Mechanica Vol. II (1736)

[We must determine] how much speed a body, acted upon by any forces and resistance, will possess in individual locations; for once this speed is known, the entire motion is perfectly understood. Furthermore, since the body would describe a different path if it were not enclosed in this channel, it will at least retain within the channel an inclination original: "conatum"; in 18th-century physics, this refers to 'conatus' or the internal striving of a body to move in a certain direction to proceed along that line in which it would move if it were free. By this inclination, it will press against the sides of the channel, and unless they possess sufficient firmness, it will actually break through them. For this reason, besides the speed which the body will have in individual locations of the channel, one must also determine the pressure it exerts against the sides of the channel, as well as the direction of that pressure, so that the firmness of the channel walls required to retain the body may be known.

Moreover, non-free motions of this kind can also be produced in other ways without a channel, as can be observed in pendulums and slings, by which a body is likewise forced to move along a given line. For with pendulums, as Huygens Christiaan Huygens (1629–1695), a Dutch physicist who did foundational work on the mechanics of pendulums and centrifugal force taught, it can be brought about that a body is forced to move along any prescribed curve. This is apparent both in pendulums suspended simply, by which the body is forced to move in a circular line, and in those which are usually suspended between cycloids A cycloid is the curve traced by a point on the rim of a circular wheel as it rolls along a straight line; Huygens discovered that a pendulum swinging between cycloidal "cheeks" is isochronous (the period is independent of the amplitude), by which the body is forced to move in a cycloid. In a similar way, it can be arranged that a body is forced to travel along any given curve.

This, therefore, is the first species of non-free motion, which occurs along a given line. Besides this, however, another species of non-free motion deserves attention, in which the path itself is not prescribed, but only the surface upon which the body is forced to move. This species of non-free motion is therefore less restricted than the former, since in this case, the body is still left the freedom to choose for itself a path situated upon the given surface.