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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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Constructio e demonstratio.
P1. titrite
uH quod pecitut. aela pel A ContinsencC A F, ducacux linea per B ee C
convemee illa cum A F in puncro quonis F: si enim non conveniac, aequidistet
AF: ertetsttur CB, ordinaciem polica adaxem AF. in parabola AB C X quia in F.
bislecca cst, in BDC Palboa Guogi ordinacim eric ducca; ipsique D P. diamerro ad
ansulos rectos. isirur D E. axis est parabole BDC: quod est contra hypochiesimi
CONCUEFCE ergO CB, Cum AF in puncco quovis F. PONATUT ergO ex F linca FD.
concingens parabolam BD C in punceo quouis D. Guontam AF est concingens,
Excauem. in Parabola AB C, linea F B, F F, F C 2 proportionales lune, led e in parabola
BD C eadem luncproporcionaless punccum isicur D concingencis D F. 3 b in diame.
EFO CI D P. Rurlum ducacur diamerer quevis alia C FI occurrens parabolis in C
_ FF, _ B C. linee in I, accaque per C Concingence CFK, qux cum B F conveniAE
in H, ducacur ex K linca K II, concingens parabolam BD C in puncco quouis FI.
Ouonlamisitur CFK linea concinsit parabola AB C, rectae K B; K L, K CC continux
Proporcionales lune: Sed e exdem quoque sunt proporcionales in parabola BDC.
isicur EI punccum concingenris TIR. in d diamerro eA ITI. ipicur componendo
cum A, D puncca daca linc agantur per A e D; contindentes; quae conveniencin
puncco quodam F. duccaque diamerro quanis CTHI; aganeur per C d FI, concin.
gentes que etiam convenienem K: ipicue daca lunc piineta F, K, P; I: Quare e
data erunepuncca B, C: gua in siR. linca esse per resolucionem ostendimus. iricue
extribuimus duarum parabolarum CBC3 BDC incerlectiones: Ouod etaE PPX
Aandum.
P R OPOSITIO CL.
Acet (CcenEsele pataDola dux ABC, F D F inverse posirx, habences
Laxes paralletoS. OpOrter C d H, puncta incerlectionum extribere.
Constructio ex demonstratio.
sIE F. DF patabole axis D B, d laccum sic quod pecitur: acCaC LL L MCA AC
 Ibid.
1 2bid.
lecrionum recta CH, qua convenier cum AC in puncro quouis J. S enimnon
conveniat, xouidister AC. reccaisicur OFI in parabola F DF, ordinacin posi-
tacltadasem DB, ad coque ee diamerrum B D in parabola c AB C ad aneulos
Secacreccos, ce qua s HL d BB, McabINecta CA, recra B D axis est patabol
ABC. quod est concra hypochelim. igirur FTC non aequidistac AC, sed produera
cum illa convenie in puncco quonis I. ducatur ergo ex I recta IB, concingens
parabolam AB C in puncco quodam B. quoniam ID recta est concirgens, linea
C8L. huius. LG, EIP, FII concinX lu Propoctionales in parabiola P D F: sed de exdem
quoquetun propostlotales in parabola ABC, punccum isieur coneaecus B li.
MCA
que E D E parabolam concingar in D, ponatur per C d HI; puncca incer
e Defin. I
uius.
a  ee  e