( 2244) 
felf (as the Mathematicians do) with fuppofed Infinites • For his 
Infinites, and more than Infi iitej of Years, Days, and Hours, 
already pafi, muft be Real Infinities^ and which have aSlually ex- 
iJted^znA whereof the lafl is given > (and yet there are more to 
foliowOMr.H^j^^flialldowelliYforhisExercile) to folve ihefe^ 
before he propofe more ^icere^s of Infinites. And this I fay, to 
fliewthatMr.A?o^/is, as much as any, concerned to folve the 
^cere's by himfelf propofed. 
In the latter part of lis firjl Paper, 
« 
HE givesus(outofhis2l<?/J^.l'r<?yB?.5.)this Mtemipt oi Squaring 
the Circle^ suppofe DT be 7DC5 and DR a mean proportional 
htweenDC andDTx the Semidian^eter DC tvill be equal to the 
^adrantal Arc KS.andDfvto TV» 
That the thmg is faife^is already fliewed in the Latin Confu-* 
tationof his publifliedia thQ PbilofophicalTranJaff ions 
for>/7laftpaft. 
As it is nowintheEnglifbs his Demonftration is peccant in 
thefe words3Cf<?/.2.//>i.3 1332,33.) Therefore— the Arc on TV, 
the Arc on KS:, the Arc on C\ cannot be in continual proportion 
(with all that follows J There being no ground for (uch Confe- 
quence. 
And the thing is manifeft * 5 for fince that^by his conftruftion, 
DC.CA.Arc on CA extended-i^^are V« the fame cantinual pro* 
DR. RS. Arc on RS extended TrS/^^mow 3 (?f the Semidiameter 
DXTV.ArconTV extended-H- ^^adrantal Arc - 
Let that proportion be whatym tvill 5 fuppofe, as 
*SttTaku I to 2 5 and confequently^DC to CA being as i to 2, 
it will be to the Arc on C A^as i to 4 ; And by the 
fame rea{on,DR to the Arc on RS5 and DT to the Arc on TV, 
muft alfo be as I to 4 : And therefore the Arcs on TV, on RS, 
onCA, thatis34DT,4DR34 DC^ will be in the fame pro* 
portion to one another, as (their fingles) DT,DR,DC : But 
thefe (by conftrucStion) are in continual proportion 5 there- 
fore thofe Arcs alfo,as they ought to be. lDdeed,if (by chang- 
ing fome one of the terms) you deftroy (contrary to the Hy- 
pothefis) the continual proportion of DT^DRjDCjyou will de* 
ftroy chat of the Arcs alfo (which are ftill proportional to 
thefe ; ) but fo long as DT, DR^ DC; be in any continual pro- 
portion j 
