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TABLE OF CONTENTS:
[DEFINITIONS]
[AXIOMS]
[POSTULATES]
[PROPOSITIONS:]
   [I] .    [XI] .    [XXI] .    [XXXI] .
   [II] .   [XII] .   [XXII] .   [XXXII] .
   [III] .  [XIII] .  [XXIII] .  [XXXIII] .
   [IV] .   [XIV] .   [XXIV] .   [XXXIV] .
   [V] .    [XV] .    [XXV] .    [XXXV] .
   [VI] .   [XVI] .   [XXVI] .   [XXXVI] .
   [VII] .  [XVII] .  [XXVII] .
   [VIII] . [XVIII] . [XXVIII] .
   [IX] .   [XIX] .   [XXIX] .
   [X] .    [XX] .    [XXX] .
[APPENDIX]
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[DEFINITIONS]

[D.I]   By that which is SELF-CAUSED, I mean that of which the
        essence involves existence, or that of which the nature
        is only conceivable as existent.

[D.II]  A thing is called FINITE AFTER ITS KIND, when it can be
        limited by another thing of the same nature; for instance,
        a body is called finite because we always conceive another
        greater body.  So, also, a thought is limited by another
        thought, but a body is not limited by thought, nor a
        thought by body.

[D.III] By SUBSTANCE, I mean that which is in itself, and is
        conceived through itself; in other words, that of which
        a conception can be formed independently of any other
        conception.

[D.IV]  By ATTRIBUTE, I mean that which the intellect perceives as
        constituting the essence of substance.

[D.V]   By MODE, I mean the modifications ("Affectiones") 
        substance, or that which exists in, and is conceived
        through, something other than itself.

[D.VI]  By GOD, I mean a being absolutely infinite--that is,
        a substance consisting in infinite attributes, of
        which each expresses eternal and infinite essentiality.
        Explanation. I say absolutely infinite, not infinite after its kind:
        for, of a thing infinite only after its kind, infinite attributes
        may be denied; but that which is absolutely infinite, contains in
        its essence whatever expresses reality, and involves no negation.

[D.VII] That thing is called free, which exists solely by the
        necessity of its own nature, and of which the action
        is determined by itself alone.  On the other hand, that
        thing is necessary, or rather constrained, which is
        determined by something external to itself to a fixed
        and definite method of existence or action.

[D.VIII] By ETERNITY, I mean existence itself, in so far as it
         is conceived necessarily to follow solely from the
         definition of that which is eternal. 
         Explanation.-- Existence of this kind is conceived as an eternal
         truth, like the essence of a thing, and, therefore, cannot be
         explained by means of continuance or time, though continuance may
         be conceived without a beginning or end. 
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[AXIOMS]

[A.I]   Everything which exists, exists either in itself or in
        something else.
[A.II]  That which cannot be conceived through anything else must be
        conceived through itself.
[A.III] From a given definite cause an effect necessarily follows;
        and, on the other hand, if no definite cause be granted,
        it is impossible that an effect can follow.
[A.IV]  The knowledge of an effect depends on and involves the
        knowledge of a cause.
[A.V]   Things which have nothing in common cannot be understood,
        the one by means of the other; the conception of one does not
        involve the conception of the other.
[A.VI]  A true idea must correspond with its ideate or object.
[A.VII] If a thing can be conceived as non-existing, its essence
        does not involve existence.

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[PROPOSITIONS:]

PROP. [I]  Substance is by nature prior to its modifications. 
Proof.- (1:1) This is clear from [D.iii] and [D.v] . 

PROP. [II]  Two substances whose attributes are different have 
            nothing in common. 

Proof.- (2:1) Also evident from [D.iii] . For each must exist in itself, and 
be conceived through itself; in other words, the conception of one does not