Mechanics, Volume I

-spect to these boundaries preserves the same position is said to be at rest; however, that which changes its position in the same respect is said to move.

Scholion 2.

Scholion: an explanatory note or commentary added to a mathematical or philosophical text to clarify a point of reasoning.

8. What has been said here regarding immense and infinite space and its boundaries ought to be considered as purely mathematical concepts. These, although they may seem contrary to metaphysical speculations, Euler is likely referring to the philosophical debates of his time, such as those between Leibniz and Newton, regarding whether space exists as an independent "thing" or merely as a relationship between objects. are nevertheless correctly applied to our purpose. For we do not assert that such an infinite space, which has fixed and immovable limits, actually exists; but whether it exists or not, without concerning ourselves, we only require that one who intends to contemplate absolute motion and absolute rest should represent such a space to themselves, and from that, judge the state of bodies as either rest or motion. For reasoning is most conveniently established in this way: that, abstracting our minds from the world, we imagine for ourselves an infinite and empty space, and conceive of bodies placed within it. If these bodies retain their position in this space, they must be judged to be at absolute rest; but if they pass from one part of this space to another, they must be judged to be in absolute motion.

DEFINITIO 3.

9. Relative motion is the change of position with respect to some space assumed at will. And relative rest is remaining in the same position with respect to that same space. Thus, taking the Earth for this space, we say those things are at rest which hold their position unchanged on the Earth; but those things move which [pass] from another position with respect to the Ear-