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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 616, page id 1815201908:0673
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1
hu.
AXPPLVOLA
PROPOSTTIOCLXVI
Inc AB, B C axes duarum pataoclarum aequalium, angulum rectum
DC aquidistantes alymprocis.
Dico (patiADEF, FCD, CDH inter sC esse xqualia.
Demonstratio.
Emonstratum est quancirarem D P H
aduplam esequancicacis DP F. in suPer
octensum est quancicacem F C D duplam
esse DCFT. iBIEUT qUanEICAS DF F aqua
lis est quanticaci D CFI: ac proinde quo-
niam EDF vna cum DF C. duplum cAt
DOTI cric quoque D F F cum D FC du
Plum DF F. isicur sunc requales quancica-
OFI. Ouod Fuirdemonstrandum.
PROPOSAAIO CEXT
Dico spacia similiter xqual incerse qua residua lunc, nimirum
concinences, quae de asymprori linc hyperbolae P. FO: punctum au
cem D Cic illud in quo parabole conveniunc; ex quo demictaneur DB,
co
LF, DI
Iluem poltis:
EBAF, FAOF, OACFI.
Demonstratio.
LeNC COa ALB D F LL. MHIICeE AC DB conuexam duplam eAsC concau
AC DC A: sunc aurem ex hypocheli aquales parabolx AFDC, AC, DB, relidux
iBITU ABDF, AODC aequales quoque lunc: quia vero tam AFDB cum
AFDC A duplum eAt ACDC: ec rurtum ACDC cum AFDC A duplum
AFD B, CTCS QUAnCIEATCS ABDF, AFD G A, ACD C aequales sunc: Sed per pra
cedenrem xquales quoque lune P. F D, DF C, D IIC, residux igitur x quales lune
ABEF, AFC A AO HC. Ouoderac demonctrandum.
LROFOAILIO CEXVIII
E cet parabola BED, hyperbolam G F. HI Vt
Derius incer a(ymipeocos AB, BC consticuram
in E, _ ducta BD hyperbolam sccecin F, para-
bolam vero in D, ex D vero ducancur DO, DH
Parallelae alymproris.
Dico quancicarem mixeilincam DF F, ex pa-
rabolica, hyperbolica e recta constancem, dimi
dix parri ASuEX DCF. esse aqualem vel quarra
EguFA DEH.
Demonstratio.
Ibeo de parabola propo L. 257. ostensum est A F D C parabolam conuexam duplam
ExB enim e D ducacur parabola B FD ad axem BA.
uamculde Lt tittid ttu, LL Patallela a
CANEUT
So