The last article of my thirteenth chapter was this, “_If there be a number of quantities propounded, howsoever equal or unequal to one another; and there be another quantity which so often taken as there be quantities propounded, is equal to their whole sum; that quantity I call the mean arithmetical of them all_.” Which definition I did there insert to serve me in the explication of those propositions of which the sixteenth chapter consisted, but did not use it here as I intended. My first proposition therefore as it standeth yet in the Latin, being this, “_the velocity of any body moved during any time, is so much as is the product of the impetus in one point of time, multiplied into the whole time_;” to a man that hath not skill enough to supply what is wanting, is not intelligible. Therefore I have caused it in the English to go thus: “_the velocity of any body in whatsoever time moved, hath its quantity determined by the sum of all the several_ (impetus) _quicknesses, which it hath in the several points of the time of the body’s motion_. And added, _that all the_ impetus _together taken through the whole time is the same thing with the mean_ impetus (which mean is defined (Chapter XIII. art. 29) _multiplied into the whole time_.” To this first article, as it is uncorrected in the Latin, you object, _that meaning by_ impetus _some middle_ impetus, _and assigning none, I determine nothing_. And it is true. But if you had been geometricians sufficient to be professors, you would have shewed your skill much better, by making it appear that this middle _impetus_ could be none but that, which being taken so often, as there be points in the line of time, would be equal to the sum of all the several _impetus_ taken in the points of time respectively; which you could not do. To the _corollary_, you ask first how _impetus_ can be ordinately applied to a line; absurdly. For does not Archimedes sometimes say, and with him many other excellent geometricians, _let such a line be the time_? And do they not mean, that that line, or the motion over it, is the measure of the time? And may not also a line serve to measure the swiftness of a motion? _You thought_, you say, _only lines ought to be said to be ordinately applied to lines_. Which I easily believe; for I see you understand not that a line, though it be not the time itself, may be the quantity of a time. You thought also, all you have said in your _Elenchus_ , in your doctrine of the _angle of contact_, in your _Arithmetica Infinitorum_, and in your _Conics_ , is true; and yet it is almost all proved false, and the rest nothing worth.