Such velocities were found to bear a simple relation to the period of time from the beginning of the fall.

Other experiments, in which balls were allowed to roll down inclined planes, corroborated the observation that the pull of gravitation gave a velocity proportionate to the length of fall, whether such fall were direct or in a slanting direction.
These studies were associated with observations on projectiles, regarding which Galileo was the first to entertain correct notions.
According to the current idea, a projectile fired, for example, from a cannon, moved in a straight horizontal line until the propulsive force was exhausted, and then fell to the ground in a perpendicular line.
Galileo taught that the projectile begins to fall at once on leaving the mouth of the cannon and traverses a parabolic course.

According to his idea, which is now familiar to every one, a cannon-ball dropped from the level of the cannon's muzzle will strike the ground simultaneously with a ball fired horizontally from the cannon.

As to the paraboloid course pursued by the projectile, the resistance of the air is a factor which Galileo could not accurately compute, and which interferes with the practical realization of his theory.

But this is a minor consideration.
The great importance of his idea consists in the recognition that such a force as that of gravitation acts in precisely the same way upon all unsupported bodies, whether or not such bodies be at the same time acted upon by a force of translation.
Out of these studies of moving bodies was gradually developed a correct notion of several important general laws of mechanics--laws a knowledge of which was absolutely essential to the progress of physical science.
The belief in the rotation of the earth made necessary a clear conception that all bodies at the surface of the earth partake of that motion quite independently of their various observed motions in relation to one another.