Mechanics, Volume I

regions The Latin text begins with the suffix of a word from the previous page, likely plagae, meaning regions or tracts of space. progress into another, and in this sense we say that the sun moves. In a similar way, on a moving ship, those things which keep the same place on the ship are relatively at rest, and those which change their place on the ship are relatively in motion.

Corollary 1.

10. Relative motion and relative rest coincide with absolute motion and absolute rest when the space or body with respect to which the motion and rest are judged is actually at rest with respect to that immense and infinite space. For if the earth truly remains at rest, those things which move and rest with respect to it are also moving and resting absolutely.

Corollary 2.

11. However, relative motion and rest differ from absolute motion and rest if that [reference] space is moving. For if the earth does not remain at rest with respect to infinite space, then those things which are at rest with respect to the earth are not absolutely at rest; and furthermore, absolute motion will differ from relative motion. Indeed, it can even happen that a body which is moving relatively may be at the same time absolutely at rest. Euler is describing what we now call Galilean relativity: if you walk backward on a moving ship at the exact same speed the ship moves forward, you are moving "relatively" to the ship but are "absolutely" stationary compared to the water.

Scholion.

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

12. It is clear that this relative state of bodies—whether of motion or of rest—can be different in innumerable ways. For according to which space is assumed as the point of reference, different relative motions and different states of rest will emerge. Thus, the fixed stars original: "stellae fixae"; these are the stars that appear to maintain their positions relative to one another in the night sky, unlike the "wandering" planets. move with respect to the earth, yet each one is at rest with respect to the others. And