Page:Philosophical Transactions - Volume 001.djvu/306

 quator cubis ; (pag. 43 line 33.) into these (p. 44. l. 5.) aqualia quator Lineis, nempe quadruplus recta : And would thence perswade you, that Mr. Rook had assigned a Solide, equal to a Line. But Mr. Rook's Demonstration was clear Mr. Hobse's Comment. Nor do I know any Mathematician (unless you take Mr. Hobs to be one) who thinks that a Line multiplyed by a Number will make a Square; (what ever Mr. Hobs is pleased to teach us.) But, That a Number multiplyed by a number, may make a Square Number; and, That a Line drawn into a Line may make a square Figure, Mr. Hobs (if he were, what he would be thought to be) might have known before now. Or. (if he had not before known it) he might have learned, (by what I shew him upon a like occasion, in my Hob. Heaut. pag. 142. 143. 144.) How to understand that language, without an Absurdity.

Just in the same manner he doth, in the next page, deal with Clavius. For having given us his words, pag. 45 l. 3. 4. Dico hans Lineam Perpendicularem extra circulum cadere (because neither intra Circulum nor in Peripheria;) He doth, when he would shew an errour, first make one, by falsifying his words, line 15. where instead of Lineam Perpendicularum, he substitutes Punctum A. As if Euclide or Clavius had denyed the Point A (the utmost point of the Radius,) to be in the Circumference, Or, as if Mr. Hobs, by proving the Point A, to be in the Circumference, had thereby proved, that the Perpendicular Tangent A E had also lyen in the Circumference of the Circle. But this is a Trade, which Mr. Hobs doth drive so often, as if he were as well faulty in his Morals, as in his Mathematicks.

The Quadrature of a Circle, which here he gives us, Chap.. 20. 21. 23. is one of those Twelve of his, which in my Hobbius Heauton-timorumenus (from pag. 104. to pag. 119) are already confuted: and is the Ninth in order (as I there rank them) which is particularly considered, pag. 106. 107. 108. I call it One, because he takes it so to be; though it might as well be called Two. For, as there, so here, it consisteth of Two branches which are both False; and each overthrow the other. For if the Arch of a Quadrant be equal to the ''Aggregate of the Semidiameter and of the Tangent of 30. Degrees, (as he would Here have it, in Chap. 20. and There, in the close of Prop. 27;) Then is it not equal to that Line, whose Square is equal to Ten squares of the Semiradius, (as, There he would have it, in Prop. 28. and, Here, in Chap. 23.) And if it be equal to This, then not to That''. For This and That, are not equal: As I then demonstrated; and need not now repeat it.

The grand Fault of his Demonstration (Chap. 30.) wherewith he would now New-vamp his old False quadrature; lyes in those words Page 40. line 30, 31. Quod Impossible est nisi ba transeat per c. which is no impossibility at all. For though he first bid us draw the Line R c, and afterwards the Line R d: Yet, Because he hath no where proved (nor is it true) that these two are the same Line; (that is, that the point d lyes in the Line R c, or that R c passeth through d:) His proving that R d cuts off from ab a Line equal B c, doth not prove, that ab passeth through c: For this it may well do, though ab lye under c (vid. in case d lye beyond the line R c, that is, further from A:) or though it lye above c, (vid. in case d be neerer, than R c, to the point A.) And therefore. unless he first prove (which he cannot do) that A d (a sixth part of A D) doth just reach to the line R a and no further; he onely proves Rh