Corollaries 5

Corollary 5

The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards without any circular motion.

The differences of the motions tending towards the same parts, and sums of those that tend towards contrary parts, are, at first (by sup the same and it is from those sums and differences position), in both cases

that the collisions and impulses do arise with which the bodies mutually impinge one upon another. Wherefore (by Law II), the effects of those collisions will be equal in both cases

and therefore the mutual motions among themselves in the one case will remain equal to the clear mutual motions of the bodies among themselves in the other. of the bodies A proof of which we have from the experiment of a ship where all motions happen after the same manner, whether the ship is at rest, or is carried uniformly forwards in a right line.

If bodies, any how moved among

Corollary 6

themselves, are urged in the direct-ton by equal accelerative forces, they will all continue to themselves, after the same manner as if they had been of parallel lines move among urged by no such forces. For these forces acting equally (with respect to the quantities of the DO dies to be moved), and in the direction of parallel lines, will (by Law II) move all the bodies equally (as to velocity), and therefore will never pro duce any change in the positions or motions of the bodies among themselves.