E2P13D4
Demonstration — Part II
Latin
Corpora (per definitionem 1 hujus) res singulares sunt quæ (per lemma 1) ratione motus et quietis ab invicem distinguuntur adeoque (per propositionem 28 partis I) unumquodque ad motum vel quietem necessario determinari debuit ab alia re singulari nempe (per propositionem 6 hujus) ab alio corpore quod (per axioma 1) etiam vel movetur vel quiescit. At hoc etiam (per eandem rationem) moveri vel quiescere non potuit nisi ab alio ad motum vel quietem determinatum fuisset et hoc iterum (per eandem rationem) ab alio et sic in infinitum. Q.E.D.
English (Elwes 1883)
Bodies are individual things (II., Def. i.), which (Lemma I.) are distinguished one from the other in respect to motion and rest; thus (I. xxviii.) each must necessarily be determined to motion or rest by another individual thing, namely (II. vi.), by another body, which other body is also (Ax. i.) in motion or at rest. And this body again can only have been set in motion or caused to rest by being determined by a third body to motion or rest. This third body again by a fourth, and so on to infinity. Q.E.D.
Modern English
Bodies are singular things (E2D1) that are distinguished from one another with respect to motion and rest (E2L1); so each one must necessarily have been determined to motion or rest by another singular thing, namely, (E2P6), by another body, which (E2AInt1) is also either in motion or at rest. And that body, too, for the same reason, could not have been in motion or at rest unless it had been determined to it by another, and that by another, and so on to infinity. Q.E.D.