To the eleventh, you say first, you have done it better at the sixty-fourth article of your _Arithmetica Infinitorum_. But what you have done there, shall be examined when I come to the defence of my next chapter. And whereas I direct the reader for the finding of the proportions of the complements of those figures to the figures themselves, to the table of art. 3, Chap, XVII., you say that if the increase of the _spaces_, were to the increase of the times, as one to two, then the complement should be to the parallelogram as one to three, and say you find not (1)/(3) in the table. Did you not see that the table is only of those figures which are described by the concourse of a motion uniform with a motion accelerated? You had no reason therefore to look for (1)/(3) in that table; for your case is of motion uniform concurring with motion retarded, because you make not the proportions of the spaces to the proportions of the times as two to one, but the contrary; so that your objection ariseth from want of observing what you read. But I “_may learn_” you say, “_these, and greater matters than these, in your twenty-third and sixty-fourth propositions of your_ Arithmetica Infinitorum.” This, which you say here is a great absurdity; but if you mean I shall find greater there, I will not say against you. This (1)/(3) you looked for, belongs to the complements of the figures calculated in that table; which because you are not able to find out of yourselves, I will direct you to them. Your case is of (1)/(3) for the complement of a parabola. Take the denominator of the fraction which belongs to the parabola, namely three, and for numerator take the numerator of the fraction which belongs to the triangle, namely one, and you have the fraction sought. And in like manner for the complement of any other figure. As, for example, of the second parabolaster, whose fraction hath for denominator five, take the numerator of the fraction of the same triangle which is one, and you have (1)/(3) for the fraction sought for; and so of the rest, taking always one for the numerator. The twelfth article, which you say is miserably false, I have left standing unaltered. For not comprehending the sense of the proposition, you make a figure of your own, and fight against your own fancied motions, different from mine. Other geometricians that understand the construction better, find no fault. And if you had in your own fifth figure drawn a line through N parallel to A E, and upon that line supposed your accelerated motion, you would quickly have seen that in the time A E, the body moved from rest in A, would have fallen short of the diagonal A D; and that all your extravagant pursuing of your own mistake had been absurd.