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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 2, page id 1815201908:0059
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1 1 1 11 1 11 1 pu1 1
sn
ru
1bs.
dian
nac
sit in extrema et media ra
. Circa
escrib
propor
uma
CINE A KV B
MIanE quadFAEA AB. F C. CL1. LII. ac promde ipla linex; quod fuit demon-
PROPOSIIIO
scur altera DO Occurrens AC, in FI. X circulo in C & I
AIrculum AB C conringnnE rectx D A, DC. et duct a AC, pon
b Ibid.
ne data rectae B)
in A, hebesi potest
H
li
strandum.
Dicorectam DC. Sectam esse
in I _E FI. VE SIE D G ad GFI.
quemadmodum cst DI ad IFI.
Demonstratio.
Vper 1O. diamerro, describatur
circulus ELK dt per HI punctum
crigatur normalirer FTL, vel FTK, ad
diameerum EFI; ponaturqueD L, crie
itaque GFII rectangulo, a hoc est
AFFC, aequale rectangulu L TTR,
sine TII quadrarum; percinene igi
cur ad eundem b circulum puncta
c 34. Ferry. Quacalu ae ancarectangulo C FIBid eAc ATIC vnacum
436. Sexii. Quadraco lO: id elt quadraris HIFi, F. D. vnde L. D. quadraco rectangulum dIDC
crib. 7. xquale; ac proinde cum PC. diameter sc circuli CP. I. exir per Pappumc ve DC 2d
er. 155. OFI. ita DI ad IFI. quod fuic demonstrandum.
Scholion.
L 35. Ferrii.
G, ita at secta
idu
tiaaque arcus
T AP C. iunctaisitur DP eAt aequalistangenti D A, ad eoque tangensinam L D
Lest: Oerapretium existimtun, auqd as peculiare nomen adiungere, quo illius coenitio
maris innore cat:; placut autem homenclaturam illi appropriare, sectionis linea. secundum
mediam ex extremam rationem proportionalem: quoniam similitudinem non exicuam habet
cum ea divisione, quae in elementis vocatur, ratio media ex extrema: differt tamen ab ea, quod
illa solum sit aequalitatis, haec vero de qua acimus, omnem omnino proportionem admittat: so-
roniam multories in hoc opere recurret divisco linea, prout prasenti propositione expolita
lam aequalitatis excludens.
dbeut
a
BC, D
circula
i
ac
um, quid
omnia DE
ari
todibitue
b extremo rdian
odem
et licat practa
ut F
nehan
aB
t
intr
potes
tian
ocales liveu
 tinecm
dati
h
a
ri
1b
tuta
aetd222 Al.
X Termino diamerri circuli AB C: luman-
seur arcus hinc inde aquales, BC. BD. e
ducta qualibet C F, qua occurrar perimetro in
E, POnatur DE incerlecans AB in 6.
Dico rectam FB. Sectam eNC in A e C. me.
dia e exrrema rarione proportionali.
Demonstratio.
Emonstracum invenicsoo CIECuIS, pro.
DOL. FOT. rectam BF ad F A. eandem habere rario.
pem, qua be erH. hoccittocam lB. ad alcerum
extremOrum F A, candem racionem obtinere, quam
C alterum extremunt, Dabel aumedium A G; ergo lecta es recta FB. in A e G.
eca  exrrema racione peoporcionali. Sccundaia explicationem praecedenei
cledcco cactalit
tal
fsiaatis anet cus
8
data re
uet 
 cus aelat
rapuncto G
 ut e e   te tut p  ue eta seteat  ut e te t t et e e  at  e uet   pt ut  se   t t ete e teq ue t pat t s  e    p s a p e spue