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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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PROEOSLTIO LXZVII
Xium quadrata Cimul Cum pea aequalia lunc quadratis cuiuscunque
Demonstratio.
Inc ABC cllipleOSaxES A B, C D, dt alia quaenis dia-
mecrorui coniunatio F FI, C: L. dico AB, CD quadrata
Simul Cumpea Eguari quadraris F HI, GT Simul sumpeis.
ducancur ordinatim linea. FI, CK quae, quia ad axes du-
CUnEuE, Perpendiculares crune; cenerum aurein lectio-
Disponatur B. Ouadeacum F C a x qualc CA quadeaTO R L
vira cum CID rectangulo id est b guadraco CK: quadra-
cum aurem F B c aequale cA quadrACO F R Vna CUm rC.
ctangulo AR B id cA d quadrato F L: vnde quadeaca dues
F. B, P C simul Cumpra aequalia sunc quadracis FL, IF,
FK, CK Simul sumpris. Sed ij Idem quadracis a qualia lune
quadeata F F, F. G, quadrarisigitur F P, F. C xqualia lunE
quadraca L B, P. C. quare cum AB; CD quadraca simul
sumpeac quadrupla linc quadracorum F B; F C d FH,
GT quadraca quadrupla quadeatorum B F, PC; pater
AB, C D quadeaca simul sumpea aequari quadraris PHI
CL. limul sumpeis. Duod erat demonstrandum.
ROPOSITIO LXXVIII
Xes. ellipleos simul sumperminimae sune omnium diamertorum
Demonstratio.
InEaxeS AC, BD et quaeuis diamerrorum coniugacios
F F, C FI: dico axes simul sumpeos minores esse diame-
eris coniuracis simul Cumpris. Ouoniam AC; BD qua-
deata limul sumpea, x qualia sunc quadeacis F F, C+ FI II-
mul sumpris: Sicaurem ee BD maxima diametrorum, AC
vero minima, eFunEFAC, B D Smul sumpEx minores te.
Ais E P, C H: isicur, e c. Quod fuit demonstrandum.
PROPOSITIO LXXIX.
VInE AB C ellipsis axes AB, C D, divili pro.
portionalicer in P. d F: ducti sque ordinarim
(que hiclune perpendiculares) lineis PG, FH:
iunsateur AC, GB, CHI, HD:
Dico quatuor quaata AC, CB, CH, HAB, Simul Cumpca, XGlat
Lconiugationis simul sumpris.
Aconiugatarum simul sumprarum.
duobus axium quadraris.
Demon.
ee  p p a psn p  as  e  p .  en e p t t a se at e u   e ete t pi at  e u e e  t    a te    t e e   e  u 1 1 1. p