On the Acceleration of Falling Bodies

...has been understood. If a plane, as it is less steep, is also made longer, the length can indeed compensate for the smallness of the speed increases in such a way that the speed acquired at the end of the motion is no less. The example brought forward concerning pendulums always agrees. Out of four pendulums with specific lengths—the first being exactly one foot, the second four feet, the third nine feet, and the fourth sixteen feet—the first actually and constantly completes four vibrations in the same time that the second completes three original: "treis." According to the law of pendulums, a four-foot pendulum should complete two vibrations for every four of a one-foot pendulum. This sequence 4, 3, 2, 1 for lengths 1, 4, 9, 16 is mathematically irregular, possibly representing an error in the source text or the specific theory Gassendi is refuting, the third completes two, and the fourth completes one. This remains true as long as they maintain the same length. From page 136 to 141.

TO ARTICLES 19, 20, 21, 22.

Regarding experiments on the impact or force of falling weights, to investigate whether the force increases along with the distance.

Several experiments were rightly required where it was claimed they could be performed with any heavy objects; this was done even though it was not permitted to complete them in even a single case. Three experiments were brought forward, nearly equal in weight, to persuade that force or speed does not increase according to the distances, but according to the square roots square roots: "radices," referring to the mathematical principle where the speed of a falling body is proportional to the square root of the distance it has fallen of the distances. These are entirely relevant to the matter. This is especially true for the experiment of water flowing out of a cylindrical vessel. The water at the top, falling into the opening, is no more hindered by the water below it than if it were falling through the air. This is because the water ahead always moves out of the way with a speed equal to its own, and the preceding water does not obstruct it.
From page 141 to 146.

TO ARTICLES 23, 24, 25, 26, 27, 28.

Regarding the experiment performed on a balance, and