part _subtriplicate_ of the whole, with intention (as in this case) to make them pass for words of signification different from the _half_ and the _third part_. Besides, from my definition of proportion (which is clear, and easy to be understood by all men, but such as have read the geometry of others unluckily) I can demonstrate the same evidently and briefly thus. My definition is this, _proportion is the quantity of one magnitude taken comparatively to another_. Let there be therefore three quantities, 1, 2, 4, in continual proportion. Seeing therefore the quantity of four in respect of one, is twice as great as the quantity of the same four in respect of 2, it followeth manifestly that the quantity of 1 in respect of 4, is twice as little as the quantity of the same 1 in respect of 2; and consequently the quantity of 1 in respect of 2, is twice as great as the quantity of the same 1 in respect of 4; which is the thing I maintain in this question. Would not a man that employs his time at bowls, choose rather to have the advantage given him of three in nine, than of one in nine? And why, but that three is a greater quantity in respect of nine, than is one? Which is as much as to say, three to nine hath a greater proportion than one to nine; as is demonstrated by Euclid, El. v. prop. 8. Is it not therefore (you that profess mathematics, and theology, and practise the depression of the truth in both) well owled of you, to teach the contrary? But where you say “_that the point K_ (in the second figure of the table belonging to this sixteenth chapter) _is not in the parabolical line whose diameter is A B, and base B I, but in the parabolical line of the complement of my semiparabola_ (_as I may learn from the twenty-third proposition of your_ Arithmetica Infinitorum) _whose diameter is A C, and base I C_.” What line is that? Is it the same line with that of my semiparabola, or not the same? If the same, why find you fault? If not the same, you ought to have made a semiparabola on the diameter A C, and base I C, and following my construction made it appear that K is not in the line wherein I say it is; which you have not done, nor could do.