After your dejection I shall comfort you a little, a very little, with this, that whereas this eighteenth chapter containeth two problems, one, “_the finding of a straight line equal to the crooked line of a semi-parabola_;” the other, “_the finding of straight lines equal to the crooked lines of the parabolasters, in the table of the third article of the seventeenth chapter_;” you have truly demonstrated that they are both false; and another hath also demonstrated the same another way. Nevertheless, the fault was not in my method, but in a mistake of one line for another and such as was not hard to correct; and is now so corrected in the English as you shall not be able (if you can sufficiently imagine motions) to reprehend. The fault was this, that in the triangles which have the same base and altitude with the parabola and parabolaster, I take for designation of the mean uniform impetus, a mean proportional, in the first figure, between the whole diameter and its half, and, in the second figure, a mean proportional between the whole diameter and its third part; which was manifestly false, and contrary to what I had shown in the sixteenth chapter. Whereas I ought to have taken the half of the base, as now I have done, and thereby exhibited the straight lines equal to those crooked lines, as I undertook to do. Which error therefore proceeded not from want of skill, but from want of care; and what I promised (as bold as you say the promise was), I have now performed. The rest of your exceptions to this chapter, are to these words in the end: “_There be some that say, that though there be equality between a straight and crooked line, yet now, they say, after the fall of Adam, it cannot be found without the especial help of divine grace_.” And you say you think there be none that say so. I am not bound to tell you who they are. Nevertheless, that other men may see the spirit of an ambitious part of the clergy, I will tell you where I read it. It is in the _Prolegomena_ of Lalovera, a Jesuit, to his Quadrature of the Circle, p. 13 and 14, in these words: “_Quamvis circuli tetragonismus sit_ φύσει _possibilis, an tamen etiam_ πρός ἡμᾶς, _hoc est, post Adæ lapsum homo ejus scientiam absque speciali divinæ gratiæ auxilio, possit comparare, jure merito inquirunt theologi, pronunciantque; hanc veritatem tanta esse caligine involutam ut illam videre nemo possit, nisi ignorantiæ ex primi parentis prævaricatione propagatas tenebras indebitus divinæ lucis radius dissipet; quod verissimum esse sentio_.” Wherein I observed that he, supposing he had found that quadrature, would have us believe it was not by the ordinary and natural help of God (whereby one man reasoneth, judgeth and remembereth better than another), but by a special (which must be a supernatural) help of God, that he hath given to him of the order of Jesus above others that have attempted the same in vain. Insinuating thereby, as handsomely as he could, a special love of God