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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 596, page id 1815201908:0653
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FI X PER B O L A.
supertciei DE O F, relinguar in ea
reliduum, minus daca Guancitare R.
Iubdinidacur in eguales parces pla-
nUm FGCFT per primam deci-
mis EocieS, VE FOL. I rclidua PaES,
minot GE quanticare R; eric illa pla.
nO FC FIC (reparec ex lubdinilio
ne per parres aquales Facta) com.
menfurabilis; planum igieur FOLI
quocies porest, auferacur ex plano
DE F C: Dicorclduum quancicatis
XEL IL. de. _ quid L C L. L commenturat quMateIM FCHC, (ve ex ciusdem subdivisione in
iussc daco K; erga quantitas FO P. I(gus minor est quancicasC K) icerum exresiduo
plani DF LC auterri poreric: ergo facta non est sublario; quories teri poruit; quod
rurlum contra suppolicum est. Reliduum ixicur it plano D P. P. C. relictum, minus est
quancitate K: quod erat demonstrandum.
lele almproco. Pratoaurem DF. G F incommensurabile sic planum
L C, C II.
quories suanctasLCL, concinee quanticarem F C, C. II.
Demonstratio.
P enim ica non licsigicurracio D R
ad FG, Caepius musciplicac ratio.
nem E C ad FTC, qua. D E FO
planum, conrinet planum FG HC,
vel contra: Siprimum, ponaturra
cio IK ad F C, cocies mulciplicans
eationem FO ad HI C, quories pla-
FnuMm DE PC concinec planum
F GFTC: minor ergo clt TAIo lR ad F C, b quam D E ad F C7; adeoque _ TK MI.
nOr D F. VIcerius dinidatur per aequales parres planum F G TI C, VE pars CiuSFLOM
Ce+ L.do. Plano Li Ci FY C commenlurabilis, cminor sE paree DEK I: cum FME ablacR ex
DE IR quocies porest, relinquaEParTEM D NOB: qua minor cA PAFECDF RI
adeoque NO linea cadicincer DB, IK: si enim D F. NO non minoc (E DBK l
sed illi aequalis, vel illamaior; Pocerit ex D E NO icerum auferri FOT P planum
quod minus est DF LK explano D F FC quod est contra suppostum. minorigi
cux eA quancitaS D F. NV O, Quancicare D E PK, et NVO lines eM inter DB, IK.
igicur rario NO ad F C maior est racione dFK ad F C. ac proinde rario NO ad
FC, magis mulciplicatrationem F C ad HI C, quam camdem mulciplicot racio
TR ad F C: gua VeM GcaeCa COMMMS est mensura planOruI FGHC.
i. NOF C. Commenturabilia Cune plana cFCFIC, adeoque cories inctciplicat racie
VO Le latoeM C ad HIC; quocies planum NOFC concinec planum
_ plg D EFC tories concinet planum FC FIC, quocies raric
ad F e uilciplicac rarionem FC ad TIC; Expius igicur planum NOF Ci COn
nec platuire F C. HC, quam D F. F. C. idem F C HC concinear. quod hieri nom po
celt
comi.
DE F C, plano K minus esse: S non, lsicue Fesiduum vel aequale; vel maius cst pla-
n0 K. H a quale; et O LL quanas commenturabilis est quancieati DL FG.
conttrucione Facta coneat, paeus  DF. F. C commensurabile a est plano
FOFIC: quod est concra liypochesim. lam vero reliduum ex D E C P relictum; ma-
PROPOSITIO CXXIX
VInE AB, BC alympeoci hyperbole DFHI, _ DF, FC, FIC paral.
Dicorationem DE. ad FC, cories muleiplicare rationem PC, 2d LIC,
deet ele
menra.
id.
stis
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