E3P57D
Demonstration — Part III
Latin
Hæc propositio patet ex axiomate 1, quod vide post lemma 3 scholiumque propositionis 13 partis II. At nihilominus eandem ex trium primitivorum affectuum definitionibus demonstrabimus. Omnes affectus ad cupiditatem, lætitiam vel tristitiam referuntur ut eorum quas dedimus definitiones, ostendunt. At cupiditas est ipsa uniuscujusque natura seu essentia (vide ejus definitionem in scholio propositionis 9 hujus); ergo uniuscujusque individui cupiditas a cupiditate alterius tantum discrepat quantum natura seu essentia unius ab essentia alterius differt. Lætitia deinde et tristitia passiones sunt quibus uniuscujusque potentia seu conatus in suo esse perseverandi augetur vel minuitur, juvatur vel coercetur (per propositionem 11 hujus et ejus scholium). At per conatum in suo esse perseverandi quatenus ad mentem et corpus simul refertur, appetitum et cupiditatem intelligimus (vide scholium propositionis 9 hujus); ergo lætitia et tristitia est ipsa cupiditas sive appetitus quatenus a causis externis augetur vel minuitur, juvatur vel coercetur hoc est (per idem scholium) est ipsa cujusque natura atque adeo uniuscujusque lætitia vel tristitia a lætitia vel tristitia alterius tantum etiam discrepat quantum natura seu essentia unius ab essentia alterius differt et consequenter quilibet uniuscujusque individui affectus ab affectu alterius tantum discrepat etc. Q.E.D.
English (Elwes 1883)
This proposition is evident from Ax. i. (which see after Lemma iii. Prop. xiii., Part II.). Nevertheless, we will prove it from the nature of the three primary emotions.
All emotions are attributable to desire, pleasure, or pain, as their definitions above given show. But desire is each man's nature or essence (III. ix. note); therefore desire in one individual differs from desire in another individual, only in so far as the nature or essence of the one differs from the nature or essence of the other. Again, pleasure and pain are passive states or passions, whereby every man's power or endeavour to persist in his being is increased or diminished, helped or hindered (III. xi. and note). But by the endeavour to persist in its being, in so far as it is attributable to mind and body in conjunction, we mean appetite and desire (III. ix. note); therefore pleasure and pain are identical with desire or appetite, in so far as by external causes they are increased or diminished, helped or hindered, in other words, they are every man's nature; wherefore the pleasure and pain felt by one man differ from the pleasure and pain felt by another man, only in so far as the nature or essence of the one man differs from the essence of the other; consequently, any emotion of one individual only differs, &c. Q.E.D.
Modern English
This proposition is evident from Axiom 1 (see after Lemma 3 and the scholium of E2P13 (E2P13S)). Nevertheless, we will demonstrate it from the definitions of the three primary affects.
All affects are referred to desire, joy, or sadness, as the definitions given show. But desire is the very nature or essence of each individual (E3P9S); therefore the desire of one individual differs from the desire of another only insofar as the nature or essence of the one differs from the nature or essence of the other. Joy and sadness, in turn, are passions by which each individual's power, or *conatus* to persevere in being, is increased or diminished, helped or checked (E3P11). But by the *conatus* to persevere in being, insofar as it is referred to mind and body together, we understand appetite and desire (E3P9S). Therefore joy and sadness are nothing other than desire or appetite insofar as they are increased or diminished, helped or checked, by external causes, that is (E3P9S), they are each individual's own nature. And so one individual's joy or sadness differs from another's only insofar as the nature or essence of the one differs from the nature or essence of the other. Consequently, any affect of a given individual differs from the affect of another individual only insofar as, etc. Q.E.D.