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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 635, page id 1815201908:0692
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P.
Egn
Cucr.
etam
ratio.
Faeio
etan
ulum
equa
TL aC
TC
CD
1C.
ilum
ent
ol.
EIZ P E K BOL A.
PROPOSTTTO CZCI
Onsticuane AB, A C quemuis a, a Per alum peunteo pun-
ctum L ducantur BC, rectis aurem b, DB, a Guaies Hatsc, LC.
Dico Dtif fole ad eandem hyperbolat culus alimpeotine Ab
DC A Ors 17loHtIsia Lco
Demonstratio.
it 3eBA LL es A 9nB OWp e
L. 23911
a  DD C. 7 24
oetesque rait houp Rescovios 
Ct A.et ee daarit sil
123 1232FL
133B B0nC). 6033199029 5 c
ei D et eiBuBorI 0ba, F De
1epe 3p HL D. VZ.L 2111
Oisdenstucs an rualiin
itc
it 90C
tans seel sup ECE A eishit. is. Buberiq ropcrirr ca3e
133iB serit C A ecEt A eri seaRHL B ect aH∞lOc1. 9. 7d 5CVZ
Ehionraliiis Is. huius rect ats quatheumiquo scaioni Ayperbolicx Occnrteni
cem incer alympeocos consticuram, Equales lui parres habere Comlcituras incoe
alymxeoeos et sectionem, hoc est si recta BC secer hypervolam in D e F, rectas
BD, FC aquales CAC InEeF (C3 IGIEUE A INECF AIYMPEOLOS ALB, H C Per panictum
E descripta ponacurhyperbola, quamcum que per F. duxeris rectam BFC, necel
larium est ve BG Gc aequalis, C E isicur cutu ac praxi v sirgus, reltac ve D L. L PCt
cineac ad eandem hyperbolam.
5. l31
onprciit
aulisosgcar epir OlpcOg8 I XI OBLOXCVISSau ovis
Inex AB, CD occurrane sibi mumo ad angulos rectos in B, et al-
ceri illarum ponantur x quidistantes F. C. 2 sumpro denique quo-
vispuncto C, in recta C B, ductisque CF, hancrectis CF xquales
Dico LL, GC esschyperbolas, de quidem oppolicas.
Demonstratio.
S ronnehibir
tl l
CPonatur eidem equidistances C L quoniam
quadracum CE aequale eA quadratis FB, BC;
eciam FC quadratum ijidem requabicur. CA
aucem, tiC quadrarum xqualc quadraco fFI,
vna cum rectansulo L H C, cum (ncF F xqua-
les FC: igicurcum FHI quadearum aquale sE
BC quadraco, criam rectangulum P FIC qua-
draco F B, hoc est C: I xequale exister exic igitur
rectangulum R HIC HOc cM DIC ad DIC;
rectangulum ve F B quadrarum ad F B quadrq.
cum hoc est ve CI, quadrarum ad quadrarum
GL. quare F F, C C hyperbolae sune e quidem
oPPORCR. Duod demonctrandum tuir.
et 3
DOnatur CH quae aequidistet AB, Iem ex
TM 1. serBeMid  A SC
e
e rritue
17
111
1
11
1I
MH. H II. BI