Mechanics, Volume I

...planets move both with respect to the earth and with respect to the fixed stars. The "fixed stars" were the distant stars that appeared not to move relative to one another, used as a backdrop for tracking the movement of planets. In what follows, however, I wish for absolute motion and absolute rest to always be understood, unless I expressly advise that the arguments being brought forward also pertain to relative motion.

PROPOSITION I.

Theorem.

13. Every body that is transferred to another place, whether by absolute or relative motion, passes through all intermediate places; it cannot arrive from the first to the last suddenly. original: "subito." In this context, the author means "instantaneously" or "without a transition."

Demonstration.

...ed? The first letters of the following lines are partially obscured by an ink blot. Regarding absolute motion, if a body were to arrive suddenly from a first location to a final one, it would be necessary for it to have been annihilated in the first and immediately produced anew in the last—something which, by the laws of nature, cannot happen unless a miracle occurs. Therefore, it proceeds from the first to a certain next place, and from this to the following one, until at last it arrives at the final one. Regarding relative motion: if the body that is placed within infinite space is actually at rest, the previous reasoning (section 10) holds. But if it moves, it too must pass through each intermediate place, and therefore relative motion will also be successive, occurring through each intermediate place. Q. E. D.: stands for Quod Erat Demonstrandum, a Latin phrase meaning "which was to be demonstrated," used to signal the end of a formal proof.

Corollary I.

14. It follows from these points also that motion cannot occur in an instant, but that time is necessary, by which from another...