Mechanica Vol. II (1736)

ON CONSTRAINED MOTION IN GENERAL.

In that case, the body will lose a finite degree of speed; in this case, however, it loses only an infinitely small amount.

Corollary 3.

15. Since, however, points of this kind are rare in all curves and are separated from one another, the body will nevertheless traverse the arc intercepted between two such points with uniform motion Motion at a constant, unchanging speed..

Scholion 1.

16. The cases in which a body undergoes a sudden finite decrease in speed cannot be any others than where the curve has cusps A cusp is a sharp point where two parts of a curve meet and then turn back, like the point of a heart shape or the tip of a crescent moon.. For in these places, the body is forced to turn back directly and strikes normally At a right angle, or head-on. against the point of the cusp. In that event, therefore, the body will not only lose a finite degree of speed, but it must lose all motion entirely; unless, perhaps, the body is assumed to be elastic In physics, an "elastic" body bounces back with its energy preserved, whereas an "inelastic" body stops or deforms upon impact., in which case it will be reflected with the same speed with which it struck, and thus it will maintain its uniform motion. For in a cusp, two elements The "elements" are the infinitely small straight-line segments that Euler uses to model a curve. constitute an infinitely acute angle.

Scholion 2.

17. Besides cusps, however, other points can exist on curves in which the radius of curvature A measure of how "tight" a turn is. A very small radius means a very sharp turn. is infinitely small; but because any two contiguous elements are placed almost in a straight line, and the exterior angle original: "angulus deinceps". In geometry, this refers to the angle between one segment and the extension of the previous one. is infinitely small, it cannot happen (as is evident from the demonstration) that the body suffers a finite decrease in speed. Therefore, since points of this kind are rare, the body will nonetheless be moved with uniform motion Also called "equable" motion; movement where equal distances are covered in equal times..