greater nor less, then it is equal. But it is neither greater nor less. Therefore, &c. If it be greater, say by how much. By so much. It is not greater by so much. Therefore it is not greater. If it be less, say how much, &c._ Which being good demonstrations are together with mine overthrown by the nothingness of your _point_, or rather of your understanding; upon which you nevertheless have the vanity of advising me what to do, if I demonstrate the same again; meaning I should come to your false, impossible, and absurd method of _Arithmetica Infinitorum_, worthy to be gilded, I do not mean with gold. And for your question, why I set the base of my figure upwards, you may be sure it was not because I was afraid to say, that the proportions of the ordinate lines beginning at the vertex were triplicate, or otherwise multiplicate of the proportions of the intercepted parts of the diameter. For I never doubted to call double duplicate, nor triple triplicate, &c., or if I had, I should have avoided it afterwards at the tenth article of the same chapter. But because when I went about to compare the proportions of the ordinate lines with those of their contiguous diameters, the first thing I considered in them was in what manner the base grew less and less till it vanished into a point. And though the base had been placed below, it had not therefore required any change in the demonstration. But I was the more apt to place the base uppermost, because the motion began at the base, and ended at the vertex. To proceed which way I pleased was in my own choice; and it is of grace that I give you any account of it at all. To the third article, together with its table, you say, “_it falls in the ruin of the second; and that the same is to be understood of the sixth, seventh, eighth, and ninth_.” For confutation whereof I need to say no more, but that they all stand good by the confutation of your objections to the second.