E3P29D
Demonstration — Part III
Latin
Ex eo quod imaginamur homines aliquid amare vel odio habere, nos idem amabimus vel odio habebimus (per propositionem 27 hujus) hoc est (per scholium propositionis 13 hujus) eo ipso ejus rei præsentia lætabimur vel contristabimur adeoque (per præcedentem propositionem) id omne quod homines amare sive cum lætitia aspicere imaginamur, conabimur agere etc. Q.E.D.
English (Elwes 1883)
From the fact of imagining, that men love or hate anything, we shall love or hate the same thing (III. xxvii.). That is (III. xiii. note), from this mere fact we shall feel pleasure or pain at the thing's presence. And so we shall endeavour to do whatsoever we conceive men to love or regard with pleasure, etc. Q.E.D.
Modern English
From imagining that others love or hate something, we will love or hate that same thing (E3P27), that is, by E3P13S (E3P13S), the mere presence of the thing will affect us with joy or sadness. And so by E3P28 (E3P28) we will strive to do everything that others love or regard with pleasure, and so on. Q.E.D.