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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1092, page id 1815201908:1149
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EX
ae
pert.
1092
CONOIDES ALEERBOLLENH.
Demonstratio.
Vm dux liyperbolae DPF, DTI ad
eandem diamecrum cranluersam DFF
consticurae sinc, ordinacim applicatxe vrius,
Ccilicee PF ad IF eandem racionem obci.
nenca cum ratione ordinacim applicatarum
alcerius FB ad PP. teela ex Cb Gab
L.li ad L. Li, candem rationem habeanc ex
constructione quam recta IF ad R F, ccram
ConstAED R K esse parabolam per ea quae li-
bro de parabola praem, Simus. Ouoniamioi-
cur eAt quadracum IF ad F F quadracum ve
circulusradii IF ad circulum radii F F. igi
cur veconoides IF ad F F conoides, ica est
conoides R F vna cum cono P F ad conoi.
des FI. vna cum cono FMI. Cs aurem prO.
policione praecedenci demonstrata aequali
casintor conoides L F _ conoides L F CuI
ConOM F. Igirur manifecta cA cciam ae qua-
licas conoidis hsperbolici IFi cum conoide
XF X ConO P F. Ouod erat deoaal.
dum.
2EOFCd222C CaCVE
Berop. 246.  Ht ellipsis ABC producens hyperbolam ED A, iuxta ca quae  libro
elliplis bero (pharoides C, Mlatigulum quoque AIE C produxerie
conum AIL C.
Dicoconoides hypet DOMCHM AD F. C. Xquale cAC sphaeroidi ABC (1-
mul Cum CONOAIF. C.
useur
C Colusicur
5. d16.
aachyperbolapraemilimus, e hy petoota conoides produxeric AD F.
RanEUE AB, CrUNE AB ex Contructione pro.
Demonstratio.
Vais ordinatim ad A C axem rectis D IBHE, po-
policionis lupra cicarx in libro de hyperbola aequa-
lis rectis D BFI, _ recta F C. aequalis axi AC. CAt
tienc ex ductu plattoru 1LB d HIL, in scipla. Ouare
CuseCuper quadratorum illorum laceribuscan.
aurem quadracum AB aequale quadcaris AII X BTI.
Tsicureciam quadeacum DHldem quadearis AIL, BHL
aequale eAt. led, quia A C, CF RQUANEUE, CrIRIM ATI,
TFI, adeoque s quadraca AFI, LFI RQUANEUF. CrgO
A quadrata D FI xouantur quadeatis IFF de BII Simul
Cumpris. Ouare superficies hrperbolica D FI dueta cii
e aequale corpus touaoe uns Magnicudinibus qua
quam radiis delcripti candem racionem incer le leruem Guam ipia Guaulala, eciam
der 129. dconoides exreuolucione superticiet ld Il aglabirur, ee sphaeroidi ABC e C91O
Paius. AIF. C. Duod tuir demonstrandum.
PRO.