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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 459, page id 1815201908:0516
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co.
est
IF.
F
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etat
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td
Fan.
tio.
P2.
ndi-
den
EII
BC
Demonstrata.
P A R A BOL
Veatur HFO parallela AC,OC.
rrens ND linca in O. Ouo-
niam INT; CI, aequidistane lineis
1) O, TTO: est aucem e G MI a Requa-
lis e Parallela D HI. criangula FC NI
cuddedqca
aequalia lanc: Ck aucem IIK _9
lisON. Ixirur ∞I, IIK simul sum
pere, lunc aequaleS HINCX DN.
PROPOSITIO CCMAII.
IEad AB C parabolx axem BD ordinatini dueta AC, acta que per A
LD_ C, continsentes conveniant in F. Ponacur auten de FC conrinoens
in B, qua AC, C F lineas secet in F de C, cum rectae detmirraneur FI
CH axixquidistantes.
Dicocraperium F LIE O, xquale esserrianBulo A F D.
ul
Demonstrario.
DOnatuE FF. paraHlelA AC.
IEIBSANEUEqE L A, FK.
Ouomam F L aequidistaE AC,
de LK est b a qualis AD, dimi:
dioc scilicee AC, triangula
ALD, IF R equalia CunE. RuF -
luni cum in criangulis PRC.
AV. L, taM baseSdR G, F. T
quam alcicuclines CTR, AD ∞
a
quales sine, Eriangula quDque FK C, A P. L. lune Met D aequalia: crapexium igitue
LIK C aequale eseriansulo AF. D. Ouod erac demonstrandum.
PR OPOSITIO CCZXV.
a cunque, ponatur aucem per A concin-
sens AD, coueniens cum C D diamerro in
D: Ponacur quoque diameter queuis BC.
occurres AD linex in F. IUnOanEuEG; AB.
Dicocrianoulum A F B ad crianoulum
AD Ccriplicacam habereracionem linea
AF ad AB.
A.O
Darabolam ABC TubFendaEA C que-
Demonstrario.
LMMIa CX RLAIAMCETO A L; AUICAMIOENHEK
FreltG CIL, BThormales ipli A D. ratio A F B
crianguli ad erlangulum AD C compolcd elt ex
racione A F ad AD, e ex Fratione IB ad FIC)
sed vetBad FTC, sic FB ad CD, id est AR ad
AE;igicur racioerianguli AF B ad AD C erIRM:
eulum compolica eA ex racione AL ad AD; e
exrarione AR ad AP est auceratio AR ad A B
Mmm 2
Bll lPacallela comcinsenciaalalis
v
n
2t
ea
111