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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 634, page id 1815201908:0691
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AIZ PER BOL A
quod squis hyperbolas concractas intgis aurdiductas eadem praxi describere desi-
634
rationem, quam achdetabeoge intencum.
PROFOMITIO CXCTII.
ctaC in C apo L Gae aequidistene cuidam C R hanc
inrer. l. Ll. L. L. media proportionales L. I.
Dico IIC ele ad eandem hyperbolam cuius AC est lacus tranluer.
Tum.
.
Demonstratio.
Tontamenim F L, EquidiltAnE R C. linear
Lac proinde ncerse, cricratio F L FFrectan.
guli, ad rectarigulu FL FT, composica ex ratio.
ne HIL ad HIL, hoc est CI, ad CL, _ ratio
nCFI ad F L, hoc est A L ad A L:igirur rectan-
gulum ALC ad AT C, est ve rectangulum
F F FF ad F L FI. Cum ergo quadrata TL; Xqua-
lia sinc rectarigulis F P. FI, eric quadracum TL ad
TI, quadracum verectagulum AL C ad ALC.
vndepacet CTTeNC ad hyperbolam cuius CB,
CAdiamCTeF, _ AC lacus rrarsnersum. Ouod
demonstrareoporruie.
PROPOSITIOCXCIV.
EcultenElese rurtus AB, CD in C.
occurrat deinde AF rectae DC in
C, lic ve AC hion subrendat angulum
Dico 1IC. ae candem esse hyperbolam
curus etacus transuerlum est.
derre augeas cancummodo lineas ordinacim policas C. FI. vel decurree secundum
i
Peassene seinuicem rectae AL, C C in C: occurrar deinde AF re.
AC D; de Policis LL. quae requidistent
cuidam CH, FanC inCeF FII, FIL. MC
diae proportionales HII.
Demonstratio
eeu plante quaMPacedenti propot.
stione.
Scholion.
qud hi fere suntrres casus, quosticet in prima pare exposut a nt in o
nferre libuit. cum veras hyperbolarum ecmeses ex bibetu.
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