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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 541, page id 1815201908:0598
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eltur
mB
ren
quo
Con.
ta ir
leni
CB
ctas
OF
Ta1.
lum
HP
101
M.
WIIIIIIII
IIY P F R BO L H.
Corollarium.
Idem pôsris lequicae lineam FFF, quo masis proac, coum popinguo-
rem heri. Octensum est enim penuleima proposicione punctum L. quo maiori in-
ceruallo dictabic a puncto FI, co ricinius Fucurum sectioni F N F. Igitur linca HIL.
quomasis procrahetur, eo lectioni propinquior Aet.
ldem voricis:
l
PROPOSITIO XIL
Dico hyperbolam productani da ahpeoton ploauctam Ita VI-
cinam heri re quouis inceruallo daro diltancia incer haec minox (Ic Fucura.
Demonstratio.
TAcuM IMCCaHAM O, PONAEUE F Y
in termino diamecri DF contingens
sectionem FNF: eric haec parallela
MO. Aac aurem rectangulum Tub RS
quae sc minor e aliaS Y aqualequa-
deaEO E P. e applicetur ad diameerum
FD ordinatim pars cius SX, qua X Y
residuum habeat equale R S. Sicque il.
la FDV. igicur F, P aequalis est XT.
cum P L V rectangulum, hoc est R SI
sic aequale quadraco FP. Duodshatre
ctangulum toper 9, e N, aequale qua-
deato FP, eric SX maior Y, nam
maior eA quam sE R S. quarC S PONatuE
Y ordinarim ad diamerrum FD, cadec
super rectam VP. sic igitur illa Z X 3
e O regnalis ap. quod G itaque ni
ec F.L. normales linc ad alzmpeoros
pacer propolicio, cum n p Posica sic X qua-
lis a. _ vihilominus F. L osten(a (c il-
la mnor: a normalibus enim ad asympro-
eos ductis à sectione, de lumicur alympro-
corum à lectione distancia. Duodh a pen
F L non Cinc normales ad FIL, CX X _ F
ducancur normales XB, F Y. cum icaque
Ap _ B D, icem AB, d F. Y parallela
SInC; dE anouti a uB, F L Y aequales, e camen lacus au ostensum sicmaius esse la
cere FL, etiam reliqua lacera reliquis laceribus, et AB, latere P. Y maiuserie, ergo
distancia F. Y minor est daca 1. Ouodtuir demonstrandum.
PROPOSITIO XIY
Nculum AC Blabcendat HIIICa AB, qua bitariam in Ci diuita, po-
adantur AB aequaes DE; qua in s lecenrur, re Dt F. rC-
etangula dcaa  Guatato A6.
Dico C F F ad candem esse hyperbolami.
   t 1i
Demon-
1
11
1
stitesti ti tu uis o supit