E3P48D
Demonstration — Part III
Latin
Patet ex sola amoris et odii definitione, quam vide in scholio propositionis 13 hujus. Nam propter hoc solum lætitia vocatur amor et tristitia odium erga Petrum quia scilicet Petrus hujus vel illius affectus causa esse consideratur. Hoc itaque prorsus vel ex parte sublato affectus quoque erga Petrum prorsus vel ex parte diminuitur. Q.E.D.
English (Elwes 1883)
This Prop. is evident from the mere definition of love and hatred (III. xiii. note). For pleasure is called love towards Peter, and pain is called hatred towards Peter, simply in so far as Peter is regarded as the cause of one emotion or the other. When this condition of causality is either wholly or partly removed, the emotion towards Peter also wholly or in part vanishes. Q.E.D.
Modern English
This is evident from the definition of love and hatred alone — see the Scholium to Proposition 13 of this Part (E3P13S). Joy is called love toward Peter, and sadness is called hatred toward Peter, simply because Peter is regarded as the cause of one affect or the other. When that causal attribution is wholly or partly removed, the affect toward Peter is wholly or partly diminished. Q.E.D.