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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1096, page id 1815201908:1153
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1096
CONOIDES H FP ERBOLLCVM
Demonstratio.
TT est GF ad NM, ita est BD ad OB, hoc
est DF. ad OI, isicur ve eA G F adNNI, iC2
CA D F ad OT. Amilia ixicur sunc criangula maxi-
ma CBF e NVIM, Parabolis inseripta, ac pro
inde corumracio est duplicata rarionis lacerum
CF, NV M. Ced in libro de parabola demonstracir
est aparabolas cam incer le habere racionem qua
triangula maxima inscripca. ergo cciam para-
bola GF F ad parabolam NIM in duplicaca
cA racione C,F ad NYM. Quod aurem criangula
Praedicta lincmaxima, guae inscribi poltune para-
bolis NIM, CR F, SicOAendo. PI, D R lunECO-
munes sectiones plani ABC recti ad basim
AGC, cum planis RTTI, CF F, etiam rectis ad
baAM. CrgO 19. IF. L I, DF CUnE rectae plano
AAC, C. ergo detin. 3. II. cciam recta sune ad li.
neaS KHI, FC. ergo Cunc axes parabolarum
RIH, OEF; liquec exgo b criangula NLM
CPF maxima CAC.
PROPOSITIO CCII
IC ABC rriangulum per axc com ductum, rectum ad balim BDC,
_ sectiones parabolicaDL F, FIC exhibences communes cum crian-
sulo BAC. sectiones HL, tII. Deinde planum agatur per A e rectam
FC, producens in parabola DL. E. Secrionem MI N.
Dico parrem coni AMI L. N ad parrem AF IG, habere rriplicatam ra-
cionem BH ad BH.
Demonstratio.
Scelntam est in praecedenci racionem para-
bolX M L NY ad parabolam FIO cNC du-
plicacam rationis F GadMN, GuCLO ad IFI.
hoc estrarionis AL. ad AI, hoc cAracionISBK
ad B FT. Ced manifectum quoque est parcem coni
AML N ad parrem coni AF PO, racionem ha-
bere compolicam exratione balis ad balim, e
exracione alcicudinis BHI ad alcicudinem BK.
Isitur A duplicaex racioni BR ad BFI, alcCrA F2-
eio BK ad B FF, addacur in sen su mulciplicario-
nis, resulcabie rario criplicaca rationis BR ad
BH. Quod tuir demonctrandum.
PROPOSTTIO CCITI
Riangulum AB C peraxem conita-
crum sccer normalirer basim BF. C;
centro baleos D erigaturDF, paral-
lela AC; limilirer ex quovis puncto dia-
mecri
8
1oa
B Ibia. Pro-
10s. 227.