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End is not Punctum, but only Signum (which he does allow non esse nonem Quanti) even this will serve our turn well enough, Euclid's Σημεῖον, which some Interpreters render by Signum, others have thought fit (with Tully) to call Punctum: But if Mr. Hobs like not that name, we will not contend about it. Let it be Punctum; or let it be Signum (or, if he please, he may call it Vexillum.) But then he is to remember, that this is only a Controversie in Grammar, not in Mathematicks: And his Book should have been intituled Contra Grammaticos, not, Contra Geometras. Nor is it Euclide, but Cicero, that is concern'd, in rendring the Greek Σημεῖον, by the Latine Punctum, not by Mr. Hobs's Signum. The Mathematician is equally content with either word.
What he saith here, Chap. 8. & 19. (and in his fifth Dial. p. 105. &c.) concerning the Angle of Contact; amounts but to thus much, That, by the Angle of Contact, he doth not mean either what Euclide calls an Angle, or any thing of that kind; (and therefore says nothing to the purpose of what was in controversie between Clavius and Peletarius, when he says, that An Angle of Contact hath some magnitude:) But, that by the Angle of Contact, he understands the Crookedness of the Arch; and in saying, the Angle of Contact hath some Magnitude, has meaning is, that the Arch of a Circle hath some crookedness, or, is a crooked line: and that, of equal Arches, That is the more crooked, whose chord is shortest: which I think none will deny; {for who ever doubted, but that a circular Arch is crooked, or, that, of such Arches, equal in length, That is the more crooked, whose ends by bowing are brought nearest together?) But, why the Crookedness of an Arch, should be called an Angle of Contact; I know no other reason, but, because Mr. Hobs loves to call that Chalk, which others call Cheese. Of this see my Hobbius Heuton-timorumenus, from pag. 88. to p. 100.
What he saith here of Rations or Proportions, and their Calculus; for 8. Chapters together, (Chap. 11. &c,) is but the same for substance, what he had formerly said in his 4th. Dialogue, and elsewhere. To which you may see a full Answer, in my Hobbius Heauton-tim. from pag. 49. to p. 88. which I need not here repeat.
Onely (as a Specimen of Mr. Hobs's Candour, in Falsifications) you may by the way observe, how he deals with a Demonstration of Mr. Rook's, in confutation of Mr. Hobs's Duplication of the Cube: Which when he had repeated, pag. 43. He doth then (that it might seem absurd) change those words, æquales
