(%9i) 
that a fixth part of ab is eq haI to the Line of B c. Put, whether it lye above it , 
or below it, ov (as W. Hobs would have it) juft upon it • this argument doth 
not conclude. (And therefore Hugemus's affertion, which Mr Hobs, Chap, 
2 1 . would here give way to this Demonftration, doth , notwithftanding this, 
remain fafe enough. ) 
His demonftracion of Chap 2$ . ( where he would prove, that fie Aggregate 
of the Radius and of the T angent of 3 c* Degrees is equal to a LinejvhoJe fquare 
is equal to 1 o Squares of the Semiradius •, ) is confuted not only by me, ( in the 
place forecitedj where this is proved to be impoffible but by himfelf alfo, 
in this fame Chap .pag^g (where he proves Efficiently and doth confeiTe,that 
this demonftracion, andrthe 4-?. Prop. of the (* rft of Euclide, cannot be both 
true. ) But, ( which is worft of ail •,) whether Euclid's Proportion be Falfe or 
True, his demonftration muft reeds be Falfe. lor he is in this Dilemma: if 
that Proportion be T rue, his demonftration is Falfe fo he grants that they 
cannot be both True, page 59 line 21. 22. And again, if that Propofition be 
Falfe, his Demonftration is fo roo ■, for This depends upon T^f, ss* line 
22 and therefore muft fail with it. 
But the Fault is obvious in His DemonflratUn (not in Euclid's Propofition :) 
The grand Fault of it ( though there are more ) lyes in thofe words, page 5 6. 
line 2 6 . Erit ergo M 0 tninui quam M R Where,mftead of minus, he fhould 
have faid majus. And when he hath mended that Error j he will find, that ihe 
major in page 5 6 . line penult , will very well agree with majorem in page 57. 
line t (where the Printer hath already mended the Fault to his hand) and then 
the Falfum ergo will V3nfh 
His SedLon of an Angle in rations data ; Chap » 22 hath no other founda- 
tion, than his fappofed Quadrature of Chap « 20. And therefore, that being 
falfe • this muft fall with it. It is juft the fame with that of his 6 , Dialogue. 
Prop 4d. which ( befides that it wants a foundation) howabfurd it ‘is, shave 
llready fhewed *, in my Hobbius Htantsn timer, page 1 19.1 ?Q. 
H \s Appendix, wherein he undertakes to fhew a Method of finding^ 
number of mean Proportionals, between two Lines given : Depends upon the 
fuppofed Truth of his 22. Chapter • about Dividing an Arch in any proportion 
given : ( As himfelf profefTeth .* and as is evident by the Conftru&ion • which 
fuppofeth fuch a Se&ion. ) And therefore, that failing, this falls with it. 
Andyet this isotherwife faulty .though tbit fhould be fuppofed True For, 
In the firft Demonftration ^ page 67 line 1 2, ProJuBa Ef inride tin I, is 
not proved • nor doth it follow from his Qmniam igitur. 
Inthefecond Demonftration} page 68 line $4 55 • Retta Lfinciditin x $ 
is not proved •, nor doth it follow from his Q^are. 
In his third Demonftration • page 7 1 • l *te 7. PrcduBd Y P tranftbit per 
M i is faid gratis ; nor is any proof offered for it. And fo this whole ftruc- 
ture falls to the ground. And with ill, the Prop. 47. El 1 doth ftill ftd&df&ft 
(wh ; ch he tells us, page 59, 6 r, 78. mull h tve fallen if his Dimonft rations 
had ftood : ) And fo, Geometry and Arthemeti ^do ftill agree, which (he tells 
us, page 78 : line ro. ) had otherwife been at odd‘. 
A nd this ( though much more might have been faid, ) is as much as need to 
be faid againft chat Piece 
— - 
Primed with Licence for J.bn Martyn , and James Atttfjtrj , 
— A— Printeis to the Pvoval .Society. 
