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.
PROP.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 the idea of God in the world of thought (objective).
Note .-- Before going any further, I wish to recall to mind what has been pointed out above--namely, that whatsoever can be perceived by the infinite intellect as constituting the essence of substance, belongs altogether only to one substance: consequently, substance thinking and substance extended are one and the same substance, comprehended now through one attribute, now through the other.