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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 305, page id 1815201908:0362
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.89
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E L LTP 5IS.
PROPOSTFTO CZIX
VIncinelliph diamerri coniugare AB, BC iungacurq; AC cui paral-
lela haclinea D E ransens elliplin in F, de occurrens diamerris coniu-
aris prorractisin D X F.
Dico criangulum E. D B crianguli C AB duplum ese.
Demonstratio.
X CeNEO B perEnctum F ducacur diameter BFTF,
cuioccurrat in K recta C K ellipuim cangens in C,
deinde exractu F ponacur ordinacim FPC. Duoniam
AC parallela est exhypochesi eangenci DF, crie a ad
diamecrum B F ordinacim polica. ergo RB, FB, IIB
lune concinuae proportionales. ergo c eA veKB ad F B,
AIC RF ad FHI. sed RB est ad FB, de criangulum
KCB ad criangulum F C B, hoc est, quia d criangula
CCB, EFB aequancur, ve criangulum E FB ad idem
criangulum CFB, hoc eAt ve F B ad C B. IBIEUF VEFB
ad CB, sC K F ad F FI. Deinde quia ex conAr. KC
cangic, de FC est polica ordinaum ad BC, rectae F B,
C B, GB TUNE CONEIHUIX. FrBO VE F B ad CB, sCFC
ad CG. Sed eriam est veiam octendi, sicur R B ad C B
ITa R E ad FTI. EFBOVE RF ad FHI, AIC F C ad C C.
Ergoreeriangulum K CF ad criangulum F CFI, Sic criangulum F. F C ad crian-
Gulum CF C. AEqLi CUM EOTA RCB, F. FB, aequaliasine, ablaco communi F BC
reliqua RC F, B F C aqualia sUINC. FrgO ex F C HT, C F C aequalia sune; ablacoigi-
cur communi FIC; aequalia rEMANOnE FIII, CTC quibus si commune addis
BHTO, FGB aequabitur CHIB. Jam vero quia AC ordinacim polica est. velupra
ostendi, ad BF, bilecta est AC in II, adeoque e criangulum C A B duplum est
crianpuli CTIB, ec DF parallela ad A C criam BileCACUE in E: CA VCEO L CF, VE-
Pore ducta ordinacim ad C B, Parallela ad C B, diamcerum coniugaca ipsi C B. ergo
e BF. bisecatur in G. proindeque P F B duplum est GFB. Aequi CHB, F C B
ostenta lune aequalia. Frgo ex eorum dupla C AB, F F B xe qualia lunc. sed criangu-
lum DE B duplum est crianguli P F B, est enim D P bilecta in P. Ergo criangulum
DE B duplum quoque est eriangrili C A B. Duod etal demonstrandum.
23. huoin3
b32. huius
erest
d70. huius