III.P57

Quilibet uniuscujusque individui affectus ab affectu alterius tantum discrepat quantum essentia unius ab essentia alterius differt.

Any affect of each and every individual differs from the affect of another individual just as much as the essence of one differs from the essence of the other.

DEMONSTRATIO: 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.

This proposition is clear from axiom 1, which see post lemma 3 and IIP13S. But nonetheless, we will show the same thing from the definitions of the three primary affects. Evey affect refers to desire, joy or sadness so as they reveal whose definitions we have given. But desire is the nature or essence of each and every one (see its definition in IIIP9S); thus, the desire of each and every individual is discordant with the desire of another so much as the nature or essence of one differs from the essence of another. Then joy and sadness are passions by which the potential power or conatus of each and every one is increased or lessens for persevering in oneself, is aided or restrained (by IIIP11 and IIIP11S). But by conatus to be persevering in oneself insofar as it refers to the mind and body at the same time, we understand appetite and desire (see IIIP9S); thus joy and sadness and desire itself or appetite insofar as it is increased or lessened, aided or restrained, that is (by the same IIIP9S) is the nature of anyone itself and to such a degree the joy or sadness of each and every one is discordant from the joy or sadness of another to such an extent that the nature or essence of one differs from the essence of another and consequently any affect of each and every individual is discordant with the affect of another so much etc.  

SCHOLIUM: Hinc sequitur affectus animalium quæ irrationalia dicuntur (bruta enim sentire nequaquam dubitare possumus postquam mentis novimus originem) ab affectibus hominum tantum differre quantum eorum natura a natura humana differt. Fertur quidem equus et homo libidine procreandi; at ille libidine equina hic autem humana. Sic etiam libidines et appetitus insectorum, piscium et avium alii atque alii esse debent. Quamvis itaque unumquodque individuum sua qua constat natura, contentum vivat eaque gaudeat, vita tamen illa qua unumquodque est contentum et gaudium nihil aliud est quam idea seu anima ejusdem individui atque adeo gaudium unius a gaudio alterius tantum natura discrepat quantum essentia unius ab essentia alterius differt. Denique ex præcedenti propositione sequitur non parum etiam interesse inter gaudium quo ebrius exempli gratia ducitur et inter gaudium quo potitur philosophus, quod hic in transitu monere volui. Atque hæc de affectibus qui ad hominem referuntur quatenus patitur. Superest ut pauca addam de iis qui ad eundem referuntur quatenus agit. 

From here it follows that the affects of animals which are called irrational (for we are in no way able to doubt that brutes feel after we know the origin of the mind) to differ from the affects of people so much as the nature of them differ from human nature.