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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 694, page id 1815201908:0751
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SP + R A L 3
Demonstratio.
Ecangula A DB Merse candem habene piovot.
cionem quam recle C D, ve Lostendimus in libre
de parabola. Sed reclL P D sime inter sC vE rectae C. D
cum line carum amlix: ergo de recte F. D (unc incet
se ve rectangula. Ergo puncta F. sunc ad parabolam per
propolic. 329. de Pacbbla. Duod erac primum:
Cogicontur donn in parabola A C B duax este
Cdx CC, in Patabola vero AF B reCtX P B,
SiC D verigue MMICLIpEa lInE EraPeZIA CC DD RF.
DO. Cacile ostehactur (quod brenicaris caula hicomic.
e0) cor duci polle CACErOS C D ac rectAS B F, _ FOI
Proinde Lraperia inseribi, ve lI aUFCFANEuF, ex veraque
parabola relinquantur superticies minores daci. ACqui
Tropexia parabolae AC B simul sumpea dupla lunc.
Trapeziorum parabola A F B SimuL lumPearum, VE P2-
cec ch elemenes cum lecta C: D dupla sinc rectarum
auc Fuclidieo lib. 12. demontabi. LaMctaigItuE F Cunc ad parabolam quae dimidia sic
prima. Cuodctat detohltalicl
68. D E. D ergo per ea quae in libro b progrestionum demonstranimus, parabola A C B du.
pogress.
Pla est Parabolx AF B. Ouod Facile etiam quivis Creometra Archime daeo discuru
AP P L I G AVF V R CS D LD A
LICTa IpITalEM A E. DB duCanCUFDC,
C; F C, P. C Parallelae incersc, adc0
quonormales ad rectam C AB, d bisc.
cencurinpunctis F, F, 1, I.
Dicopuncta PF; I,I ese ad spiralem.
quae dimidia sic spiralis prima ac proin-
decriam hic spiralem cu parabola Crm-
Dolizare: Led hxc secunda lpira non erie
circularis, ac elliprica. Ouod Furura
Cc dimidia lpiralis primx eodem modo
demonstrabirur quo in parabola. Ouod
Fucura sic spixalis elliprica sic ostendo.
ReCtADC, DC; F C, F C producantUE
vlque ad pcripheriam circuli in C ae M;
e bileca rectas C C in K. rectas vero
NIC in N. Frunc punctaK, R; F, F. ad
ellioim ve colligitur ex Archimed. 5. de
conoid. Ouoniam isitur recte DC. luncad rectas FC, ve rectae GC 2d
rectas KC, nam ex constructione veraeque bilecta TUINC. FrUnEpermU.
cando e inverrendo rectx R C ad rectas FC, ve rectae CC ad rectasDC.
Similicer octendemus rectas NC esse adrectas IC, ur rectae M C ad rectas
E C. habec isicur sele quond hanc propricrarem elliplis ad spiralem secun-
dam, vr circulus ad primam. Sed clarius adhuc ostendamus proposirum.
Pet Archimed. 5. de Conoid. circulus C O est ad ellipsim K K, ve B P, h0C
q  et e   epies et  e ut ptat e e t tt t e A  tat ste tt te te   e   e   te    tit a t t et t      t   t      e  t  1 1 s s