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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 794, page id 1815201908:0851
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# Lines: 39 recognised, mean confidence 0.84
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794
LHCF. _Gua. Gat Pa L i Ce aGua L+ Plano aleto i dd.
cirudinem HIC hoc eA AD. Ouod erac demonstrandum.
PROPOSILLO+ C +L
alica, Comane ade acetelle aguartu porcasion
ordinacim, luperaxe Ci fLve diametro circulus delebaut. L, gul lo-
cus cader incra parabolas vepatee cx 126. parabolx.
Dico AB parabolam ductam in varabolam B C. Xqualem este semicy-
lindro cuiusbalis sericirculus FB es alricudo CHnilu nunbeu
. R ctmE .M e ei
DVCEYS PLANI
vertionem rationis EC est ad BF VE FTF ad TE, rectangula igitur FFOH
ABEanE AB, B C parabo lX aequales re similes ee sicu Tub alcernio po-
emonstralio.
AEXCoN-
ver sa 300.
prab.
669. 2
sireulis
Omplerectaneulum BK, BL Auque insinritis AEBDCK, iunec pun:
1ell. 115. 5 1C
ata GF, TIF; IID. Duoniam CHI axis parabolarum aqualium AB.
BC, laceri recto xqualis est, lineis OF a xquales sunc AB, e lincis ITD, id
eAt lineis ITF aequales BC. rectangula igieur AB C aequalia sune rectangulis
SFHI id Cs b GFI, FB. ICa Teclangara CILFB aGuaM TectanSIS LLR
cum enim EFC axis parabolarum se requalis laceri recto, IIB est xqualiS ipA CR.
igitur AB ductain B C. parabolam, producicorpus, xequalcilli quodhe ex ductu
plani FB in planum BK, hoc eAt lemicylindro cuius basis est semicirculus FB al.
cirudo CK, hoc eA C. FI. Quoderac demonstrandum.
le sc aato aecaltua dc um patabolarum lubalterne poluca-
rum, lateriluo recto aequalis: delcriproque luper AC ve diametro,
circulo L. AK, qui rorus inera parabolas cader, ponantur ex A e D, ordi-
narim ad AD axem linCX A F, DC.
Dicogualuaecolat L.B alctamnlc, Corpus ploaucere aqualc.
cubo cuiusbalis est quadrarum lineae AD, una cum cylindro cuius balIs
est circulus L. AK, e alrirudo AD.
hoc eKtrectis BK. ergo rectangula AB C aequantur rectangulis F BR. parabola
mon-
PROPOSTTTO CXLIN.