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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 531, page id 1815201908:0588
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Mpto.
resde.
s
CeTUT
ilero
Conii
neam
M8I.
quod
coni
elion
PFO.
1aH.
vet.
eto
FB
K,
Gull
UI
tii.
61
DM.
12.
t
31
HY P E RBO L A.
Vocetur aurem lectio huiulmodihyperbola: cuus dametet caea L L3 d
ordinacim ad illam applicacae, FIR, FD.
PROPOS
lnc ad verricem laperticies dux conca Guatust retlet se Puntert:
Dhabeant aurem circulos aequales CDF, te aparallelos, quo-
rum cenera IE, Is diamerri CF, L Hl: Pontaue L.DMomali ad diame-
trum CF; ducatur (ccundum L. D, planum non per vetilcem quod se
ctiones faciar in veraque luperticie, lineas DL. O, CMI.
Dico veram que lectionem hyperbolam esse.
Demonstratio.
Brncta N, O, verriceslinelectio-
LNAM DF O, GMN: Cumpris.
que quibuluis distanciis NZ, OV,
per V _ X ducaneur BR, ST
aequidictances CF, FH: _ PEF
BR, ST lineas, plana agaHEuE
BOR, SPT, Parallela circulis
CDF, FCFI, exhibencia in planis
DEO, GMN communesincerle.
ctiones XP, OV: quoniamigi-
cur plana BOR, CDF aequidi-
canc, communes incerlectiones
OV, DL, in plano DLO a Pa
rallela lune: _ quia DL ad C B
diamerrum normalis est, recta quo-
que OV ad B Rnormalis eR: igi-
EUE vE NV O rectangulum b ad
ad recrangulum NI. O, Ec qua-
deacum VO ad quadracum I. D,
typerbola est igirur sectio DI. O.
Deinde quia circuli CDF
FOTI xquidistane, c communes
quoque incersectiones DL, MO
parallelae lunc: _ cum L D norma-
lis Sic ad diameerum CF3 recca
quoque MC normalis est ad F II3
inde ex ZP normalis ad ST:
quadrarum d igitur Z P ad MC, quadratum CsE VENZ O recrangulum est adrC. sExtA
crangulum NM O. quare ex sccrio CMWY hyperbola cA.
Vocentur aurem hyperbolx OM PT, D L.O sectiones oppolcx: quarum com-
munis diameter est cransuerla NVO.
LRoPOstIIO MI.
c16. 0nde.
cime
Irculorum aequalium AB C, D E. F in planis requidistantibus de-
Alcripeorum centra coniungat recta GFI, Bitaltan a u 25 per
Etaque AF, quae occurret CrFI in I, circumasaturhac eadem, manente
punCto I, DEr CITCUIOTUM PCFIMCErOS ABC, DFF, doncc in cundem
locum redierie a quo caepic circum duci: erecta deinde KB orchoOn
ad
quam polico plano AC FD signanre diamerros AC, D F parallelas, du-
tsd
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