There is in my fifth lesson a proposition, with a diagram to it, to make good, I dare say, at least against you, my twentieth chapter concerning the dimension of a circle. If that demonstration be not shown to be false, your objections to that chapter, though by me rejected, come to nothing. I wonder why you pass it over in silence. But you are not, you say, bound to answer it. True, nor yet to defend what you have written against me. Before I give over the examination of your geometry, I must tell you that your words, (p. 101 of your _School Discipline_), against the first corollary are untrue. Your words are these: “_you affirm that the proportion of the parabola A B I to the parabola A F K is triplicate to the proportion of the time A B to A F, as it is in the English_.” This is not so. Let the reader turn to the place and judge. And going on you say, “_or of the impetus B I to F K as it is in the Latin_.” Nay, as it is in the English, and the other in the Latin. It is but your mistake; but a mistake is not easily excused in a false accusation. Your exception to my saying, “_that the differences of two quantities is their proportion_,” (when they differ, as the no difference, when they be equal), might have been put in amongst other marks of your not sufficiently understanding the Latin tongue. _Differre_ and _differentia_ differ no more than _vivere_ and _vita_, which is nothing at all, but as the other words require that go with them, which other words you do not much use to consider. But _differre_ and _the quantity by which they differ_, are quite of another kind. _Differre_ (τὸ διαφέρειν, τὸ ὑπερέχειν) _differing_, _exceeding_, is not quantity, but relation. But the quantity by which they differ is always a certain and determined quantity, yet the word _differentia_ serves for both, and is to be understood by the coherence with that which went before. But I had said before, and expressly to prevent cavil, that relation is nothing but a comparison, and that proportion is nothing but relation of quantities, and so defined them, and therefore I did there use the word _differentia_ for _differing_, and not for the quantity which was left by subtraction. For a quantity is not a differing. This I thought the intelligent reader would of himself understand without putting me, instead of _differentia_, to use (as some do, and I shall never do) the mongrel word τὸ _differre_. And whereas in one only place for _differre ternario_ I have writ _ternarius_, if you had understood what was clearly expressed before, you might have been sure it was not my meaning, and therefore the excepting against it was either want of understanding, or want of candour, choose which you will.