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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 642, page id 1815201908:0699
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196. B1-
TTZ D ER BOL A.
Demongrum.
d
ad ACC rccladeulum.
GT. AIMILIECF IPHS MI F. aquales OH.
ne E F aequales BD, X F ut aqu a-
aEUEPEXTerCA OO) ParaIIela L L, qua
rectas C L bifariam diuicat. quoniam CO
aequales lune dimidiis CL id est BD, sive
DFI, CrunE CO aquales RB, lune autem
GNT, vel ML aequales K, G FI, hoC CAOI.
igicur K C reliqua xquales sunc rectis ON.
octenlum vero esaONC esse hyperbolam
isicur _ D MM esthyperbola; ac proinde
etiam BFC, est enim rectangulum NGM
ad NCM rectangulum hoC est rectanOU.
lum POF, ad P C P. verectangulum ACC
eROPOSTTTO CCZII.
NIE Acentrum circuloru PaLaC DBD, EF G, quossecetre.
cta FHI orchosona ipsi diametro communi A F. diaeEri aUFeM AI
OCCUTFANE FFY in KKE, _ circulis in II, MM: candem hanE rectis A,
KM aequales IE L: d lincis A, IE L aequales IEN quae diaetTO A P. ae qui
diSteNE.
Dico NN hyperbolam este e quidem parallelam ac aequalem hyper.
bolx CL. B.
Demonstratio.
DRaecedenti propolcione oltentum ett C F B esse ad candem hyperbolam. quia
LverD A, KI aequales sune ex constructione rectis RN, eE A, KMT aequales II.
neis K L, ablaris aequalibusnimirum RL, 2 rectis KRN, _ A, RM, 2 rectis A, RI
remanebune recte LN aequales A, MI, ac proinde J. N linex xquales incerle. vn.
u de cum CLB conster eseb hyperbolam, constat quoque NNF. eAchy perbo
lam; ex quidem simlem ec aqualem CL. B. Quodtuic demoncteandum.
PROPOSIFIO CCXIII.
Ecent invicem, aequales circuli in punctis AB: ductamq: AB (CCenE
diametri DC F IN F F: X peF F. F. ponaneur aequidistantes FIF Or.
chosona ad P. B. Ransdenique rectis C, F. F x quales F. C, e P. HIxqua
les diametro DCF: rectis quoque F C, tanc ae quales HI.
Dico CC, IL esschyperbolas oppolICaS.
Demon