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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 549, page id 1815201908:0606
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40
TLX DF
Demonstratio.
Tcad ABC hyperbola diamereiiim
DB, orlinacim applicaci AC, cui
per B vercicem diamerri aequidistans
ponacur F B, dico illain concingere
sectionem. Si enim non concingac, oc
currac denuo tirperbola in quodani
puncto I: divilaque FB bitariam in
OPonarur diamecer CD: cumigieur
TiB aequrdistans A C; Bifariam lecetur a di2meero D
mecro b, Fariam quoque diuita: quod herinon porest, cum ad D B diamerrum or- huint.
dinacim ponacur applicaca: isicur P. B lisperbolamnon lec
crac demonstrandum.
ii5.
id (22 S.
111- 1
EE Ec. SeC, CAFIZS.E
1939(1IC I
R O POSIINL
Ainis coniingenshyperbolam, verique
alympeocorum occurrie.
Demonstratio.
DEcta AB concinsacliyperbolam ACD in A.
dico AB productam verique asympeororum
occurrere. Sin vero, agmidistee AB alymproco
TiF; Policaque per A guanis linea F A D, duca
curxquidistons FTL, qux AB. linex Occurrat in
P hyperbolx in C: quoniam ipicurcam A T, P. FI
linex quam F. A, III aequidistane, recte F A, FII
requales lunc: est alirem F A b maior HIO, igitur F
de IxImaior cst H C. puctum igicur Icadirintra (c:
ctionem, adcoque AB, recta hyperbolum non
concingic: non igitur AB aquidictar alymproco
VF: SCd vETiqUEOcCUErIE
Corollarium.
(lnc Cequicur primo dedinarim policas, verimque ad asympiocospercineete, cum
cangenci requidistenti
Sequitur secundo rectas omnesinera asymproros posieas, que diamecri non surie,
cisque non aequidistane, cildem occurrere.
Sequitur cerris lineas omnes quae diameeri non tunc; sectioni in duobus caneum
punctis occurrere; quodpacet, cum demonstracum sic, rectam omnem occurrencom
sectioni que nec concinslenec alymproco equidictar, ica a sectione diuilam cHe. ve
Parces incerelectionem ec alimprorosintercepre, sincincer sexquales, icc poser di-c Coroll. 1f.
uidivitalinca in quacuor punctis ve rectansula quaTOE Xqualia exIUES aE lub paE. huius.
cibus linex divilx.
ic _ A C ab eadem diz
10d
Disin. 25
L OE aatl
Sedaum in perimetro lectionis punctum contingenrem duccrei
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