an follow.

IV. The knowledge of an effect depends on the knowledge of the cause,
and includes it.

V. Things that have nothing in common with each other cannot be
understood by means of each other--that is, the conception of one, does
not involve the conception of the other.

VI. A true idea must agree with its original in nature.

VII. Whatever can be clearly conceived as non-existent does not, in its
essence, involve existence.

PROPOSITIONS.

I. Substance is prior in nature to its accidents. Demonstration. Per
definitions three and five.

II. Two substances, having different attributes, have nothing in common
with each other. Dem. This follows from def. three; for each substance
must be conceived in itself and through itself; in other words, the
conception of one does not involve the conception of the other.

III. Of things which have nothing in common, one cannot be the cause of
the other. Dem. If they have nothing in common, then (per axiom five)
they cannot be conceived by means of each other; _ergo_ (per axiom
four,) one cannot be the cause of the other.--Q. E. D.

IV. Two or more distinct things are distinguished among themselves,
either through the diversity of their attributes, or through that of
their modes. Dem. Everything which is, in itself, or in some other thing
(per ax. one)--that is (per def. three and five,) there is nothing out
of ourselves (_extra intellectum_, outside the intellect) but substance
and its modes. There is nothing out of ourselves whereby things can be
distinguished amongst one another, except substances, or (which is the
same thing, per def. lour) their attributes and modes.

V. It is impossible that there should be two or more substances of the
same nature, or of the same attributes. Dem. If there are many different
substances they must be distinguished by the diversity of their
attributes or of their modes (per prop. 4.) If only by the diversity
of their attributes, it is thereby conceded that there is, nevertheless,
only one substance of the same attribute; but if their diversity of
modes, then, substance being prior in order of time to its modes, it
must be considered independent of them--that is (per def. three and
six,) cannot be conceived as distinguished from another--that is
(per prop, four,) there cannot be many substances, but only one
substance.--Q. E. D.

VI. One substance cannot be created by another substance. Dem. There
cannot be two substances with t