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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 578, page id 1815201908:0635
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AYPERBOL A.
exondim. T7T CF a 2d TC, ita F. D de B L CtGBM +C ad OFI, hioc est CB ad BD,
Aliter Corollarium hoc demonstratur.
Ica C F ad DF.
PROPOSITIO XCTI
D cu
buldam L ee L, per quae actx conringentes aequidistant rectis AK, HC,
ddico roctangulum ADL dd HI Ci C. rectangulum, camdem rario.
nem concinere, quam habet quadratum Bl ad B L quadracum.
Demonstratio.
TIne AB, BC alimpeoci hyperbolx D E F angulum rectum consti-
; de guauis dux DE, FO ponancur, quae obviene sectioni
in D, C, E, F, alsumpris aurem in hyperbole perimerro punctis qui-
52
3
calata alielcuo alstabco
ponancur diameri B, BL
(1. YD 5. 2391
toru ABC rectus elli
continsentesper I de I. dua
dupla lunebrectarum BL B L
illaruurque dimidia ijsdem a
qualia: sed octensum est rectan-
bulum ADK concingencis, ie
Ecquadraci, dimidio cNe X.
quale, vei sc rectanrulum
AOFDSIfIO XCIII
VInE AB, AC asympeoei hyperbOIX EHIP: astumpeo deinde puncto
quodam incra illam D, Ponaneur DB, DC alymprocis equidistan.
ces, occurrentes sectioniin ponctis F _ F; ex quibus duCanEUE E G, FC
Parallelae iidem asymproris, act 2 denique D A qua occurrar sectioni in
HI, per HI (inc L M, IK parallelx asympeocis.
Dico lMt parallelogrammum ad L. R Paralle.
logrammum, eam rationem continere quae est
incerlincas DB, B F.
Domonstratio.
Lbead DC. hooen AC adABoIA CABD
ad CF: igicut ve DB, ad DC, iea est DH ad DF,
hoc CA F C ad G L igItIE A C ad AB, CA vEF C 10
t aAC. ddF. De AB AdBC. IBicuI AOL
enic in directum, a LM, LK parallelogramma ad com-
nunem alsmectum IK. L. M comticuca lunc: unde li-
hilia suneineccle, adebque in duplichcaratione DL La
5. quia vero D B, BI. BF CpropOrciBIAlES TUNE, VE D
ad TR. sc eD B cs ad B P: icur paralleIBGFamMA PNI
T K duplicacam hotene incer se rationem recte DB ad
BLi  CD BA BP. Qvod eta Heion Arun le
PRO.
HOC contingentis in L, dimidio quadeaei. Igicurrectangulum A D R ad HCC
rectangulum est, re quadrarum B I ad BI. quadrarum. Duod fuic demonstrandum.
22. hui
F1. Depro-
 Lo s  .d C. + 5. X W2 F
ressionibu