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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1074, page id 1815201908:1131
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DelLCoMAETaILCAE.
CONOIDES AXDERBOLLCNM.
TE AB C hyperbOlA qUAMLRCCHCAHE EquidiCtAnEeS D C, EP, pOna-
curquererria AB, qua palallelis occurrac in punctis LL e C, neque
Dico rectangulum F. CF ad DFIC
eandem habere rarionem quam habee
reccangulum ACB ad AHLB rectan.
gulum.
Demonstratio.
CiX cenerohyperbola demissis diamerris re.
Cctarum AB S F F, guX Occurrane peri-
merro hiyperbole in punctis NY _c M, ponan-
TuT COnTINGEHECS NO, MO. COnCUTrenE BX
in puncto quodam O. nam xquidistanEeS (UNE
ordinarim applicacis AB, FF; quae sibi oc.
CUTPUBE; cricque per 27. cerrii conicorum
rectangulum A GB ad F G: F, VE CA NO qua-
dracum ad MO quadracum. Sed ecium per
eandem propolicionem est rectangulum
ATIB ad DFTC, vequadratum NO adMO
quadratum. Igitur ve rectangulum E G F ad
DFTC, ita est AG B ad AFTB. Duod Fuic
demonstrandum.
Ine in hyperbola bine pa-
D rallele AB, CD, _FF, CHI
Cibioccurrentes in lXK.
Dicorectangulum C ID ad
AKB, candem CONTInCrC FA-
tionem quam recrangulum
F IF ad CKHI rectangutum.
Demonstratio.
Vngancur puncta TK recta lined.
quae conveniat cum perimerro in
C QM. cric itaque per praecedenrem re rectangulum P RM ad recranguluM L INI.
iea cam rectangulum GRII adF IF, quam ARBreccangulum ad C ID rectangu.
lum. lsicue veseclangulum C lD 2d AFB sect angulum, ita eAt Ec casulum FIF
a  rectangolum.
eROPOSITIO CLXVIII. LEMM A.
LEMMA PROLODETIO CLXIZ.
1074
a2d. hyperb.
L F. VI.