Also concerning heat, light, and divers other qualities, which have degrees, there lieth a question of _how much_, to be answered by a _so much_, and consequently they have their quantities, though the same with the quantity of swiftness: because the intensions and remissions of such qualities are but the intensions and remissions of the swiftness of that motion by which the agent produceth such a quality. And as quantity may be considered in all the operations of nature, so also doth geometry run quite through the whole body of natural philosophy. To the principles of geometry the definition appertaineth also of a _measure_, which is this, _one quantity is the measure of another quantity, when it, or the multiple of it, is coincident in all points with the other quantity_. In which definition, instead of that ἐφαρμογὴ of Euclid, I put coincidence. For the superposition of quantities, by which they render the word ἐφαρμογὴ, cannot be understood of bodies, but only of lines and superficies. Nevertheless many bodies may be coincident successively with one and the same place, and that place will be their measure, as we see practised continually in the measuring of liquid bodies, which art of measuring may properly be called ἐφάρμοσις, but not superposition. Also the definitions of _greater_, _less_, and _equal_, are necessary principles of geometry. For it cannot be imagined than any geometrician should demonstrate to us the equality and inequality of magnitudes, except he tell us first what those words do signify. And it is a wonder to me, that Euclid hath not anywhere defined what are equals, or at least, what are equal bodies, but serveth his turn throughout with that forementioned ἐφάρμοσις, which hath no place in solids, nor in time, nor in swiftness, nor in circular, or other crooked lines; and therefore no wonder to me, why geometry hath not proceeded to the calculation neither of crooked lines, nor sufficiently of motion, nor of many other things, that have proportion to one another. Equal bodies, superficies, and lines, are those of which every one is capable of being coincident with the place of every one of the rest: and equal times, wherein with one and the same motion equal lines are described. And equally swift are those motions by which we run over equal spaces in any time determined by any other motion. And universally all quantities are equal, that are measured by the same number of the same measures. It is necessary also to the science of geometry, to define what quantities are of one and the same kind, which they call _homogeneous_, the want of which definitions hath produced those wranglings (which your book _De Angulo Contactus_ will not make to cease) about the angle of contingence.