Page:Philosophical Transactions - Volume 001.djvu/304

 Touch the Circle, it may with in In-side at another place Cut it, &c.) But I should sooner take this to be a confutation of his Quadratures, than a Demonstration of the Breadth of a (Mathematical) line. Of which, see my Hobbius Heauton-timorumenus, from pag.. 114. to p. 119.

And what he now Adds, being to this purpose; That though Euclid's Σημογ, which we translate, a Point, be not indeed Nomen Quanti; yet cannot this be actually represented by any thing, but what will have some Magnitude; nor can a Painter, no not Apelles himself; draw a Line so small, but that it will have some Breadth; nor can Thread be spun so Fine, but that it will have some Bigness; (pag. 2, 3, 19, 21.) is nothing to the Business; For Euclide doth not speak either of such Points, or of such Lines.

He should rather have considered of his own Expedience. pag. 11. That, when one of his (broad) Lines, passing through one of his (great) Points, is supposed to cut another Line proposed, into two equal parts; we are to understand, the Middle of the breadth of that Line, passing through the middle of that Point, to distinguish the Line given into two equal parts, And he should then have considered further, that Euclide, by a Line, means no more than what Mr. Hobs would call the middle of the breadth of his; and Euclide's Point, is but the Middle of Mr. Hob's. And then, for the same reason, that Mr. Hobbs Middle must be said to have no Magnitude; (For else, not the whole Middle, but the Middle of the Middle will be in the Middle; And, the Whole will not be equal to its Two Halves; but Bigger than Both, by so much as the Middle comes to:) Euclide's Lines must as well be said to have no Breadth; and his Points no Bigness.

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 Rh