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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 60, page id 1815201908:0117
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=117
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

  i 1 . 1 1. 1 . 11. 1 1. 1
P _ OGR F SSION FC
P R OPOSITIO VITI.
IInEEreS maonicudines AC, AB, AF; _ F F aqualis (IC C B.
DicO S A C minima CHIIIII, d CD MIInOr difforentia, e BF.
veriulque ditterencia, eCla line concinue proportionales, iBlas quo-
quemasnicudines LC, AB, A F ese in continua rariolC.
Demonstratio.
a3. Secundi. D F AanOnIUM F A C L XGULaEUE FCCTAHIBIIO F C A vna Cum quadratO C A, rectan-
B1. Sccundi. Lculum aucem F C A aequatur brectangulo AC B, _ rectangulo AC BF (id cA
c17. Sexri. couadrato B. Cu aC. C bF Ponum Commua) ab praccilacuanuee
EF; id est ACB, quia aquales Cunc CB, F. F: igitur rectanoutm lAC aequatur
d4. Secudi. Gua ato AC3C B3 celectangulo AC B bis, hoc elt quadraro a AB; ta eu
el Sentr. ures proporcionales maxnicudines AC, AB, AP. Quoderat demontrandum.
dC.
lat
Mliter.
TT BC ad CA, sC FB ad BC, i CH L L. IBIur componendo ve B A ad GA.
.
Sc BF ad F. F, hoc est BF ad BC: ergo permucando et componendo LA ad
BA, VE B Aad C. H. Saouctac demonstrandum.
Corellarium.
relcix; cruncrurtun AC
TauTeM A C, CB, R F Fuerune proportionales, ee B F aqualis C B minori difte-
dem est, que Plopocibusal pola.
AB. AF concinux proportionales. Demonstracio ca
kOFOStLIO 1X
Int in concinua analodta AB, AC, AB, dMminori disterentia BC,
aequalis sIE FD
C
Dico minimam AB, c MC CLCa BC, deinde _ C F,
veriusque dinctenra elentiam, esse proporrionales.
Demonstratio.
C3. Sccundi.  Fctangulum D AB Eaquatur rectangulo D B A, ec quadrato AB: rectangulum
BI. SccuL aurem D B A B XquatuE rectangulis ABC, _ AB F D, id ch LMuS tCuanou-
l0 AB C (suncenim F D, B C linex aqualeS) e rectangulo AB C F: CF~O rectAN-
Sutu AB, aquatur quadraro AB, ec rectangulo AB C bis, a praletCateca.
ulo ACL: quaccacua del ac: aguacit guacale aieclati aABC Oto
ex quadrato BC: Acsut Cum AB, AC, AD ponantur concinux proportionales.
7. Sexri. ex Cellangulum hD AB aequalequadrato AC; ergo quadrarum AB, rectangulum
A BC BIS. arectangulum AB C F Simul Cumpea, aquancur quadraco AB, Fectan-
eto ABC BI, a guadraco BC simul sumpris. Peaque dempeis communibus qua-
deaco AB, ee rectanoulo AP C bis, aegualia remanene quadracum BC, _ reCtAM-
gulum BC e GlaleAB. DC.Cmes Crua Proporrionales. Suo etae
deonulandum.
Alter.
        n