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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 90, page id 1815201908:0147
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   e 1 1 11. 1 11
R
C
GR F SSIONF
Ex AC. BD) equalIa TuNErectangula BDC, ACD; erso rectansulum ABCD.
aeguacur rectanpulo A C D bis, cum quadrato, : _ quia (UINE CONEIMUX B A, C A,
F. A, rectangulum B A F, ae quale est quadrare C A: Ieaque s rectangulo ABCD
b +. Secuai. C D A P. canquam rnam lincam) aGaa eacitatis CD, C A, et rectangulo AC Ld
PR OPOSITIO
LXV
Donacurlinca AB, diuisa in cres prepotionales AB, CB, DB: dui
Dicorectangulum CDF, rectalt oAB aGalC CHC.
Demonstratio.
a2. Secunai. addas rectangulum B AF: e rectangulo ACD bis, cum gitadrato C D, addas qua.
aracum C A, crunc rectangula B ACD, B AF, (id estrectansulum a ex B A in
bis, id est b quadraco AD. Ouoderat demonstrandum.
bus aurem C B, DB, in directum consticuancur aequales, BF, BL;
c docundi. ) Voniam AB, CB, DB, ponuniur concinux; eric recrangulum ABD (id est
squadrato CB; ergo reccangulum A D B; cum quadraco DB, aequatur rectangulo
CDC, cum quadraco DB. Quocirca ablaco comumt quadraco DB reccanioulum
ScrecranoUIum A D B cum quadrato D B) aequale, quadrato C B: acqui eriam
85. Socunai. (cum ex dacis C F bilceta sc in B) recrangulum CD F cum quadraco D B; equacui
CD F, reccangulo AD B xea CI. Suod tuic demonau.
PROPOSITIO LAMII
IIE AB ad A C, vE AD ad AF
lub AD certIL:
Dico primo rectangulum (ubpHma AB, _ DL aMCICHCd quar
Ex e cerrixe, xquarirectans  Iub BC, differentia primae e secunda; de
secundo rectangulum sub prima AB; _ BF differencia priML 
quarta, xquari duobus rectangulis Tub AC; BD, e sub AB, BC.
monpratio.
AVIn AC VE A B ad AC, siC A D ad A F itaque ineKCCHdO d MMIaendO VE C B
ad B A, SC F D ad D R; quarE rCCLAHBMOIH L. L AL B aguacut seccanoiilo
C2Sccui. D ACB. quod crat primum. Deinde cum (ic R L. A al D H, HC C A da BA, creO
rectato L AB Lguacu Ccao DAC, HoC et.sectangulo DC A cum
C4. Socunai
quadraco CA. Duod li aurem a rectangulo F AB absuleris quadracum AB, Tema-
nec receangUlum E B A; _ E idem abculeris a rectangulo D C A cum quadraco
C A. Temanenececcanulum 1C. R, reccangutum CBA bis Cutu guacaio ve
Tcaque cum coca Fuerine x qualta, erunc ablaro communi, xqualia adhuc reliqua; re-
Crangul um nemPC F. B A, e rectangula D C A semet, C B A bis, _x quadratum
BC limul Cumpea. aequi recrangulum ACB, equale cst rectangulo ABC cum
ladraco B C; cui li addas rectangulum A C D, orictur SrCCtanGUIUM A CBD.
quod cum rectangulo AB C aequale crir reccangulo APB C bis cum quadratoBC
e rectangulo AC D: qua cum limul sumpra aqualia esse ostenderim recrangulo
EB A, eric quoque rectangulum AC, B D cumrecransulo AB C xqualC reCtan-
Bulo F. B A, quod erat demonstrandum.