Salv.And have you no other conceit thereof than this?
Simpl.This I think to be the proper definition of equal motions.
Sagr.We will add moreover this other:Velocities are said to be equal, when the spaces passed are proportionate to their time. and call that equal velocity, when the spaces passed have the same proportion, as the times wherein they are past, and it is a more universal definition.
Salv.It is so: for it comprehendeth the equal spaces past in equal times, and also the unequal past in times unequal, but proportionate to those spaces. Take now the same Figure, and applying the conceipt that you had of the more hastie motion, tell me why you think the velocity of the Cadent by C B, is greater than the velocity of the Descendent by C A?
Simpl.I think so; because in the same time that the Cadent shall pass all C B, the Descendent shall pass in C A, a part less than C B.
Salv.True; and thus it is proved, that the moveable moves more swiftly by the perpendicular, than by the inclination. Now consider, if in this same Figure one may any way evince the other conceipt, and finde that the moveables were equally swift by both the lines C A and C B.
Simpl.I see no such thing; nay rather it seems to contradict what was said before.
Salv.And what say you, Sagredus? I would not teach you what you knew before, and that of which but just now you produced me the definition.
Sagr.The definition I gave you, was, that moveables may be called equally swift, when the spaces passed are proportional to the times in which they passed; therefore to apply the definition to the present case, it will be requisite, that the time of descent by C A, to the time of falling by C B, should have the same proportion that the line C A hath to the line C B; but I understand not how that can be, for that the motion by C B is swifter than by C A.
Salv.And yet you must of necessity know it. Tell me a little, do not these motions go continually accelerating?
Sagr.They do; but more in the perpendicular than in the inclination.
Salv.But this acceleration in the perpendicular, is it yet notwithstanding such in comparison of that of the inclined, that two equal parts being taken in any place of the said perpendicular and inclining lines, the motion in the parts of the perpendicular is alwaies more swift, than in the part of the inclination?
Sagr.I say not so: but I could take a space in the inclination, in which the velocity shall be far greater than in the like space taken in the perpendicular; and this shall be, if the space in theperpen-
