Lectures de Potentia Restitutiva, or of Spring

The resistance of the medium original: "Impediment of the medium"; referring here to air resistance hinders the exactness of it. If the object is launched with triple, quadruple, quintuple, or sextuple the initial velocity, it shall touch the floor at almost triple, quadruple, quintuple, or sextuple the initial distance. I shall not need to show the reason why it moves in a Parabola, as it has been sufficiently demonstrated long ago by many others.

If the body is launched by the spring at the floor level but shot upward at some angle—knowing the velocity with which it is moved when launched, the angle of inclination The angle at which the object is aimed relative to the vertical or horizontal plane. to the perpendicular, and the true velocity of a falling body—you may easily determine the length of the shot original: "Jactus"; a Latin term for a throw or a cast. and the time it will spend in traveling that distance.

This is found by comparing the time of its ascent with the time of the descent of heavy bodies. The ascent of any body is easily known by comparing its velocity with the angle of inclination.

Let a b in the fifth figure represent 16 feet, or the space descended by a heavy body in one second of time. If a body is shot from b, along the line b f with a velocity as much faster than that equal motion of 16 feet in a second as this line b f is longer than a b, the body shall fall at e. For in the same amount of time that the slanted, uniform motion would make it ascend from b d to a c, the accelerated direct motion downward will move it from a c to b d. Therefore, at the end of one second—when the motions equal and balance each other—the body must be in the same horizontal line in which it started, but moved across by the distance b e. This method will also determine the points it passes through in all the intermediate spaces.

Let the parallelogram a b p q then represent the whole velocity of the ascent of a body by a uniform motion of 16 feet in a second, and the triangle p q r represent the whole velocity of...