To this I answer, not willingly, but in service to the truth, that, by the same argument, he might as well prove that God had a beginning. Thus, in case he had not, there must have passed an infinite length of time before Mr. Hobbes was born; but there hath passed at this day more than that infinite length, by eighty-four years. And this day, which is the last, is given. If this be an absurdity, have we not then an argument in nature to prove that God had a beginning? Thus it is when men entangle themselves in a dispute of that which they cannot comprehend. But, perhaps, he looks for a solution of his argument to prove that there is somewhat greater than infinite; which I shall do so far as to show it is not concluding. If from this day backwards to eternity be more than infinite, and from Mr. Hobbes his birth backwards to the same eternity be infinite, then take away from this day backwards to the time of Adam, which is more than from this day to Mr. Hobbes his birth, then that which remains backwards must be less than infinite. All this arguing of infinites is but the ambition of school-boys. TO THE LATTER PART OF THE FIRST PAPER. There is no doubt if we give what proportion we will of the radius to the arc, but that the arc upon that arc will have the same proportion. But that is nothing to my demonstration. He knows it, and wrongs the Royal Society in presuming they cannot find the impertinence of it. My proof is this: that if the arc on T V, and the arc R S, and the straight line C D, be not equal, then the arc on T V, the arc on R S, and the arc on C A, cannot be proportional; which is manifest by supposing in D C a less than the said D C, but equal to R S, and another straight line, less than R S, equal to the arc on T V; and anybody may examine it by himself. I have been asked by some that think themselves logicians, why I proceeded upon ⅖ rather than any other part of the radius. The reason I had for it was, that, long ago, some Arabians had determined, that a straight line, whose square is equal to 10 squares of half the radius, is equal to a quarter of the perimeter; but their demonstrations are lost. From that equality it follows, that the third proportional to the quadrant and radius, must be a mean proportional between the radius and ⅖ of the same. But, my answer to the logicians was, that, though I took any part of the radius to proceed on, and lighted on the truth by chance, the truth itself would appear by the absurdity arising from the denial of it. And this is it that Aristotle means, where he distinguishes between a direct demonstration and a demonstration leading to an absurdity. Hence it appears that Dr. Wallis’s objections to my _Rosetum_ are invalid as built upon roots. TO THE SECOND PAPER.