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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 276, page id 1815201908:0333
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=333
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
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paue ngun
E L L. IP SIS. I i
duaseducere semidiamerros quae lectorem constituanexqualem sectori AF B: PrO
constructione juncta AB; ducatur ex F Pemidiameter quecunque ED: Cum a CxL
recta ducacur D I Ccomiencum auferens aequale legmenco AB iungacurque II.
PATCE TFDTCMCBCMGA RctOTI AFB. 19O1Z 5.12L∞5.131IC
eROBOSIF1O L. X1.
InE ABC, DBF sectores equales: iuncti(que AC, D F duCAEUE
Dex B quaevis linea BC. lCcans AC lineam in F: dein lectori ABC
hacequalis lector DB LI lececq; HTB linea, rectam F.D in l. 1 suprom
Dico tam AC, DP. IIHCas quam BG, FIB in F e l proporrionali
tex esse dinilas.BoCd
Demonstratio.
VnGATUT AG, OC, DFE HF. Ouoniam exhyporhes
sCctOreSTaM ABC, DBHI, quam ABC, DBF Cune
aequales, crune ex reliqui GBC, TIB F. X qualcs. quare
AC B criangulum aquale eriangulo D FIB, de criangu-
Jum COB aquale criangulo HIF B. quare vecriangulum
B A C ad criangulum G CB, sic BD FI criangulum ad
criansulum BHI R, scd (quod Facile cx1. 6. eAt demonstra-
EH) raciOneS reCtarUM AF, FC, ex DT, TF, cadem sne
cum racionibus criangulorum B AG, C CB, _ BDII.
BTTF. Ergoo cciam, AF est ad FC, VE DI ad TF.
Deinde cum rrapezia C+ ABC, BDTIF aqualia sinc (est
enim ceriangulum B A Gs criangulo BD TI, e criangulu
BC C, criangulo B FTF, aequalc) sc aurem _ AC B crian-
sulum daequale criansulo D F. B, eric reliquum eriangulii
uale religuo DFTF: igieur ve AO C criangulum ad criangulum AC B,
onsra id est c ve G F ad F B GC D FTF criangulum ad criangulum D BB id ost ITI ad
ext IB. Ouoderax demonstrandum. 1a WL LB: WilBPB. elC1
rib  hueilhoeg0rsantM23 
P R O P OSGI. T Y O WIL. X I. I.
3 cet  et CCWlBAA EHBe
lug
Inc iam AC, C linet in F. de L proporetonalices diuila: nxlricur
DEF F e I, CCMiametr BC BH. aitrgV
a
Dico AB G, DBHI sectores, eAC aequaleS. rocileup.
TelT. A 11010So mo
Demonstratio.
∞:CT 7 et.  R 91P 1099E7ONE, E leV
I erG iHE AICCTUTEL N, A H C minOr alcerO: Hac AB K sector aqualis sectori
DBLB secetque BR InCa rectam AC in L, quoniam ABR, D BHI sectores
luncxequalessi Exis perprimam parxemhuius AL, 2d P. C, ve D IadIF. Aequi eciam
AF CA 2st F Co vE D L, ad, IF, igicur ve AF ad F C. Sc AF ad L C, quod heri
non porest: quia punctum. P. cadic vlera aut ciera F. quare sector AB K non est
ae qualis sectori DBHP nec alius quilquam praeter AB C. Duod crar demonstran.
dum.
21L Eiritp 22 20 5St. E I C eD F A i. GuEG ViIrBSIEHEE
D5
13rABIL BOBP. et adiiist 2S 1 2 ei trorcliit 39p C NSCColC
tituih cdits. sCOgBG etBNOG C2H ∞Bu
urole upuant nodui colrup ninsud et iLC  Y R ovb 2310Bl a q R O.
la 33t it CI dY A AlniBOM: N C A e13.
10g0, 3uxuorp 220 st _ 7 A. oral zuslot ay tcory slus siul oire
27C
2bid.
bCorol. 60.
nins.
Egcit
(e  ue i e  ttis u et ue t p  ut  sa pst a      at  u e  t et  e  pe ue   e e u te e    su a  nai