Scholium

Galileo discovered Law 1, 2, and Corollaries 1, 2 as bodies:

• falling in the duplicate ratio of the time [as seconds squared]
• moving in a parabola as projectiles

The uniform gravity of a body acts equally in equal particles of time on that body to create equal velocities. In the whole time, gravity impresses a whole force and generates a velocity proportional to that time.

The space traveled per time are proportional to the velocity and time together in a duplicate ratio of the times*.

When a body is thrown upwards, its uniform gravity impresses forces and removes its upward velocities proportional to the times. At the time at the highest point, all the upward velocities [in unity] are removed.

If a body is projected in any direction, the resulting motion is compounded with the motion arising from its gravity.