Mechanica Vol. II (1736)

[so that it] can [move] uniformly, it is necessary that it be pulled along the normal A line perpendicular to the path of motion. MO by a force = $\frac{v^2}{r}$ This is a foundational version of the formula for centripetal force ($F = mv^2/r$). Euler is demonstrating that to keep a body on a curve, a specific amount of force must be applied toward the center of curvature.. From this, it can be understood that the body strives with just as much force toward the opposite side; otherwise, that force would not be needed to keep the body on the curve. Therefore, while a body is forced to move in a channel Euler uses "canalis" to refer to any physical constraint, like a tube or a groove, that restricts a body's movement. AM, and its striving Original: "nisus." In 18th-century physics, this refers to the internal "effort" or tendency of a body to move in a certain direction, what we might now call inertia or centrifugal tendency in this context. is not removed by a normal force, it will actually exert this striving upon the channel. For this reason, such a channel must possess enough strength to sustain this pressure.

Corollary 6.

27. It appears, therefore, that a body in motion can produce an effect without any loss of speed; this effect, of course, consists in a specific pressure.

Corollary 7.

28. Thus, pressure can arise from motion alone. Therefore, just as motion is generated from pressure or from forces Original: "potentiis." Euler uses "potentia" to mean an active cause of motion or a force., so also pressure can arise from motion.

Scholion 2.

29. From this it is understood—as we have already hinted above in Book One—that it is uncertain whether motion is due to forces, or indeed whether forces are due to motion. For we see both exist in the world—namely forces and motion; which of the two is the cause of the other is a question to be decided both by reason and by observations. To reason, it seems very little agreeable to attribute "innate strivings" to bodies, and much less to establish forces as existing by themselves. Furthermore, [the cause of] these phenomena...