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E3P32D

Demonstration — Part III

Latin

Ex eo solo quod aliquem re aliqua gaudere imaginamur (per propositionem 27 hujus cum ejusdem I corollario) rem illam amabimus eaque gaudere cupiemus. At (per hypothesin) huic lætitiæ obstare imaginamur quod ille eadem hac re gaudeat; ergo (per propositionem 28 hujus) ne ille eadem potiatur, conabimur. Q.E.D.

English (Elwes 1883)

From the mere fact of our conceiving that another person takes delight in a thing (III. xxvii. and Coroll.) we shall ourselves love that thing and desire to take delight therein. But we assumed that the pleasure in question would be prevented by another's delight in its object; we shall, therefore, endeavour to prevent his possession thereof (III. xxviii.). Q.E.D.

Modern English

From the mere fact that we imagine someone rejoicing in something, we will love that thing and desire to rejoice in it ourselves (E3P27). But by hypothesis we imagine that his joy would be an obstacle to our own. We will therefore strive that he does not obtain it (E3P28). Q.E.D.

Depends on (2)

Propositions