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._ 20.) wherewith he would now
New vamp his old false quadrature, lyes in those Words _Page_ 49. _line_
30, 31. _Quod Impossibile 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 to the Sine of R 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_:) And therefore, unless he first prove (which he cannot do) that _A c_
( a sixth part of _A D_) doth just reach to the line _R c_ and no further,
he only proves {294} that a sixth part of _ab_ is _equal_ to the Sine of
_B c_. But, whether it _lye above it_, or _below_ it, or (as Mr. _Hobs_
would have it) just _upon_ it; this argument doth not conclude. (And
therefore _Hugenius's_ assertion, which Mr. _Hobs_, _Chap._ 21. would have
give way to this Demonstration, doth, notwithstanding this, remain safe
enough.)

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 tha