In like manner, When _Euclide_ and others do make the _Terme_ or _End_ of a Line, a _Point_: If this _Point_ have _Parts_ or _Greatness_, then not the _Point_, but the _Outer-Half_ of this Point ends the Line, (for, that the _Inner-Half_ of that Point is not at the End, is manifest, because the _Outer-Half_ is beyond it:) And again, if that _Outer Half_ have _Parts_ also; not this, but the _Outer_ part of it, and again the _Outer part_ of that _Outer part_, (and so in _infinitum_.) So that, as long as _Any thing of Line_ remains, we are not yet at the _End_: And consequently, if we must have passed the _whole Length_, before we be at the _End_; then that _End_ (or _Punctum terminans_) has _nothing of Length_; (for, when the _whole Length_ is past, there is nothing of it left.) And if Mr. _Hobs_ tells us (as _pag._ 3.) that this {292} _End_ is not _Punctum_, but only _Signum_ (which he does allow _non esse nomen Quanti_) even _this_ will serve our turn well enough. _Euclid_'s [Greek: Semeion], 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 intitled _Contra Grammaticos_, not, _Contra Geometras_. Nor is it _Euclide_, but _Cicero_, that is concern'd, in rendring the Greek [Greek: Semeion] 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_, his 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 Heauton-timorumenus_, from _pag._ 88. to p. 100.