Again, you would prove the angle of contact, if it be an angle, to be of the same kind with a rectilineal angle, out of Euclid (III. 16); where he says, _it is less than any acute angle_. And it follows well, that if it be an angle, and less than any rectilineal angle, it is also of the same kind with it. But, to my understanding, Euclid meant no more, but that it was neither greater nor equal; which is as truly said of heterogeneous, as of homogeneous quantities. If he meant otherwise, he confirms the opinion of Clavius against you, or makes the quantity of an angle to be a superficies, and indefinite. But I wonder how you dare venture to determine whether two quantities be homogeneous or not, without some definition of homogeneous (which is a hard word), that men may understand what it meaneth. In your eighth chapter you have nothing but Sir H. Savile’s authority, who had not then resolved what to hold; but esteeming the angle of contact, first, as others falsely did, by the superficies that lies between the tangent and the arch, makes the angle of contact and a rectilineal angle homogeneous; and afterwards, because no multiplication of the angle of contact can make it equal to the least rectilineal angle, with great ingenuity returneth to his former uncertainty. In your ninth and tenth chapters you prove with much ado, that the angles of like segments are equal; as if that might not have been taken gratis by Peletarius, without demonstration. And yet your argument, contained in the ninth chapter, is not a demonstration, but a conjectural discourse upon the word _similitude_. And in the eleventh chapter, wherein you answer to an objection, which might be made to your argument in the precedent page, taken from the parallelism of two concentric circles, though objection be of no moment, yet you have in the same treatise of yours that which is much more foolish, which is this, (p. 38, l. 12): “_Non enim magnitudo anguli_,” _&c._ _“_The_ magnitude of an angle is not to be estimated by that straddling of the legs, which it hath without the point of concourse, but by that straddling which it hath in the point of the concourse itself._” I pray you tell me what straddling there is of two coincident points, especially such points as you say are nothing? When did you ever see two nothings straddle?