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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 277, page id 1815201908:0334
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E L L PP SIS.
e CSSEISI.
114.:
ACP AO P, O S VTIO L XLII, 1llic
3
1et 1 et
Vine due quaeuis diamerri AB, AC, iunctisque illarum extremicari-
bus, ducancur due quaenis aliae diameeri AD, A P SiC ve iunct a DF.
SInE ABC, ADE criangula aequalia: divisis autem BC, D P. BIta-
riam in F ex C1, aganeur per F e C, diametri AFI, AI: que si in Lde
C, proporcionalirer line diuile,
Dico BAC) D AF sectores eNeaequales.
Demonstratio.
Voniam AYI, AI diametri in F et C proporcionali.
Lcersunediuile, crunc BHC, D LF Scgmenta 2 xqua
lia: Cune aucem ex liypocheheriangula ABC, AD P. xqua-
lia: sectores isicue B AC, D A F. sune inter se aequales
Duod erac demonttranclum.
eROPOSTTIO EX
HInE duo sectores D ABC, DFPF, ductisquere.
Dais AC, L. MI, _ bilectis in FI, de C7; duCANEUE
diametri DHB, D C. L. Sic aurem rario D C ad DI
minor ratione D FI ad DB.,
1. (11
Dico sectorem DELF radiorem, este, (eCOTs
DABC.
Constructio es demonstratio.
Toniam D C est ad D L in minori proportione quâm
LD HI ad DB. Fiac DR ad D I, vi DFI ad DB. m2-
iorigicur erie DK quam D C _ punctum R cadet inter
C ac I. Per K ducatur ordinarim Y RM; iunsancurque
DE, DMI; Scomenta igitur T. IMI, ABC B xequalia CunE.
Duare sectores oriam cDI. IM, D ABC. sunc aequales.
ac proinde sector. D F IF maior cA sectoroD ABC. Quod
erac demonstrandum. i. I, etli uB C18. 3 20677 1i pIR
IPROPOSIETOLE
nt
11313
NInE ABC, D B F. sectores duu inxquales, (IC
DOVe ABC, DBE criangula sine equalia:
Dico ABC, DBF sectores simul Cumpros aequ
3331()1V~1F.  
Demonstratio. D V
Vm sectores sinc ex hypochesi inxequales, sit maior
BDGF. quia ergo criangulum DB F ex hypoches
aequacurcriangulo B AC crir sesmentum DCF maius
seomenco A C, abscindatur dicaque F C segmencum ipsI
AC aeguale iurgancurque BG, CD; de F B producta in
Ei ducarur F D. quid Egicor Pegmenta GB; AC. aqualia 
(unc, c’etiam sectores aeguales luHe, adeoque ee crianou
Tum GF B, criansulo AC B, hOC est criangulo BDF X-
quale cric. quare BP, DG me parallele adeoque ele-
emencum OF, hoc ett legmentum AC aquale cAt le-
emenro DE; sectores itaGUeAB AC BFDS Equancur.
M m 3
253. tuius.
Shuin
d
uius
u
111