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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1149, page id 1815201908:1206
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.83
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124G
OY ADRATVRA CTRCVLI.
piarectana ata Guoccungae canaem aucaneur parallelx, eodem plane mcta
quorsi sumus in quadeacura prima propolic. Sr. _e aliquoc eam praecedécibus demon-
Arabiinus C F BD, ductum in F. NMB aquale corpus eficere Colido quod Ac CX
SFBR, ducto in alcicudinem T: imo cocam parabolam AV I. ductam in para-
bolam eotam AL Z., aequale corpus producere cxlindro qui sic ex lemicirculo
ASA T in alcirudinem Y. Ouod erar demonstrandum.
PR OPOSILAO LXIX.
VIc parabola AC V axchhabens AL, qualece ordinacim polica
ACEI, VDIL. PorauGuC F II parallela axi.
Oporcear solido quod tir ex Pegmenro parabolico CFHl n le lub-
alcerre ducto, exhibere aquale solidum cxlindricum cuius balis sc le-
smencum aliquod cireulare.
Conpru uonsiratio.
LFI, BR, agualeS BMT, L. NI: cum
Facta N P aequali R FT, POnaEuT PO
parallela aXi. crune igitur puncta
T. MN ad Parabolam, legmencum-
que parabolicum P NMTO aequale
erir aC SmilC sEGIMCHEO D CF TT, _
policum subalcerne. Deinde Super
AL delcribe circulum, cuiOCEUE-
TANEF: C, BD in S eC R: X LUPCF
recta SF. _ quadam alia T, haErC-
etangulum aequale ei quod rectis
CE, F. Ncontinetur, Crit igIEuF per
Praeced. legmentum parabolicum
CFBD in se ductum subalcerne,
hoc est in E DYAIB, SCOmenEuM X-
quale segmenro circulari SF BR,
ducto in alcicudinem T. Acquile
omencum parabolicum CFBD
ductum in E NTM B, XgnacUE a CC.
BICHEOFEBTI, ducto in F NMB,
_ leGIeNIO DCFII; ducto in
FP OB, Vnacum DCF Hauctoin PNM O. eroo naC ea conda qua mimium 
AINE Cx HF DELAACIOMM L NML B,CZDCEAIMLEOB; CADCFHMMIIHMOiigq
e
Simul sumpea aequaneur (olido quod sc ex S F. B R ducto in alcicudine P. Ia vero quo. quarca 2.
niam parabolicum sermencum C F. B D, breduximus ad rectitineum, eciam Colidum b Parse s.
ex F F BFI in F. DTM B, reductum est ad parallelepipedum. Fiacioicurparallelexi- Parab.
Dedum alcicudinem habens T, xequa le solido exF F. B FI in F. N M B; quod quiaiam
oltendiminus esse solido ex SE BR, ducto in alticudinem T, cciam parallelepipedu
ipsiaquale in Y alcirudine minus est (olido ex SFBR in alcicudine Y. ac proin-
indecius basis eric minor plano S F BR. Sic igicur basisilla segmencum BFB d. Prx-
cerea quoniam termencum DCH redeos ad lecmct, eelat toncum ex cibid
DCFHI in F POB, ad parallelepipedu redactum est. Fiac ergo parallelepipedum
in alcieudine L. Xquale Tonoex BCFIL FPOB. Homamane oltendi lu
pra StBKCin T, aequari LL BHl in L.NMB. aBCFHMEFOB, Macum
DCFUMENNO: cAGHCBLBdI L. aguaODR LLBLLMIBAIMB.
manifestum est soliclum ex SBdR in Y, equari Colido ex CFlD in LlOB.
rua cum DCF EI in P NM O. ergo parallelexipedum quod paulo ance in alcicu
e
E
dinc
a Demon-
strucur
imiliter ac
GlaF L. L, aqualiS AB, d rectis
l   at  e  et e  u e te  te ete  e   et     e  te   et te  t te  ste  e  e te e  s et   u e  o e t pe  t  e    s e   r 1s e  p 11