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far as they are said to continue； their ideas will also involve
existence； through which they are said to continue。
*****NoteIf anyone desires an example to throw more light on
this question； I shall； I fear； not be able to give him any；
which adequately explains the thing of which I here speak；
inasmuch as it is unique； however； I will endeavour to
illustrate it as far as possible。 The nature of a circle is
such that if any number of straight lines intersect within it；
the rectangles formed by their segments will be equal to one
another； thus； infinite equal rectangles are contained in a
circle。 Yet none of these rectangles can be said to exist；
except in so far as the circle exists； nor can the idea of any of
these rectangles be said to exist； except in so far as they are
comprehended in the idea of the circle。 Let us grant that；
from this infinite number of rectangles； two only exist。 The
ideas of these two not only exist； in so far as they are
contained in the idea of the circle； but also as they involve the
existence of those rectangles； wherefore they are distinguished
from the remaining ideas of the remaining rectangles。
IX。 The idea of an individual thing actually existing is caused
by God； not in so far as he is infinite； but in so far as he is
considered as affected by another idea of a thing actually
existing； of which he is the cause； in so far as he is affected
by a third idea； and so on to infinity。
》》》》》ProofThe idea of an individual thing actually existing is
an individual mode of thinking； and is distinct from other modes
（by the Cor。 and Note to Prop。 viii。 of this part）； thus （by
Prop。 vi。 of this part） it is caused by God； in so far only as he
is a thinking thing。 But not （by Prop。 xxviii。 of Part i。） in
so far as he is a thing thinking absolutely； only in so far as
he is considered as affected by another mode of thinking； and he
is the cause of this latter； as being affected by a third； and
so on to infinity。 Now； the order and connection of ideas is
（by Prop。 vii。 of this book） the same as the order and connection
of causes。 Therefore of a given individual idea another
individual idea； or God； in so far as he is considered as
modified by that idea； is the cause； and of this second idea God
is the cause； in so far as he is affected by another idea； and
so on to infinity。 Q。E。D。
ProofWhatsoever takes place in the object of any idea； its
idea is in God （by Prop。 iii。 of this part）； not in so far as he
is infinite； but in so far as he is considered as affected by
another idea of an individual thing （by the last Prop。）； but （by
Prop。 vii。 of this part） the order and connection of ideas is
the same as the order and connection of things。 The knowledge；
therefore； of that which takes place in any individual object
will be in God； in so far only as he has the idea of that
object。 Q。E。D。
X。 The being of substance does not appertain to the essence of
manin other words； substance does not constitute the actual
being （forma） of man。
》》》》》ProofThe being of substance involves necessary existence
（Part i。； Prop。 vii。）。 If； therefore； the being of substance
appertains to the essence of man； substance being granted； man
would necessarily be granted also （II。 Def。 ii。）； and；
consequently； man would necessarily exist； which is absurd （II。
Ax。 i。）。 Therefore &c。 Q。E。D。
*****NoteThis proposition may also be proved from I。v。； in
which it is shown that there cannot be two substances of the
same nature； for as there may be many men； the being of
substance is not that which constitutes the actual being of man。
Again； the proposition is evident from the other properties of
substancenamely； that substance is in its nature infinite；
immutable； indivisible； &c。； as anyone may see for himself。