His demonstration of _Chap._ 23. (where he would prove, that _the aggregate of the Radius and of the Tangent of 30. Degrees_ is equal to _a Line, whose square is equal to 10 Squares of the Semiradius_;) is confuted not only by me, (in the place forecited, where this is proved to be impossible;) but by himself also, in this same Chap. _pag._ 59. (where he proves sufficiently and doth confesse, that this demonstration, and the 47. _Prop._ of the first of _Euclide_, cannot be both true.) But, (which is worst of all;) whether _Euclid's_ Proposition be False or True, his demonstration must needs be False. for he is in this Dilemma: If that Proposition be _True_, his demonstration is _False_, for he grants that they cannot be both True, _page_ 59 _line_ 21. 22. And again, if that Proposition be False, his Demonstration is so too; for _This_ depends upon _That_, _page_ 55. _line_ 22. and therefore must fall with it. But the Fault is obvious in _His Demonstration_ (not in _Euclid's Proposition_:) the grand Fault of it (though there are more) lyes in those words, _page_ 56. _line_ 26. _Erit ergo M O minus quam M R_ Where, instead of _minus_, he should have said _majus_. And when he hath mended that Error, he will find, that the _major_ in _page_ 56. _line penult_, will very well agree with _majorem_ in _page_ 57. _line_ 4 (where the _Printer_ hath already mended the Fault to his hand) and then the _Falsum ergo_ will vanish. His Section of an Angle _in ratione data_, _Chap._ 22 hath no other foundation, than his supposed _Quadrature_ of _Chap._ 20. And therefore, that being false, this must fall with it. It is just the same with that of his 6. Dialogue, _Prop._ 46. which (besides that it wants a foundation) how absurd it is, I have already shewed, in my _Hobbius Heauton-timor._ _page_ 119. 120. His _Appendix_, wherein he undertakes to shew a Method of finding _any number of mean Proportionals, between two Lines given_: Depends upon the supposed Truth of his 22. Chapter; about _Dividing an Arch in any proportion given_: (As himself professeth: and as is evident by the Construction; which supposeth such a Section.) And therefore, that failing, this falls with it. And yet this is other wise faulty, though _that_ should be supposed True. For, In the first Demonstration; _page_ 67. _line_ 12. _Producta L f incidet in I_; is not proved, nor doth it follow from his _Quoniam igitur_. In the second Demonstration; _page_ 68. _line_ 34. 35. _Recta L f incidit in x_; is not proved; nor doth it follow from his _Quare_.