Si nihil commune cum se invicem habent, ergo (per axioma 5) nec per se invicem possunt intelligi adeoque (per axioma 4) una alterius causa esse non potest. Q.E.D.
English (Elwes 1883)
If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.
Modern English
If they have nothing in common with each other, then they cannot be understood through each other (E1A5); and so one cannot be the cause of the other (E1A4). Q.E.D.