My thirteenth article you say is ridiculous. But why? “_The impetus last acquired cannot_” you say, “_be equal to a time_.” But the quantity of the impetus may be equal to the quantity of a time, seeing they are both measured by line. And when they are measured by the same described line, each of their quantities is equal to that same line, and consequently to one another. But when I meet with this kind of objection again, since I have so often already shown it to be frivolous, and no less to be objected against all the ancients that ever demonstrated any thing by motion, than against me, I purpose to neglect it. Secondly, you object “_that motion uniformly accelerated does no more determine swiftness, than motion uniform_.” True; you needed not have used sixteen lines to set down that. But suppose I add, as I do, so as the last acquired impetus be equal to the time. _But that_, you say, _is not sense_; which is the objection I am to neglect. But, you say again, supposing it sense, this limitation helps me nothing. Why? _Because_, you say, _a parabola may be described upon a base given, and yet have any altitude, or any diameter one will_. Who doubts it? But how follows it from thence, that when a parabolical line is described by two motions, one uniform, the other uniformly accelerated from rest, that the determining of the base does not also determine the whole parabola? But fifthly, you say, _that this equality of the impetus to the time does not determine the base_. Why not? _Because_, you say, _it is an error proceeding from this, that I understand not what is_ ratio subduplicata. I looked for this. I have shown and inculcated sufficiently before, but the error is on your side; and therefore must tell you, that this objection, and also a great part of the rest of your errors in geometry, proceedeth from this, that you know not what proportion is. But see how wisely you argue about this duplication of proportion. For thus you say _verbatim_. “_Stay a little. What proportion has duplicate proportion to single proportion? Is it always the same? I think not for example, duplicate proportion_ (4)/(1) = (2 in 2)/(1 in 1) _is double to the single_ (2)/(1). _Duplicate proportion_ (9)/(1) = (3 in 3)/(1 in 1) _is triple to its single_ (3)/(1).” Let any man, even of them that are most ready in your symbols, say in your behalf (if he be not ashamed) that the proportion of nine to one is triple to the proportion of three to one, as you do. In the fourteenth, fifteenth, and sixteenth articles, you bid me repeat your objections to the thirteenth. I have done it; and find that what you have objected to the thirteenth, may as well be objected to these; and consequently, that my answer there will also serve me here. Therefore, if you can endure it, read the same answer over again.