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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 542, page id 1815201908:0599
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Peres
ma
67. huin
AZPERBOL A.
Demonstratio.
DRoducta GC in R, VECR, SC aequalis C C, BOnanEUE AL, BN aequidistan:
ces C:L: cum AB, DF aequidistene, e AB in C diuisa sic bitariam, CFIE _E D F
in I bitariam dinila; quare DI quadeaca, aequalia lune quadraris P Iuna cumare.
Ctangulis DL F. sed ec D I quadrata, aequancur eriam F I quadratis, una cum re-
etangulis DF P; aequalia igitur lunc quadeaca P I, una cum rectangulis D L. F, qua-
dracis FI, una cum rectangulis DF L: Cunc aurem perhypochesim quadrara L. Iid
est AC, rectangulis D F F aequalia, reliqua igitur D L. F ae qualia sune quadraris
FT. quia vero AL ipsi C G _ DI. ipS AC aequidistac, ve DL ad L A, AC AC
est ad GC, _ ve DI ad AC, id est LI, AC AL hoc eA GT, 2d C C: ergo
etiam ve DL ad L NI, SIC AL sivc TO, ad GR; _ tE DL ad L F, SCIC ad TR:
rectangula isitur D L E proporcionalia sunc rect angulis GTR: TUNC auceM D L P
rectangula ostensa aequalia quadraris PI, isitur C IK rectangula proporcionalia
sune quadearis E P: quare C F F ad b eandem sunc hyperbolam simili modo R qua-
draco E B aequalia hane rectangula DNT F, ostendentur puncta MMTC esse ad
hyperbolam: _ quia quadrara A C, G B, adeoque ec rectangula DF F, DMF ∞.
qualia UnE, FCAX FD, M F. aequales quoque Cunc: un de x residUX F. M in I, bil.
secta sune, de FCM ad candem hyperbolam.
eROPOSITIO XV.
IIdem policis:
Dico AC, C B eAsC alymPEOTOS.
Demon.
 ee e e s u t te e  t  a te  e t s e  es t ut e es  t st e i a  t  e i  t qe     te  et   t      et e e  e e   t te   t