(nu) 
An Acc$mft of a fmafl TraSi ^ enthukd 
tHOM^ HOB BBS ^adratura Circuli^ CuhAtio Sfhdra^ Bu* 
flicatio Cuhi , (kcundoEdita j) Demo Re futata ^ Auth^ 
^O^. WALLIS. S. r. D. Geom, Prof. Saviltano. 
OxonUi 166^. 
Since Mr. Hc?^/^^ thought himfelf obliged to make Xome Re- 
ply to Dr Wallis's confutation of what he hadj not long fince, 
publifli'c upon this Argument 5 Dr, WalUs made no ftay at 
a l to recomthis Anfv^er and fecond refutation. Concerning 
which vteftiall give you a brief account , fuggefted by Dr. Wdl- 
lis himfelfj oiMr. j^^^fe'^ fundamental miftake in his late 
Quadrature of the Circle, referring the Reader to the Trad it- 
felffor theJF/^fW, which is therein the firft. 
Mr. Hi?^^;, confidering,That, in cafe it fliould A/i/'j^^'fifo luck- 
ily ( which was not neceffary) that C^Y ( the bafe of aright- 
angled Triangle Q^Y A equal totheSedor LC A 3 and confe- 
qaently the Square Q^R ST equal to the Circle B CDE,) 
fliould, by the Arch CL^ k cut juft in the midjl dt P then wouUy 
^otonlj ( which to his purpofe was neceffiry )^^P L , C P Y, 
he equal each to other (^h^ZdiM^^ of A L P Y common both to the 
Trivingle and the Sedor 5 ) hut more-over (which was not neceffa- ^ 
ry ) each of them equal to the half of P A V 5 ( luppofing C A V 
taken equal^by conftrudien , to L A P : ) all which is true ^ in cafe 
ofiucha lucky hap: 
And finding then (which is true alio ) that this couldmt All 
haffen^ unlefs that interfe&ion at P , were tnthe line A Q ( drawn 
from the Center A to the middle of C G^) Decaufe this muft needs 
pafs through the middle of QJf, 
Concluded , That it mu(l needs fo happen^or elfe it was imposfthle 
for Any right- angled Triangle ^ as (Vy A (like tOj and pare of 
G C A3 ) to be equ'd to the sector L C A o- h^czxxkjn any othsr, as 
q y A the interfe^ionof C La:3 J q y /J/p, muldmt iejufl in th^ 
midjl of q y s and therefore ( which he fuppofd neceflaryj but was 
not ) qp A notjull thehalfe of q y A. 
Not confideringC which is his fundamental miftake ) that^ if 
q pL and Ci^y he equal each to othrQthou^h neither of them be 
equal 
