Lastly, you object “that motion is accidentary to a point, and consequently not essential, nor to be put into the definition.” And is not the circumduction of a semicircle accidentary to a sphere? Or do you think the sphere of the sun was generated by the revolution of a semicircle? And yet it was thought no fault in Euclid to put the motion into the definition of a sphere. The conceit you have concerning definitions, that they must explicate the essence of the thing defined, and must consist of a _genus_ and a _difference_, is not so universally true as you are made believe, or else there be very many insufficient definitions that pass for good with you in Euclid. You are much deceived if you think these woful notions of yours, and the language that doth everywhere accompany them, show handsomely together. Or that such grounds as these be able to sustain so many, and so haughty reproaches as you advance upon them, so as they fall not, as you shall see immediately, upon your own head. I say a point hath quantity, but not to be reckoned in demonstrating the properties of lines, solids, or superficies; you say it hath no quantity at all, but is plainly nothing. The first of the petitions of Euclid is, “that a line may be drawn from point to point at any distance.” The second, “that a straight line may be produced.” The third, “that on any centre a circle may be described at any distance.” And the eighth axiom (which Sir H. Savile observes to be the foundation of all geometry) is this, “_Quæ sibi mutuo congruunt, etc._ Those things that are applied to one another in all points are equal.” All or any of these principles being taken away, there is not in Euclid one proposition demonstrated or demonstrable. If a point have no quantity, a line can have no latitude; and because a line is not drawn but by motion, by motion of a body, and body imprinteth latitude all the way, it is impossible to draw or produce a straight line, or to describe a circular line without latitude. Also if a line have no latitude, one straight line cannot be applied to another. To them therefore that deny a point to have quantity, that is, a line to have latitude, the forenamed principles are not possible, and consequently no proposition in geometry is demonstrated or demonstrable. You therefore that deny a point to have quantity, and a line to have breadth, have nothing at all of the science of geometry. The practice you may have, but so hath any man that hath learned the bare propositions by heart; but they are not fit to be professors either of geometry or of any other science that dependeth on it. Some man perhaps may say that this controversy is not much worth, and that we both mean the same thing. But that man, though in other things prudent enough, knoweth little of science and demonstration. For definitions are not only used to give us the notions of those things whose appellations are defined, for many times they that