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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 643, page id 1815201908:0700
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2914.
es CV
2
1
N O
auten
ett 61
S
bolam
rainde
angu.
AOC
CII.
tis A
aequi
xper
qi
L. XI
B. VI
160.
Or.
ua.
AYP ERB OL A.
Demonstratio.
Scensum est propolcione 2n2. huius GG, TY
esschrperbolas, reltac igitur ve octendamus
illas oppolicas esse sectiores; quoniam R E lineis
aQUalES PONUNEUT F C vel FTL, X DCF Xqua-
les E FT, rectanoula CFP L ae qualia sunc rectan-
gulis FF. D, id eA A E B; igICHE VE A F B ad AF B
rectangulum, ica est rectangulum O F Iad G F L
rectangulum; oppolica isitur lunca sectiones (C,
TE, cum nC AP B, _ HIH rectaelinea.
PR OPOSITIO COXIV.
irculum ABC concingAHE AD, CF
ixquales e parallelae; coniuncta aurem
DF. dividatur in FF punctis; per guae po:
MAnEUF FG, que aequidictent AD. Rantq
rectangulis B FC aqualia quadrara F FI.
Dico HLH esse ad eandem hyperbolam.
Demonstratio.
DRoductis GF, AaNE FN aqualCS FHT: _
Ponaneur PN _ OR, aequidistanteS DP)
incelligaeur insuper duci quecunque IRV oc.
currens circulo in V de Z: quoniamisieur 1O.
TK, TE, proporcininles sune ex anguluS FIR Cx
hypochesi rectus, lincae PZ. FR, L V b propor-
cionales sune, vndle ZFV rectangulum, id ese
BF C3 aequale est quadFaTO FK id cA. quadrato
TK vel FP; id estirectangulo SF T vna cum
quadeaco F Iid est SO, id est rectangulo B. SC:
recrangula igitur BI C id est ex hypochesi, qua-
deaca FHI; maiora lune reccangulis SFY id cst
quadearis FP: igicur F II quadeara xqualialune
quadracis F P vna cum reccangulis NVPHI, (ede
FH quadraca, id est perihypochesim reccangula
BF C, aqualia ostensa sunc rectangulis S F P vna
cum recrangulis BS G, ablaris isitur aequalibus,
nimirum quadeatis FP; de Fecrangulis SFT,
manene BSO rcccingula, id est quadrata 5.
vel PK, aequalia reliquis N P H recrangulis: xC-
E∞6O.
crangula iBitur N P H id est R M K, aequalia sunt quadracis P K id eA FTM ~ qu’ a puius
re puneca HHt ad chyperbolam sunc, culus soxpolica ett NN.
sel PROBOSITTO CCZV.
d36. had:
ins.
IE A B axis parABOTL M LL, ad quem ordinaLIII pONANEUT F; C D X-
Dico AD D et ad easidemhyperbolam cuius diamerer A B; d lacus
raciluectum lacest recto pusab olà ate a quale.
a EX
Detor-
quales rectis AL. L3tnag1