Table of Propositions

of Universal Harmony

XXIV. One can represent the squaring of the circle, the doubling of the cube, and all things in the world subject to quantity, by the same means as sounds. 42. Mersenne suggests that the mathematical ratios found in music can be used to model or solve famous geometric problems like "squaring the circle" (creating a square with the same area as a circle).
XXV. In what way sound is different from light, and in what way it is similar to it. 44.
XXVI. How the Echo is made, or the reflection of sounds. 48. Treatise on the Echo. 50.
XXVII. What the distances and lengths of the vocal line of the Echo are: whether one can know the place from which it responds, and how long the said line must be to create an Echo of as many syllables as one wishes. 56.
See the 22nd Proposition of the third book.
XXVIII. Explain all the appropriate shapes for making artificial Echoes, conic sections, and their principal properties. 59. This is done in the following Propositions, from the 23rd to the 32nd Proposition of the book on the Voice, and in the fifth Proposition of the book on the utility of harmony; which must be joined to this one.
XXIX. Determine if sounds break—that is to say, if they undergo refraction—like light, when they pass through different media. 63. Refraction is the bending of a wave (like light or sound) as it passes from one substance, like air, into another, like water.
XXX. By how much the sound of the same instrument is lower graue: low-pitched or deep in water than in air: and whether one can infer from this how much thinner rare: less dense air is than water. 67. See also the first Proposition of the book on Utility.
XXXI. Whether a high-pitched aigu: sharp or high in pitch sound is more agreeable and more excellent than a low-pitched one. 71.
See also the third Proposition of the 4th book on Composition.
XXXII. Determine if there is any movement in nature, and what is necessary to establish it. 74.
XXXIII. Consider the movements of bodies in general, and the species Original: "espece," referring here to types or categories of movement. in which they occur. 76.
XXXIV. Demonstrate whether a string stretched by a peg, or by a weight, is equally stretched in all its parts; and whether the force that bends it communicates its impression sooner and more strongly to the parts that are near it than to those that are further away.

I. Explain the proportion of the speed with which stones and other heavy bodies descend toward the center of the earth; and show that it is in the duplicate ratio Original: "raison doublee." In 17th-century mathematics, this refers to the square of a ratio. This proposition discusses Galileo’s law of falling bodies, which states that the distance fallen is proportional to the square of the time elapsed. of the times. 85. On which see the 29th Proposition of the third book, and particularly its second Corollary.
II. If a falling weight from a given space did not increase its acquired speed at the last point of that space, it would cover a space double the first in an equal amount of time, if it continued its fall at that same speed acquired at said last point: from which it is inferred that a falling stone passes through all possible degrees of slowness. 89.
Corollary I. On the path that the weight would take in the last half-second Original: "demie seconde minute." when falling from the surface of the earth to its center. 91.
Corollary II. Show in what time a stone would fall from the Stars, the Sun, or the Moon, to the surface or the center of the earth. 92.
III. Determine the shape of the movement of heavy bodies that would fall