Notebook on Mechanics and Natural Philosophy

Let c be the center of a circular motion between the ends of a chord original: "corda"; in geometry, a straight line segment whose endpoints both lie on a circular arc. ab. This chord is pulled by two weights, p and q, which are equal to each other; and the perpendicular A line at a right angle (90°) to the chord. from the center c shall be d, which falls in the middle of said chord ab.

[A geometric diagram of a circle with a vertical chord labeled 'a' at the top and 'b' at the bottom. The center is labeled 'c'. A horizontal line 'cd' meets the chord at its midpoint. Radii extend from the center 'c' to points 'a' and 'b'. A vertical line extends downwards from a point on the circle.]

But if c is the center and the chord is ab, between the ends of which there is circular motion moved by a weight p, which is equally distant from the center of said motion c: I say that the perpendicular from the center c above said chord is d, and that this perpendicular is shorter than any other line drawn from that center to the upper part of said chord. By the law of equilibrium, said weight will keep this chord equally distant from the center c, as appears at f, which is the center of the chord ab. This chord is pulled by two weights, p and q, which are equal to each other; these weights, by the principles of the balance, will remain on this chord at equal distances from the perpendicular cd. This perpendicular is shorter than any other line drawn from the center c to the chord ab. I say that the perpendicular cd is the shortest line that can be drawn from center c to chord ab; and the further these lines move away from the perpendicular cd, the longer they become, and consequently more oblique Slanting or at an angle; not Steiner/perpendicular.. Because they are more oblique, they move further away from the perpendicular of the weight, which is p when the chord is straight. Therefore, the chord, being oblique, will be weaker in resisting the weight p; and the weaker it is, the more it will be bent by that weight, and that weight will be lower than its opposing weight q.

[A geometric diagram showing a circle with a vertical chord ab and center c. Multiple lines are drawn from the center to various points on the chord. Two small circles representing weights p and q are suspended from different points on the chord, illustrating the tension and angle of the string.]

The more the chord ab is bent toward the center c, the less distant that chord will be from the center. The perpendicular of the center c is cd; and I say cd is shorter than any other line drawn from the center c to the chord ab. I say that the further these lines move from the perpendicular cd, the longer they are and consequently more oblique. Because they are more oblique, their resistance will be less; and because of this lack of resistance, the chord ab will be moved more quickly by circular motion than by perpendicular motion. Therefore, said chord is said to be weaker than the perpendicular; thus, the chord is said to be less capable of resisting the weight p, and the chord will be less bent by that weight p.