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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1001, page id 1815201908:1058
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.87
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V N CYLA CYELNDRTCA
sed rectangulum C OM L ad rectanGUIUM LOTR, habCE FaTIONCM COmPOTILAMI
ex CO ad F O, X CX raTIONC ML ad TH. Igicur eriam superticies rngulares il
dis rectangutis aquales ex ijdem racionibus lunc composicxe. Ouod crat demonstran-
dums
P ROP OSITIO LX.
YNoula cuius alcirudo par diametro baleos;
Secetur plano FOHIL quod axiaquidistet
e recta AN. exhibens communem interlectio-
nem cum bali ellipeica AHI C rectam III, e Per
H1 planum ponacur HI LK quod basi AB N x-
quidistet.
Dico eodem excessu superare superticiem cy.
lindricam BOFIK superficiem rectaguliFOII
quo superticies rectanguli LHIL. excedir ongula-
rem HIKC.
Demonstratio.
Scentum esta superticiem vngularem BOFTC X
qualem esse rectangulo ANM D, hoc est quoniam
alcicudo ingulae ponicur par diamerro AN, rectangulo FC: L. Igitur Arictimeri-
ce proportionales lune superticies B CFFTK, rectangulum FOFT, rectadgulum IFTL,
ee lupersicies FIKC. Ouod crac demonstrandum.
P ROP OS I FIO IL. XI.
Vbcendant AB, BC aequales ar-
 cusin balirngulari ABL.5 d se
cundum rectas AB, BC ducanuE
Plana ABF, BF. F C, quarum com
munes incerlectiones cum ba(I ClII
prica A E. D L SINE ReCtE AF, FF; e
secundum has lineas plana ponaneur
duxe rocca sinc ad plana ABF, BF FC
exhibentia communes lectiones cum
Superticie rnoulari cylindrica arcus
ANE, E PF. 11 1
Dico luperticies vigulares AOF. B
BE D FC proportionales diuitas esse
hoc est eandemrationem esse superHi-
ciei ANEB ad BEFC Superticiem,
qualis est superticiei ANFE. O A ad (u
pertCIeM EPFD F.
100I
a
q. hiiu.
Demon
(e ei e   su t  ut i pi e u te st  t u u  u  ete ui  u p e    et u   t   t e ee  a te e  p e   o  e     e   s nt