_Explication_, I say absolutely infinite, but not in _suo genere_; for to whatever is infinite, but not in _suo genere_, we can deny infinite attributes; but that which is absolutely infinite, to its essence pertains everything which implies essence, and involves no negation. VII. That thing is said to be free which exists by the sole necessity of its nature, and by itself alone is determined to action. But that is necessary, or rather constrained, which owes its existence to another, and acts according to certain and determinate causes. VIII. By eternity I understand existence itself, in as far as it is conceived necessarily to follow from the sole definition of an eternal thing. AXIOMS. I. Everything which is, is in itself, or in some other thing. II. That which cannot be conceived through another, _per aliud_ must be conceived, _per se_. III. From a given determinate cause the effect necessarily follows, and _vice versa_. If no determinate cause be given, no effect can 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.