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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 653, page id 1815201908:0710
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rant
aqui
uemal
BP
UE
Igic
haben
deca
alym
nAtrai
Paca
ClIS
DE
ico
ALXPERBO
DicosFeedd hrperbolam
cuius asympeoci luntA B, BC.
Demonstratio.
Voniam DD hyperbola alpm-
LpcocoshabecrectaS AB, BC; et
FectX D F. alymptoco AB aequidi-
canc, igicur parallelogrammaCDB
aequalia sunc inces se lune aurem p2-
rallelogramma CFP Cmilicer incer
sexqualia cum sinc composita exijs-
dem racionibus ex quibusparallelo-
jus alymproci lune AB; BC. Duodtuic demonstrandum.
PR OPOSITIO CCXAXI.
TInE AB, BC denuo alymprori hyperbolxe DD: ductis insuper dia-
merris BD hanc BE ad B E, in cadem rarione cum lineis BD BD.
Dico F. F essendcandem hyperbolam cuius alrmprociliine AB, BC:
  et s 1
Demonstratio.
Oramma G: D F. sunE Compolica, isitur eriam suNE F F ad candem hyperbolam cu- a EF 4b.
a
iind.
sulum F FB ad F. FB. criatomu d ete criangulum DEB, ad DFB crian-
eolum, cum linc tigure similes, ac proinde in duplicaca ratione lacerum homologo-
rum. Tgitur PaTEF eriam P. F. esse bhyperbolam gux alympcocos AB, BC COM verdum.
munes habet cum hyperbola D D. Quod tuic demonstrandum.
deseit et i
A PROPOSITIO CCKXXI.
DOnaneur enim linCX P P, D F quae alymptoco B C aequidistene: eric icague criaH:
acellipleos extrea actet AB maior, minor C D, policis au-
Lcem C. F. ordinarim ad axem AB, hanc rectis AC, aequales P, OII.
Dico AHH essc hyperbolam cuius diamerer AB.
Demon-
er  nrtu 
1IIIII