  body  mu-
tually recede,  or  mutually  approach  one  another.
Therefore  (per  Ax.  4),  they  will  not  occupy  more  or
less  space.  If  the  parts  of  some  body,  for  example
a  sponge,  are  compressed  the  bodies  between  the  parts
will  be  occupied.  What  we  can  thus  clearly  perceive
occupy  less  space  than  before  (per  Ax.  4).  And  if,
again,  the  body  expands  and  the  pores  are  filled  by
some  body,  there  is  a  rarefaction,  but  no  more  space
will  be  occupied.  What  we  can  thus  clearly  perceive
by  the  senses  in  the  case  of  the  sponge,  we  can  con-
ceive by  the  understanding  to  be  true  with  all  bodies,
although  the  pores  of  these  cannot  be  perceived  by  our
senses.  Therefore,  rarefaction  and  condensation  are
clearly  conceived,  etc.     Q.  E.  D.
It  seemed  best  to  give  this  at  this  place  in  order  to
overcome  these  prejudices  concerning  space,  rarefac^
tion,  etc.,  and  in  order  that  the  mind  may  be  ready  to
understand  what  follows.
Proposition  I.
Although  hardness,  zveight,  and  the  other  sensible
qualities  of  a  body  be  removed,  the  whole  nature  of
that  body  will  nevertheless  remain.
64     PRINCIPLES  OF  DESCARTES'  PHILOSOPHY


DEMONSTRATION.
