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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 79, page id 1815201908:0136
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Lemma.
TFuerinerres B. A. D As C A in concinua analopia, rectangulum supet maxima
us AB.
AB, _ excessu CD lecunca laPC CerCa; Hon et iC ss Geacuco CIE IP.
Demonstratio.
Voniam enim B A, D A, C A sunc continux proportionales, crit vE B A 2 A L L. Huim
1. AC D D ad DC. Ouare rectana B AC D, _ BD A aGUAHTUL. SCa . SexII.
Cllat t BA, non ele Maius quadrato dimiaia AB C VEPACCE ervO neque C5. Secnndb.
rectanculum B ACD maiuseric quadraco dimidia AB. Ouod crac demonstrandu.
TKOLOSTCIOZXXIX
Acamaxim a erium concinuarum, ee excessu quo media superaE m P
nimam, exhribere MCCTAML LL MMMMIIITAII.
Constructio es demonstratiu
ctanoun Abes asuale Guactaum f: Quomam ers per lemma pracedensqua.
dratum F F, id est rectansulum AB C, non maius est quadraco dimidiae AB. pacoc
ica d secari posse AB, ve rectangulum sub parcibus; Lquale AE quadraLO F F. lca-
que dividatur recta AB, in puncto D, verectangulum ADB xquale sic quadraco
F. L. Dicopunctum D este quod problema loluies hac enim recta C7, aequalis linca
DC: crit ieaque rectangulum AB CD aequale rectangulo AD B, cum verumque
5. Secundi.
seglia le sEquadratO P F; ergO vE AB adc AD, ica eA BD ad D C: E iam a rect at - C 16. Sexsi-
sulo ABC D, auferas rectansulum BD C; remanebic rectan guluni AD C; s VCFO
2 rectarigulo ADB, auferas idem BD C, reliquum erit rectangulum A C D B: acqui
EOta ABCD, AD B sunc xqualia, ieaque ablaco communi, crunc de reliqua rect an-
sula ADC, AC. DB xqualia iicer (C; isItuF vE BD ad DC, Fid eA (SicuEiam ORet F14. Sent
si) ve B A 2d D A, sic D A dd C A. Suncigicur eres in concinua analooia AB, AD,
AC; _ CD aequalis C, eA excessus, quo media AD, excedic minimam AC. Fa.
dum igitur eA quod requirebatur.
Aca sic AB linea Manm aexium PrOPOMONAuI, d C aqualis excestui quo
media superac minimam: oporreat isicur invenire mediam ex minimam. Aac re-
ER O POSITIO AL
aloclobuscaCcBuS, crium masnicudinum in continua analosia
existentium, exhibereeres continuas.
Constructio ex demonstratio
AceCeus AC. C B, Guiponan-
cur in directum; de CrISANEUE AD
 Patallela, quainter se candem ra-
cionem scriene quam AC ad CB; 8
ducta pet puncta D _ F rectaDF, con
veniae cum AB producta in puncto quo.
dom P. Dico Factum quod postulaturo
sidra