E3P15D
Demonstration — Part III
Latin
Ponatur mens duobus affectibus simul affici, uno scilicet qui ejus agendi potentiam neque auget neque minuit et altero qui eandem vel auget vel minuit (vide postulatum 1 hujus). Ex præcedenti propositione patet quod ubi mens postea illo a sua vera causa quæ (per hypothesin) per se ejus cogitandi potentiam nec auget nec minuit, afficietur, statim et hoc altero qui ipsius cogitandi potentiam auget vel minuit hoc est (per scholium propositionis 11 hujus) lætitia vel tristitia afficietur atque adeo illa res non per se sed per accidens causa erit lætitiæ vel tristitiæ. Atque hac eadem via facile ostendi potest rem illam posse per accidens causam esse cupiditatis. Q.E.D.
English (Elwes 1883)
Let it be granted that the mind is simultaneously affected by two emotions, of which one neither increases nor diminishes its power of activity, and the other does either increase or diminish the said power (III. Post. i.). From the foregoing proposition it is evident that, whenever the mind is afterwards affected by the former, through its true cause, which (by hypothesis) neither increases nor diminishes its power of action, it will be at the same time affected by the latter, which does increase or diminish its power of activity, that is (III. xi. note) it will be affected with pleasure or pain. Thus the former of the two emotions will, not through itself, but accidentally, be the cause of pleasure or pain. In the same way also it can be easily shown, that a thing may be accidentally the cause of desire. Q.E.D.
Modern English
Suppose the mind is affected simultaneously by two affects: one that neither increases nor decreases its power of acting, and another that either increases or decreases it (E3Post1). From the preceding proposition it is clear that whenever the mind is afterwards affected by the first through its true cause, which, by hypothesis, neither increases nor decreases its power of thinking, it will immediately be affected also by the second, which does increase or decrease its power of thinking, that is (E3P11S), it will be affected with joy or sadness. The first thing is therefore not through itself but accidentally the cause of joy or sadness. In the same way it is easily shown that it can be accidentally the cause of desire. Q.E.D.