Acceleration ( Force ). This is what one calls the force or the cause which accelerates the motion of a body. When one examines the effects produced by such causes and is unable to know the causes themselves, the effects must always be given independently of any knowledge of the cause, since they cannot be deduced from it: it is in this way that not knowing the cause of gravity, we learn through experimentation that the space which is described by a falling body is a ratio to the square of the time. In general in the various motions of which the causes are unknown, it is evident that the effect produced by the cause, whether in a finite time or in an instant, must always be provided by the equation between the times and the distances: when this effect is known and the principle of inertial force is supposed, we need only Geometry and calculus to discover the properties of these types of motion. It is thus useless to have recourse to the principle which everyone uses today that the accelerating or decelerating force is proportional to the element of speed; a principle which is applied on this unique axiom which is both vague and obscure that the effect is proportional to its cause. We will not consider at all if this principle is a necessary truth, we will admit only that the proofs that have been given until now do not seem to us very persuasive: nor will we adopt it, as some Geometers have, as a purely contingent truth, which would thereby destroy the certainty of Mechanics, and would reduce it to nothing more than an experimental science. We will be content to observe that, true or doubtful, clear or obscure, it is useless to Mechanics and that consequently it should be banished from it.