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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 622, page id 1815201908:0679
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FIX P E R BOL
Constructio E demonstratio.
CInc ABC, D F. F alymprocihy.
Perbolarum OPQ, NST, po
Crisque axibus BO F. NV ducancur
OON R de quidistances atympro.
eis AB, D F:i dico spacium intini
EUM INTEE alY MPEOEOS ABC e
lyperbolam OPO consticucum
Vad spacium intinicum hyperbole
concaua NSF, cam habere ra
xcionem, quam aB C+ criangulum
habec adcriangulum N F K. Rane
concinux proporrionales BC, BHI
BI,BC, dc. Factoque re BG ad
BEI, sIC FK ad P L, ContinUICTUE
FaTIO FR, E L in MI, XC F; erigam-
curque HIP, IG, CR, deC. icem
LS, M T, F V. _c. aequidistantes
alympeoris AB, DF. quoniam
igicur BC, BHI, BI, BC PrOPOr.
cionales lunc, d OG, PHI, 1
R C aequidistane asymPEOTO AB.
aequalia lunc (comenca PC, H.
R L,ecc. Sine cermino sic concinua.
ea: Similicer aequalia Cune leomen-
+g NT, SM, TP MMCtermino; seomenta ioicor OFL, PI,O C, ec. in infinirum
simul Cumpea, id est cora hyperbola concaua O PO sine cermino producta, est ad se.
216. De EmencA inAniCa NE, SM, TF, RC. in infinicum, a ve legmentum OFI ad Cegmen-
proressioni cum NL, id eAb fgura OB P ad Fsuram S F. N. vlcerius pOSITIS peF N et O, Con-
b 1o. hu cingencibus Od, Na, ducantur illis parallelX per S _ P, linex ZB, y co. vt BC
ius.
ad BFI, id est ctTP ad OC, Scper hypochelim eAt F R ad E L, id cA SL, ad NR
c74 huius. sed De OG ad PFI, (C O 8d 2d Pc de vENK ad SF, scN a est ad SZ, veici-
lPer
menca.
cur Odad Pa, sC N a ad5Z, est aurem ve Od2d co P, sic ea B ad dB, id est v Bad
c7+ huins. OB. _ VENa 2d5Z, SCZ F 2d a F, id est B F ad NC, isicur ve OB ad y B, (CNF
adBF, ex F Natriangulum ad eriangulum EBZ, ve BOd ad Br acriangulum: sed
est quoque triansulum BOd ad criangulum cP B, ve a N E criangulum ad eriangu.
Ium ZSF, quia ioitur ee a N F crianoulum est ad residuum criangulum SBF, ve
dOB ad residuum criangulum P Y B, ec ve dOB ad a N E, sic P q B ad S6 B. led
FEX anc. VE BO dcriangulum ad crianoulum FN a siCFP Op seomentum ad seomeneum
penulsima. S NB, reliduaigicur figura P O B ad residuam SF N, ek vecriangulum dOB ad
aNE, criangulum, id est ex ance demonstratis crianoulum a P B ad criangulum
814. huius. Z SF, id est ve ance oscendi B P FT criangulum ad crianoulum LSF. id elc. BOC
eriangulum ad criangulum RNTF. vide cum olcentum sc hyperbolas concauas,
BOPOR, E NS TV in intinitum procluctas illam incer le obtinere rationem,
quam tiouea PB O, S F DF, parcc esse ve B OC crianoulum ad criangulum R NT R SC
BOP Ohyperbolam concauam ad hyperbolam F. N S T. Ouod erar polculacum
5.
ac104.
PROPOSITIOCLZXV
Lpelbola Communem habences aiamcerum ccanlucllata, Ocaia
Ccim posicas ex iildem erectas punctis, habent proporcionales; et con.
Demon
  d eaae a eoea