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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 638, page id 1815201908:0695
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aquales DI, _ F 6.
I. Buius.
1.
A Y P ER BOL A.
TKOFOSITTO CCII.
Trepli ABC diameret IL A C, contingences ad A de C, AD; C P:
Dcinde DF aquidistent AC, ductis in super L. D, Ranerectis L, BD.
Dico AI; d CC hyperbolas este oppo.
CIEas.
Demonstratio.
DOnaneur IK que aequidistene AD: cclinc ist.
Tux TR aequales D A. quia vero BM lincis X.
quales lune DF, e DI aequales L, BD, rectari-
sula DFF idest AKC, xqualia sune rectangulis
BDM, id es quadraris D A suC IR. igicuT ARC
ad AK C, rectangulum est vE TK quadeacum ad
quadratum IK. vnde AI, punctaa ad tixperbolem
lunc. similicer ostendam puncta C CC, ad hyper-
olam estc. quia vero AII, C CC hyperbol
communi saudenc cransuerta AC, OPPOlIEX CFUNE
blectiones AII, C66.
1
en OPOSItIO CCTTI
Virculum ABC cuius diametet
L+AC; contingane quocuis DB.
occurrenres diamcrro in B: crectis
aurem parallelis DF, RanEDB re.
ctis aequales DF.
Dico A C. este ad eandem hypet
bolam cuius diamerer cranlierta
Fi5 BE E
1
EAC.
Demonstratio.
Droniam BD contingences sune, re
20 Actangulis AD C xqualia sune quadra
ca D B id est exhypochesi quadraca D F.
quare AD C ad ADC rectangulum, est
sE D E quadrarum ad quadracum DP.
igicur A, P F. puncta ad lisperbolam lunt
cujus cranluerta diameter AC. Duod tuie
demonstrandum.
 cc
0
aurerbv Et
eche . ulona
11 1121L. 1 ( it e 1
B RO.
AF23 CNC
iet