Proof.--In proportion as a mental image or an emotion is referred to more objects, so are there more causes whereby it can be aroused and fostered, all of which (by hypothesis) the mind contemplates simultaneously in association with the given emotion; therefore the emotion is more frequent, or is more often in full vigour, and (V. viii.) occupies the mind more. Q.E.D. PROP. XII. The mental images of things are more easily associated with the images referred to things which we clearly and distinctly understand, than with others. Proof.--Things, which we clearly and distinctly understand, are either the common properties of things or deductions therefrom (see definition of Reason, II. xl. note ii.), and are consequently (by the last Prop.) more often aroused in us. Wherefore it may more readily happen, that we should contemplate other things in conjunction with these than in conjunction with something else, and consequently (II. xviii.) that the images of the said things should be more often associated with the images of these than with the images of something else. Q.E.D. PROP. XIII. A mental image is more often vivid, in proportion as it is associated with a greater number of other images. Proof.--In proportion as an image is associated with a greater number of other images, so (II. xviii.) are there more causes whereby it can be aroused. Q.E.D. PROP. XIV. The mind can bring it about, that all bodily modifications or images of things may be referred to the idea of God. Proof.--There is no modification of the body, whereof the mind may not form some clear and distinct conception (V. iv.); wherefore it can bring it about, that they should all be referred to the idea of God (I. xv.). Q.E.D. PROP. XV. He who clearly and distinctly understands himself and his emotions loves God, and so much the more in proportion as he more understands himself and his emotions. Proof.--He who clearly and distinctly understands himself and his emotions feels pleasure (III. liii.), and this pleasure is (by the last Prop.) accompanied by the idea of God; therefore (Def. of the Emotions, vi.) such an one loves God, and (for the same reason) so much the more in proportion as he more understands himself and his emotions. Q.E.D. PROP. XVI. This love towards God must hold the chief place in the mind. Proof.--For this love is associated with all the modifications of the body (V. xiv.) and is fostered by them all (V. xv.); therefore (V. xi.), it must hold the chief place in the mind. Q.E.D. PROP. XVII. God is without passions, neither is he affected by any emotion of pleasure or pain.