Complete Works, Volume Three

of Chapters and Articles

3. While the hands hang freely during walking, they move only forward; and when they seem to be bent backward, they are actually at rest. From this, a ball dropped while the hand is stretched forward moves twice as fast (just like the hand) as the trunk of the body; and while the hand appears to go backward, the ball falls in a straight vertical line. 479

4. Experiments concerning a ball thrown directly upward from a carriage or a horse (even when moving very swiftly) and falling back into the hand. Many other such things occur because the motion of the carriage or horse, impressed upon the hand, is combined with the hand's own motion. This creates a truly mixed motion, even though to the eye it appears as no other than the hand's own motion. 480

5. Various experiments concerning a ball, or another projectile, which falls back into the same part of a ship when thrown upward while the ship is moving. If dropped from the top of the mast, it falls at the foot of that same mast. Whether it is driven with equal force toward the prow or the stern, it covers an equal space over the ship, even if the space is unequal with respect to the air. The cause is said to be the composition of the ship's motion and the hand's own motion. Meanwhile, the eye observes no other motion than the hand's own, because the motion of the ship is common to both the observer and the projectile. 481

6. To investigate the cause of both natural motion, whose impetus continually increases, and projectile motion, whose impetus decreases. It is first established that the acceleration of a falling heavy body occurs such that the distances acquired are in the duplicate ratio original: "duplicata ratione"; this refers to the square of the time, following Galileo's law of falling bodies where distance is proportional to time squared of the times in which they are acquired. Furthermore, the line that a projectile describes obliquely through the air is parabolic. This matter is demonstrated from a diagram designed to make both of the preceding points understood. 483

7. From this, it is gathered that a stone thrown from a moving ship to the height of the mast, and falling back down the same height, describes a line that appears straight to the sight but is actually parabolic. Similarly, a stone dropped from the top of the mast describes a semi-parabola. This is due to the composite motion consisting of the perpendicular motion (from the hand or gravity) and the horizontal motion (from the ship). Nothing of either motion is lost due to this composition,

but just as much space is traversed both perpendicularly and horizontally as if the motions were separate. The times of ascent and descent are equal. The velocity increases in descent in the same proportion as it decreases in ascent; this happens just as if there were no motion of transport original: "motus translatitius"; the overall motion of the ship or vehicle carrying the object. The proportion of increasing and decreasing velocity along a parabolic line is the same as it is along a perpendicular line. In composite motion, the distances acquired upward or downward are indeed unequal during equal moments of time; however, forward, or along the horizon, they are entirely equal. No matter how open or narrow the parabolic or semi-parabolic lines are, provided the height is the same, they are described in equal time. Finally, a projectile force, even a cannonball, fired directly upward from the foot of the mast while the ship is moving, will fall back to the foot of the mast. ibid.

8. It is also explained why, when two people are playing together inside a moving ship and throwing a ball back and forth with equal force from the prow and the stern, one does not meet the ball closer and the other further away. This is because the motion of the ship, common to both, adds as much power to the ball thrown by one as it moves the other person away; and it takes as much from the ball thrown back by the latter as it moves the former forward, through a wonderful compensation. 487

9. There is no motion that is not natural, just as there is no motion that is not from natural principles. There is no motion that is not violent, just as none (excluding the first-created) is not from another source. That motion is natural which happens either spontaneously or without resistance; that motion is violent which happens against nature or with resistance. Uniformity is the character of natural motion; inequality is the character of violent motion. Properly speaking, therefore, only circular motion is natural, especially celestial motion. Straight motion, however, is violent, such as that of an object projected upward or even an object falling downward. ibid.

10. Since the motion of a stone, whether dropped or falling back from the height of a moving mast, is composed of the perpendicular and the horizontal, the horizontal rather than the perpendicular...

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