Definitions Axioms Prop. I. Substance is by nature prior to its modifications Prop. II. Two substances, whose attributes are different, have nothing in common Prop III. Things, which have nothing in common, cannot be one the cause of the other Prop. IV. Two or more distinct things are distinguished one from the other either by the difference of the attributes of the substance, or by the differences of their modifications Prop. V. There cannot exist in the universe two or more (...) substances having the same nature or attribute Prop. VI. One substance cannot be produced by another substance Prop. VII. Existence belongs to the nature of substance Prop. VIII. Every substance is necessarily infinite Prop. IX. The more reality or being a thing has, the greater the number of its attributes Prop. X. Each particular attribute of the one substance must be conceived through itself Prop. XI. God, or substance consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists Prop. XII. No attribute of substance can be conceived, from which it would follow that substance can be divided Prop. XIII. Substance absolutely infinite is indivisible Prop. XIV. Besides God no substance can be granted or conceived Prop. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived Prop. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways--that is, all things which fall within the sphere of infinite intellect Prop. XVII. God acts solely by the laws of his own nature and is not constrained by anyone Prop. XVIII. God is the indwelling and not the transient cause of all things Prop. XIX. God and all the attributes of God are eternal Prop. XX. The existence of God and his essence are one and the same Prop. XXI. All things, which follow from the absolute nature of any attribute of God, must always exist and be infinite, or, in other words, are eternal and infinite through the said attribute Prop.. (shrink)