Mechanics, Volume I

...body, [once it] can be understood how motion is either conserved, or generated or altered by powers potentiae: external forces or agencies, I proceed to determining and examining the motion itself of bodies acted upon original: sollicitatorum by powers in any manner. And first, I consider rectilinear motion motion in a straight line as the easiest to determine; this arises if a free point is either impelled from rest into motion by a single power, or if, while already moving, it is either accelerated or retarded in the direction of the power itself. I have dedicated the third and fourth Chapters to this inquiry: in the former I treat rectilinear motion in a vacuum original: in vacuo, and in the latter, rectilinear motion in a resisting medium original: in medio resistente of any kind.

For although resistance can be reduced to powers properly so-called, it seemed advisable in this treatise to discuss the alteration of motion by resistance separately. I do this both to follow others who have written on this subject, and also because of the essential difference that exists between absolute powers and resistance. An absolute power, or one properly so-called, has a fixed direction that does not depend on the body's motion, and furthermore, it acts upon a moving body in the same way as it does one at rest. By contrast, the direction of resistance is always situated in the [same line as] the body's motion, and its magnitude depends on the body's speed original: celeritate.

And although in nature no resistance is observed other than that which is proportional to the squares of the speeds Euler refers to the physical law of fluid resistance, which typically varies with the square of velocity, I have nonetheless treated all other types of resistance as well. I have done this both to present the solutions to several problems concerning motion in a resisting medium, and especially so that many excellent...