Article the sixteenth. Here we come to the controversy concerning the _angle of contact, which_, you say, _you have handled, in a special treatise published; and that you have clearly demonstrated, in your public lectures, that Peletarius was in the right. But that I agree not sufficiently, neither with Peletarius nor with Clavius._ I confess I agree not in all points with Peletarius, nor in all points with Clavius. It does not thence follow that I agree not with the truth. I am not, as you, of any faction, neither in geometry nor in politics. If I think that you, or Peletarius, or Clavius, or Euclid, have erred, or been too obscure, I see no cause for which I ought to dissemble it. And in this same question I am of opinion that Peletarius did not well in denying the _angle of contingence_ to be _an angle_. And that Clavius did not well to say, _the angle of a semicircle_ was less than _a right-lined right angle_. And that Euclid did not well to leave it so obscure what he meant by _inclination_ in the definition of a _plane angle_, seeing elsewhere he attributeth inclination only to acute angles; and scarce any man ever acknowledged inclination in a straight line, to any other line to which it was perpendicular. But you, in this question of what is inclination, though you pretend not to depart from Euclid, are, nevertheless, more obscure than he; and also are contrary to him. For Euclid by inclination meaneth the inclination of one line _to_ another; and you understand it of the inclination of one line _from_ another; which is not inclination, but declination. For you make two straight lines, when they lie one on another, to lie ἁκλινῶς, that is, without any inclination (because it serves your turn); not observing that it followeth thence, that inclination is a digression of one line _from_ another. This is in your first argument in the behalf of Peletarius (p. 10, l. 22), and destroys his opinion. For, according to Euclid, the greatest angle is the greatest inclination; and an angle equal to two right angles by this ἀκλισία, should not be the greatest inclination, as it is, but the least that can be. But if by the inclination of two lines, we understand that proceeding of them to a common point, which is caused by their generation, which, I believe, was Euclid’s meaning; then will the _angle of contact_ be no less an _angle_ than a _rectilineal_ angle, but only (as Clavius truly says it is) heterogeneous to it; and the doctrine of Clavius more conformable to Euclid than that of Peletarius. Besides, if it be granted you, that there is no inclination of the circumference to the tangent, yet it does not follow that their concourse doth not form some kind of angle; for Euclid defineth there but one of the kinds of a plane angle. And then you may as much in vain seek for the proportion of such angle to the angle of contact, as seek for the _focus_ or _parameter of the parabola of Dives and Lazarus_.