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necessarily is, and in God alone.  Q.E.D.  (Part i., Prop. xv.)

*****Note--The multitude understand by the power of God the free
will of God, and the  right over all things that exist, which
latter are accordingly generally considered as  contingent.  For
it is said that God has the power to destroy all things, and to
reduce them  to nothing.  Further, the power of God is very often
likened to the power of kings.  But  this doctrine we have
refuted (Pt. i., Prop. xxxii., Cors. i. and ii.), and we have
shown  (Part i., Prop. xvi.) that God acts by the same necessity,
as that by which he understands  himself; in other words, as it
follows from the necessity of the divine nature (as all admit), 
that God understands himself, so also does it follow by the same
necessity, that God  performs infinite acts in infinite ways.  We
further showed (Part i., Prop. xxxiv.), that  God's power is
identical with God's essence in action; therefore it is as
impossible for us  to conceive God as not acting, as to conceive
him as non-existent.  If we might pursue  the subject further, I
could point out, that the power which is commonly attributed to
God  is not only human (as showing that God is conceived by the
multitude as a man, or in the  likeness of a man), but involves a
negation of power.  However, I am unwilling to go over  the same
ground so often.  I would only beg the reader again and again, to
turn over  frequently in his mind what I have said in Part i.
from Prop. xvi. to the end.  No one will  be able to follow my
meaning, unless he is scrupulously careful not to confound the
power  of God with the human power and right of kings.

IV.  The idea of God, from which an infinite number of things
follow in infinite ways, can  only be one.

>>>>>Proof--Infinite intellect comprehends nothing save the
attributes of God and his  modifications (Part i., Prop. xxx.). 
Now God is one (Part i., Prop. xiv., Cor.).  Therefore  the idea
of God, wherefrom an infinite number of things follow in infinite
ways, can only  be one.  Q.E.D.

V.  The actual being of ideas owns God as its cause, only in so
far as he is considered as a  thinking thing, not in so far as he
is unfolded in any other attribute; that is, the ideas both  of
the attributes of God and of particular things do not own as
their efficient cause their  objects (ideata) or the things
perceived, but God himself in so far as he is a thinking thing.

>>>>>Proof--This proposition is evident from Prop. iii. of this
Part.  We there drew the  conclusion, that God can form the idea
of his essence, and of all things which follow  necessarily
therefrom, solely because he is a thinking thing, and not because
he is the  object of his own idea.  Wherefore the actual being of
ideas owns for cause God, in so far  as he is a thinking thing. 
It may be differently proved as follows:  the actual being of
ideas  is (obviously) a mode of thought, that is (Part i., Prop.
xxv., Cor.) a mode which expresses  in a certain manner the
nature of God, in so far as he is a thinking thing, and therefore 
(Part i., Prop. x.) involves the conception of no other attribute
of God, and consequently  (by Part i., Ax. iv.) is not the effect
of any attribute save thought.  Therefore the actual  being of
ideas owns God as its cause, in so far as he is considered as a
thinking thing, &c.   Q.E.D.

VI.  The modes of any given attribute are caused by God, in so
far as he is considered  through the attribute of which they are
modes, and not in so far as he is considered through  any other
attribute.

>>>>>Proof--Each attribute is conceived through itself, without
any other part (Part i.,  Prop. x.); wherefore the modes of each
attribute involve the conception of that attribute,  but not of
any other.  Thus (Part i., Ax. iv.) they are caused by God, only
in so far as he  is considered through the attribute whose modes
they are, and not in so far as he is  considered through any
other.  Q.E.D.

<<<<<Corollary--Hence the actual being of things, which are not
modes of thought, does  not follow from the divine nature,
because that nature has prior knowledge of the things.   Things
represented in ideas follow, and are derived from their
particular attribute, in the  same manner, and with the same
necessity as ideas follow (according to what we have  shown) from
the attribute of thought.

VII.  The order and connection of ideas is the same as the order
and connection of things.

>>>>>Proof--This proposition is evident from Part i., Ax. iv. 
For the idea of everything  that is caused depends on a
knowledge of the cause, whereof it is an effect.

<<<<<Corollary--Hence God's power of thinking is equal to his
realized power of action-- that is, whatsoever follows from the
infinite nature of God in the world of extension  (formaliter),
follows without exception in the same order and connection from

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