your incredulity; but for the knowledge of this, expect it at some other time, namely, when you shall see the matters concerning local motion demonstrated by our Academick; at which time you shall find it proved, that in the time that the one moveable falls all the space C B, the other descendeth by C A as far as the point T, in which falls the perpendicular drawn from the point B: and to find where the same Cadent by the perpendicular would be when the other arriveth at the point A, draw from A the perpendicular unto C A, continuing it, and C B unto the interfection, and that shall be the point sought. Whereby you see how it is true, that the motion by C B is swifter than by the inclination C A (supposing the term C for the beginning of the motions compared) because the line C B is greater than C T, and the other from C unto the intersection of the perpendicular drawn from A, unto the line C A, is greater than C A, and therefore the motion by it is swifter than by C A. But when we compare the motion made by all C A, not with all the motion made in the same time by the perpendicular continued, but with that made in part of the time, by the sole part C B, it hinders not, that the motion by C A, continuing to descend beyond, may arrive to A in such a time as is in proportion to the other time, as the line C A is to the line C B. Now returning to our first purpose; which was to shew, that the grave moveable leaving its quiescence, passeth descending by all the degrees of tardity, precedent to any whatsoever degree of velocity that it acquireth, re-assuming the same Figure which we used before, let us remember that we did agree, that the Descendent by the inclination C A, and the Cadent by the perpendicular C B, were found to have acquired equal degrees of velocity in the terms B and A: now to proceed, I suppose you will not scruple to grant, that upon another plane less steep than A C; as for example, A D [in Fig. 5.] the motion of the descendent would be yet more flow than in the plane A C. So that it is not any whit dubitable, but that there may be planes so little elevated above the Horizon A B, that the moveable, namely the same ball, in any the longest time may reach the point A, which being to move by the plane A B, an infinite time would not suffice: and the motion is made always more slowly, by how much the declination is less. It must be therefore confest, that there may be a point taken upon the term B, so near to the said B, that drawing from thence to the point A a plane, the ball would not pass it in a whole year. It is requisite next for you to know, that the impetus, namely the degree of velocity the ball is found to have acquired when it arriveth at the point A, is such, that should it continue to move with this self-same degree uniformly, that is to say, without accelerating or retarding;in
