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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 344, page id 1815201908:0401
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AIIIIIIII
12
LL IPSIS
Demonstratio.
quidem pacet DF bisecari in C; in CpH aurem bilecari quoq: A C colliges Cx 42
truius. Cuare ca in ellipsi quam in circm lectores AGC, DK I bilecancuT. ergo lC.
20 cum permucan do lixpochielim, segncum AB C sic ad sermencum D R F, ve
ellipsisad circulum, etiam sector A CC crirad sectorem DR L, hoc cs (veian
octendi) sector AC B; ad sectorem DLL, rt ellipiis ad circulum. Fe quoniam est
sector AG B ad sectorem D KL, Vemplis ad circulum; etic quoque legmentum
ALB ad seomentum AM F, Vcellipss ad cireulum. Ergo diumerri LG, MIR PF0.
porcionalicex in H et L. lunc duvila. Quadorac demonstrandum.
DSITIO CLXEXIX
navence lgura: sifueric lesenrum ABC ad sexmeneum
i Dico esse de criangulu aximum ABC ad ertangulum maxitmum
DEF BE ABC eltipiss ett ad circuluIDEF.
Demonstratio.
culum AC cocum lesMencum ABC ad eorum sesmencum D F. F.
ixicur ee reliquum criansulum A B N est ad reliquum criangulum D E O DE ABC,
ellipsis ad circulum DP. D. Quoderat demonstrandum.
erian sulum inseripcume larimuti A F C. (1 Fuerinc ABC, A F. C exiangu.
Aco e semicircaum ABC aequalem
EX B ee F ducantur diateeri B G, FK, iunGANEUTGIE DK, KF, OA, OC, d
Lguoniam e verticibus maximorum triangulorum duetx lunc diameeri; in circule
Aor A GB est ad seCtOrEM DRF, VE sectOF A G C ad SCCtOrEM DRF. Tam ve-
Adc
CC, Ve clApSIS
DE F, ve ABC ellipsis ad circulum DFF.
(7F ABC cllipss est ad citculum DEF, sic ostendimus in priori segmenca
AIB, BC. eHC ad seBENES DM B, BF. Ouare cum eriam ex hypoches
PR OP OSIT1O CXC.
ScoABC semicirculo inseripeum criangulum maximum ABC; (IC
laaquallai
saurem de AE C semiellips que communem A C habcat diametrum,
TemicllipC AFC.
demon
nEnHEHE puncta B et F. O uoniam erlangula
ABC; AF. C lupc Cacem BaM delcripea per
spechen a aesdalia; criciuncta BF. Parallela
rectae ACi adeoque cum cam AB C. quan A L. C
1 e s e tte se  e  Au e e ete e t 1 e    a  e  e e t    e   e   e e e   e      e   e   u    p p. 16