E3P31D
Demonstration — Part III
Latin
Ex eo solo quod aliquem aliquid amare imaginamur, eo ipso idem amabimus (per propositionem 27 hujus). At sine hoc nos idem amare supponimus; accedit ergo amori nova causa a qua fovetur atque adeo id quod amamus hoc ipso constantius amabimus. Deinde ex eo quod aliquem aliquid aversari imaginamur, idem aversabimur (per eandem propositionem). At si supponamus nos eodem tempore id ipsum amare, eodem ergo tempore hoc idem amabimus et aversabimur sive (vide scholium propositionis 17 hujus) animi fluctuationem patiemur. Q.E.D.
English (Elwes 1883)
From the mere fact of conceiving that anyone loves anything we shall ourselves love that thing (III. xxvii.): but we are assumed to love it already; there is, therefore, a new cause of love, whereby our former emotion is fostered; hence we shall thereupon love it more steadfastly. Again, from the mere fact of conceiving that anyone shrinks from anything, we shall ourselves shrink from that thing (III. xxvii.). If we assume that we at the same time love it, we shall then simultaneously love it and shrink from it; in other words, we shall be subject to vacillation (III. xvii. note). Q.E.D.
Modern English
From the mere fact that we imagine someone loves something, we will love that thing too (E3P27). But we are assumed to love it already; a new cause of love is added, which sustains our prior affect, so we will love what we love all the more steadfastly.
Again, from imagining that someone shrinks from something, we will shrink from it too (E3P27). But if we suppose we love it at the same time, we will simultaneously love it and shrink from it, which is to say, by E3P17S (E3P17S), we will undergo vacillation of soul. Q.E.D.