E4P34D
Demonstration — Part IV
Latin
Homo exempli gratia Petrus potest esse causa ut Paulus contristetur propterea quod aliquid habet simile rei quam Paulus odit (per propositionem 16 partis III) vel propterea quod Petrus solus re aliqua potitur quam ipse Paulus etiam amat (vide propositionem 32 partis III cum ejusdem scholio) vel ob alias causas (harum præcipuas vide in scholio propositionis 55 partis III) atque adeo inde fiet (per definitionem 7 affectuum) ut Paulus Petrum odio habeat et consequenter facile fiet (per propositionem 40 partis III cum ejus scholio) ut Petrus Paulum contra odio habeat atque adeo (per propositionem 39 partis III) ut invicem malum inferre conentur hoc est (per propositionem 30 hujus) ut invicem sint contrarii. At affectus tristitiæ semper passio est (per propositionem 59 partis III); ergo homines quatenus conflictantur affectibus qui passiones sunt, possunt invicem esse contrarii. Q.E.D.
English (Elwes 1883)
A man, for instance Peter, can be the cause of Paul's feeling pain, because he (Peter) possesses something similar to that which Paul hates (III. xvi.), or because Peter has sole possession of a thing which Paul also loves (III. xxxii. and note), or for other causes (of which the chief are enumerated in III. lv. note); it may therefore happen that Paul should hate Peter (Def. of Emotions, vii.), consequently it may easily happen also, that Peter should hate Paul in return, and that each should endeavour to do the other an injury, (III. xxxix.), that is (IV. xxx.), that they should be contrary one to another. But the emotion of pain is always a passion or passive state (III. lix.); hence men, in so far as they are assailed by emotions which are passions, can be contrary one to another. Q.E.D.
Modern English
Peter, for example, can be the cause of Paul feeling sadness because Peter possesses something similar to what Paul hates (E3P16), or because Peter alone possesses something Paul also loves (E3P32S), or for other reasons (E3P55S). The result is that Paul hates Peter (E3DA7), and consequently it easily follows that Peter hates Paul in return (E3P40S), and that each tries to harm the other (E3P39), that is, (E4P30), that they are contrary to one another. The affect of sadness is always a passion (E3P59); therefore, in so far as men are driven by affects that are passions, they can be contrary to one another.