Table of Propositions

...from the top of a tower, or from another given height, assuming that the earth moves, & makes every day a full revolution on its axis. 93.

IV. Bodies that would descend to the center of the earth cannot describe a semicircle: where one sees the line they would describe, if one assumes the daily movement of the earth. 96.

V. To explain the uses, & the practices that can be deduced from the preceding Propositions, as much for Mechanics as for several other things; & how one can measure all sorts of heights by the fall of weights, & find the fall in a given time, or the time required, when the fall is given. 99.

VI. To determine if the stars fell from the same place by a straight motion, which changed into the circular one they now have, as Galileo original: "Galilee"; referring to Galileo Galilei (1564–1642). Mersenne was one of the primary translators and defenders of Galileo’s work in France. imagines, & to give the manner of calculating their falls, their distances, & their circular motions. 105.

VII. To explain the movements of weights on planes inclined to the horizon, & the proportion of their speed: & to examine if falling bodies pass through all possible degrees of slowness. 108.

VIII. To demonstrate if a body can descend by an inclined plane to the center of the earth; & the manner of describing a line so inclined that the weight always presses upon it equally at every point. 113.

IX. To explain another easier geometric way to describe a plane of equal inclination: & to examine the shape of the movement of a globe rolling on a horizontal plane, & if rolling is faster than sliding coulement: literally "flowing," used here to mean a body sliding along a surface without rotating. 119.

X. The plane being inclined to the horizon by a given angle, to determine the force that can support the given weight on said plane. 121. But the entire Treatise on Mechanics added at the end of the following third book determines much more exactly & fully everything belonging to this subject, & to several mechanical difficulties.

XI. To determine if the speed of falling bodies increases according to the ratio of the line cut in mean and extreme ratio The "mean and extreme ratio" is the classical geometric definition of the Golden Ratio.; where one sees several properties of this section, & the manner of cutting this line to infinity. 125. Add here the 18th Proposition of the fourth book of Instruments. 125. On which see the Advertisement placed at the end of the fifth book of Composition.

XII. To examine if falling bodies always increase their speed, or if they decrease it; & if there is some point of equality at which they begin to descend at a steady speed. 128. Mersenne is investigating the concept of "terminal velocity," where a falling object stops accelerating due to air resistance.

XIII. To explain several experiments of the fall of bodies toward the center of the earth by a circular line. 131.

XIV. To explain how much a ball, which descends or rises through a quarter circle, goes faster, & is heavier in one place than in another, & of what length it must be to make each of its turns, or returns in a given time. 133. This proposition discusses the physics of the pendulum, which was a critical development for accurate timekeeping.

XV. To give the manner of making clocks, & watches within a minute of an hour, which divide the day, the hour, & the minutes into as many equal parts as one wishes, & the utility of these clocks. 135.

XVI. To explain how circular motions prevent, or help