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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 558, page id 1815201908:0615
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11
aCoroIl. 39.
29. hut
+. tour
Coroll. 15
TE Y PE R BOL A.
Demonstratio.
INC ABC DEF sectiones coniugata incer alya
Eocos GHT, GL COnCTIEUEX, PON anEuF aucem dix.
mecri coniugacx CFB, CD. dico iunctam DB aequidi.
AaTC A(yMPEOTO RC: ee li DB quacunq: ae quidittans
Ponatur alimptoco ErFI, dico rectas ex B et D adG
cenerum ductas, diamerros esse coningatas: aganEUE, per
B _ D contingentes IFI, TK occurrent illX alympto.
co CI in. vno eodemque puncto P; cruneque in Vb _
B bitariam dinilx: IgICUE VEKD ad DI, SC HTB ad
BT, ergo _ DB xequidiStaE K C asympeoro, quod
cracprimum. sic iam D B paraltela, R C2B _C Cx B _ D
rectx ducancur BC, D Ci ad cenerum . dico CB,
CD diametros ese coniugataS. AII VEED, PONAEUTCTM
diamecer coningara DC. iunctaigicur DM, aquidistac
RFI, adeoque e ipsi D B. quod ablurdum: non igieur
M C diamerer coniugata est ipA D Cr, Sed sola BC.
PROPOSITIO ZLV.
InE AB, AC alymptori coniugacarum se-
Dctionum DEF, OLTI. Politaque diamerro
AFI, agacur per HI concingens IL B OCCUETeNS
alympeoro in D. Donatur aurem ex Bconcingens,
DE F hyperbolam in F.
Dieo AE. diamerrum esse coniugacam ipti
AFI.
Demonstratio.
VngantUr HTF. Ononiam BR, CB contingentes
TUnE, crunE in TY _ F bitariam c divila. Vndc HIF
aequidistac RC; _ AP, AFI diam etris sunt coniug.
Ex. Ouod erat demonstrandum.
eROPOSTTIO XLVI
Eperbolam AB C inter alyMPEOTOS Con.
Aicuram, sccet recta F D, in punctis A, _C
almproris ponancus aquidictantes 56.
Demonstratio.
Dico LAF rectangulum aequari rectansulo R C. C.
rontam l. CC, lincx au
ltanc, CD elt ad D A, vE CGac
A l: led vE CD ad D A, SIC A F ad F, C,
(quia AD, C P c linex aequales (UINC)
IgICAESE AE ad CF CA, DE C C 2d
AT. esE AUECMM VE AF ad C F, SCAF
2d C RiigITUEVE C C ad AI, SC AF 2c
C.R