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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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eMC LACC A
PROPOSATIO LXIII.
Arxe sinerres concinua prepe onales, AC, CD, DL. aDL 
SCo Quaaratum AB, aqualc esse quadcaris AD, CB.
Demonstratio.
cca licin B.
Via AC, C D, DF Sunein CONENUa prOPOrtiOnC, quadTALIH C D LXGUIALUIEFC- 217. Sexsi
clatguto ACDF. HoC est (quoniam D F bilecta ponitur IIB) rectanoulo
RCDB bis Cumpeo. ale u verisque commune aadatur rectangulum CDB BIS.
elic quadcacum CB, cum FectansIo CDB bis, aequale rectangulo ACDB bis.
cum rectangulo CDB bis; jux quacuor rectangula consticuuneo rectanoulum bI. Secudi.
AD B bis. Rursum ergo communi addico quadraro DB, erir quadracu C D. C
rectangulo CDB bis, d quadraco D B, id est cquadearum CB, xequale rectangv. C +. Sccun-
10 ADB bis, cum quadraco DB: itaque communi addico quadraco AD, cricre.
ccangulum AD B bis, cum quadracis DB, AD, id est d quadeacum AB, ae quale qua. d ubid.
dracis CB, AD: Quod erac demonstrandum.
LLOFOoTEIO LMEI.
Vinccrese in concinua analogia AB, BC, C D, _ dividatur C D
Sbitarian MIF.
Oeo uadrarum AC, a Gualt Glladratis AC, F. B.
Demonstratio.
Vn sinc continux proporrionales AB, BC, CD, CrIEDE BC CAd C B, HC A C et. cuius.
ad DB. Hiee reccangula CBD, A CD aequancur. Sed reccanoistum C BD est
rectangulum CD B, cum quadraro DB, hoc est (quoniam ex daris C D bilcera cA
in B) recrangulum R DB bis, cum quadrato DB: rectansulum verO ACD, CA rC-
crangulum AC F, bis; eroOrectangUIUm F, DB bis, cum quadraco D B, XGUAEUERE-
crangulo ACF bis: _ communibus addicis quadraris A C, CF, SInC F D, CrunE
receangulum F D B bis, _ quadraca BD, F D, AC, Simul Cumpea, aequalia rectan-
sulo ACF. bis, _ quadraris AC, CF: Acqui reccangulum F D B bis; cum quadra-
eis DB, F. D, AC, ae quale cA quadraco FP, B, ex quadraro AC; recrangulum veroF4. Secun-
ACF bis, cum quadratis AC, C P, xquancurs quadrato AF s erBO quadrata P. B,  ibia.
AC XQUaNEUT quadraLO AF. Ouod cras demonstrandum.
eROPOSIFIO LXV.
TOnrinux proporrion AlesHInEAB, A C, AE, ec ex BC, lumi poLL
Scorcratisalum LubBA ex Tub C D, A L, camquam rna linca col.
Aructum, aequari quadrato AD.
1bD aequalis AC.
Demonstratio.
D ECCanGUIUm B A CD, BXC UNEUTRCCEangUIO BC DICHTGHAALLO CD, d h L. Secun-
reccansulo BD C) una cum i: cransulo C. D. ua a flates Milil B0l iu sccundi.