t 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_.

In his third Demonstration; _page_ 71: _line_ 7. _Producta _Y P_ transibit
per _M_;_ is said _gratis_; nor is any proof offered for it. And so this
whole structure falls to the ground. And withall, the _Prop._ 47. _El._ 1
doth still stand fast (which he tells us, _page_ 59, 61, 78. must have
Fallen, if his Demonstrations had stood:) And so, _Geometry_ and
_Arithmetick_ do still agree, which (he tells us, _page_ 78: _line_ 10.)
had otherwise been at odds.

And this (though much more might have been said,) is as much as need to be
said against that Piece.

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