You begin your reprehension of my thirteenth chapter with a question; whereas _I_ divide proportion into arithmetical and geometrical. You ask me what _proportion it is I so divide_. Euclid divides an angle into right, obtuse, and acute. I may ask you as pertinently, what angle it is he so divides? Or, when you divide _animal_ into _homo_ and _brutum_, what animal that is, which you so divide? You see by this, how absurd your question is. But you say the definition of proportion which I make at Chap. II. art. 3., namely, that proportion is the comparison of two magnitudes, one to another, agreeth not, neither with arithmetical, nor with geometrical proportion. I believe you thought so then, but having read what I have said in the end of the last lesson, if you think so still, your fault will be too great to be pardoned easily. But why did you think so before? Is it not because there was no definition in Euclid of proportion universal, and because he maketh no mention of proportion arithmetical, and because you had not in your minds a sufficient notion thereof yourselves to supply that defect? And is not this the cause also, why you put in this parenthesis (if arithmetical proportion ought to be called proportion)? Which is a confession that you know not whether there be such a thing as arithmetical proportion or not, notwithstanding that on all occasions you speak of arithmetical proportionals. Yes, this was it that made you think that proportion universally, and proportion geometrical, is the same, and yet to say you cannot tell whether they be the same or not. It is no wonder, therefore, if in such confusion of the understanding, you apprehend not that the proportions of two to five, and nine to twelve, are the same; so you are blinded by seeing that they are not the same proportions geometrical. Nor doth it help you that I say the difference is the proportion; for by difference you might, if you would, have understood the act of differing. At the second article you note for a fault in method, that _after I had used the words antecedent and consequent of a proportion in some of the precedent chapters, I define them afterwards_. I do not believe you say this against your knowledge, but that the eagerness of your malice made you oversee; therefore go back again to the third article of chapter II. where, having defined correlatives, I add these words, _of which the first is called the_ antecedent, _the second the_ consequent. This is but an oversight, though such as in me you would not have excused.