Table of Propositions

The following list continues from previous propositions regarding the physics of strings and sound.

...not the ratio of the strings. 177.
XII. To provide the difference between sounds made by metals, woods, and stones. 181.
XIII. To provide the different weights of all the various species of wood used in our observations. 182.
XIV. One can determine the length of strings and the difference of their sounds by the difference of the weights stretching said strings; and the difference of said weights by the difference of the sounds and by the length of the strings. 184.
XV. To determine why a greater weight, or a greater power, is required to bring a string of double length to Unison The sounding of the same pitch by two different sources than to bring one of double thickness to it; and whether Unison indicates an equal tension in all kinds of strings. 189.
XVI. What the strength of strings and other cylinders parallel to the horizon is; what the ratio of their lengths is to their strengths, and what the difference is in their strengths considered according to the different arrangements that cylinders or parallelepipeds A six-sided solid figure where each face is a parallelogram, like a box can receive. 193.
XVII. The low pitch original: "graue" of sounds is greater as the bodies from which they come are less brittle, and as their parts are better bound together, provided that no hindrance occurs. Wherein many things regarding the principles of Chemistry are seen. 198.
XVIII. The density and rarity of bodies is, it seems, the cause of their sounds being different regarding low and high pitch original: "graue & à l'aigu". Wherein the principles of Chemistry are again discussed, as well as those of the hardness and weight of bodies. 201.
XIX. To explain the different qualities of bodies that make sound lower or higher, clearer or duller, and weaker or stronger, etc. 204.
XX. To explain several particulars of falling bodies and the speed of their fall. 205.
XXI. To explain the movements of a weight attached to a string likely referring to a pendulum, and their circumstances and uses. 208.
XXII. To determine the exact measurements of the vocal lines of the Echo, and the uses that can be deduced from them for Philosophy and Mechanics. 213.
XXIII. To explain several circumstances and properties of movements, both natural and violent, whether oblique or perpendicular; wherein one sees the examination of the thoughts and experiments of Galileo The famous Italian physicist and astronomer, whose work on motion was contemporary to this text on this subject. 221.
XXIV. To explain several conclusions drawn from this entire third book. 226.

Three Propositions of the Mechanical Treatise.

I. Given a plane inclined to the horizon, and the angle of inclination being known, to find a power which, pulling or pushing along a line of direction parallel to the inclined plane, supports a given weight upon the same plane. 7. Note that before this Proposition, one finds five Axioms and a Scholium A marginal note or explanatory commentary which must be understood.
II. When the line of direction by which a power supports a weight on an inclined plane is not parallel to the same plane, the inclination of the plane and the weight being given, to find the power. 13. Wherein the four following Scholia must be seen.