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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 221, page id 1815201908:0278
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averbu
ut Eit 3UG 1MIIBS A
S.TEII LCE dEAS:
DCeraque cheoremara, quxe in hisce prolesomenis adteremus, proponi criami ac
demonstraria Sereno Antinsen i Philosophoac Creomerra, Mololecundo de le-
ctione cogi. Omminomihi memoria exciderae cractaram à Screno candem ontema-
ceriam: jam enim agnilunc riginci ee amplius quod auchorem on seerim.
Velimicaque, qui hac leger plasii reum niene faciac; sedcogicet, l demccps tor-
caste quaedam mihi cum serenus communia occurrene, mihicadem, pa DerenO
olim, pouisteincidet
TR orerbacp A3 eb  
OPIOSITXYO PF
Ncono scaleno st a vercicesinea ad perpendiculum aetmutatur, a pet
dverricem, cencrumbalis; ac punctum a perpendiculo denoracu pla-
num adacuE, p ilcop il e oyHstan AB EHI
Dicocriangulum per hanc sectionem Factum concinere maximam de
minirmam linearum quae in Cuperkicie conica exhiberi postunt.
Demonstratio.
Riplex est hic catus: vel punctum perpendicu.
lo denocacum incra peripheriam baleos ex-
iltic, rel in ipsa peripheria, vel denique exrra iplum
circulE. Pro primoioicaE Ca(U BONAEUECONUS AB C
e baleosceneruim Fi: vertexaucem B: a quo demis-
la perpendicularis, occurrac balinera peripheriam
in puncto D, perquod ec per centrum, agatur Pla-
num quod pertingac rique ad B coniverticem; ex-
hibebichaec sectio criangulum A B C: nam ex COn-
Aructione coni BA, BC sunc redtxe lincae; octenden-
dum est icaque AB esse minimam omnium linca-
rum, BC rero maximam quae in luperticie conica
existunE.
Ducta quanis B G siponatIE ex G re- l15
eta GDF; quoniam ADC per centrum B
EPANSIE, exIE A D minoc a quam C D rHCII
e quadearum AD, minus quadeato CD: MC
addiroque communi quadrato DB. 5 quar 1b∞,
deaca AD, DB, minora Cunecquadeacis A.
ED, DB. angulus aurem GDB D rectus RAMC
est, quemadmodum e angulus ADB: igi-
cux quadratum AB, aquacur ciquadraris in
AD, DB, quadracum vero GB aqua-
cur quadratis CD, DB. ergo quadeatum
AB; minus est quadraro CB. ergolinca
A B minor recta BC.
Lodem pacto oltenderur recta BC om-
nium maxima: ex puncto quippe quovis F,
S duCacur quaevis FB: _E PeF D PONAEuE
5
FD, quia AD C peF CenErUM EranSE, sD C maior est quam F F. vnde quadraca d7. terrii.
CD, DB maiora lunc quadracis ED, DB, sed cum rurlum anguli CDB, FDB
Eincrecti, quadrarum CB quadraris C D. DB, ex quadrarum F B quadrais FD.
ADASE CIZEOM ES CIONY
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b oup ni  Eitris exuxili Si
anlu he zygeresoib
er odito sid A.) OuL
D_PMM
ED EisC ZL SIB
5i
2. criu.
e L dblia
13
15
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1