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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 394, page id 1815201908:0451
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394
P AK RBOLH
 S. Clrii AX ∞3PXitC, 1 13 . D e la et s. 2B 3123, :d Y L∞ E A gcust Ccn
. 2.2 Demonstrario.  bi D Br. e L
VONiIM GF, FTF, CF proporcionales sunc, TPF est ad C F, vE G F ad HF.
LhOC CADE A F ad HIF, hoc est ve AB ad FTB: igicur diuidendo FTC est ad
CF, ve ATY ad HB. Duod erat demonttrandum. I utisctqrautl
ic
ai
L.rmuou
DArabolam ABC cuius diamerer AD, _ ordinarim ad illam polica
CD, Concingat in A linea AL, quam in P. secer diamieter C P. iun
Ccilq; Pinctis AC, ducatur diameter guaecum que F C, Sccurrens parabo.
Ex in B. deinde act â per ornam linca HIl, gux F C FeCtX OECUIEE
(nI, e AD diamLI cCatuT ex Glinea C3R parallela D C+ ilu
Dico Varaet cut L. B ae quari parallelosrammo K B. 1: 91 HIV
31 111
1. (.C
n il Demonstratio. colo mmo
1p
L1. 2 115 et el 12. C EH
JT AC ad GC; sc AF ad FF, id est HB 1d
BI: SedvE 2 AG ad GC, SiC F B ad B C: igi.
TUE VE FTB ad BI, siC FB ad B EF; TUNE aUECM An-
suli ad B oppolici xquales. igitur parallelogram.
mum F. B aequalc b cs paralICloSraMO K B. Ou0d
erac demonttrandum.
1M1
1
PROPOSTTIO LXX.
i
IE ABC, parabola diamerer AD divila
DIn E _C F; VEAF, AF, AD Cint proportio,
DicoFTCrquidiltare diamerro _D, _x contra (i HI C xquidistet dia
MEETO AD, X Pet LL OTMMITACHM POnatuE FB, dicOAF, AF, AD eAeprO.
Demonstratio.
Vm AE, AF, A D proportionales UnE, recta
quoque cCD, B F, C L in concinux Cuncana.
10gia. sed de DC, FB, F FT d quoquE TUNEPrO.
porcionales; aequalesisitur sunc LF F, GF linea.
quare HIC aequidistate diameero AD, quodtui
primum.
Siciam ETO patallela AB, e per EE ordinarim
applicetur BF; dico AF, AF, AD quoq; in con-
L+. Mm. Ma esse analogi Cenim CD, BF, FTF, linex sproporcionaleS LInC, et GF, X
GaecE HIF, CrunE _ CD, BF, C F. concinux proporcionales. vnde AD, AP, AB
35. SI Conciua quoque lunc analosia. Quo d exat demonstrandum.
nt
ER OPOS IFL LALI
eLO
POSITIO LXIX
nales, policilque ordinarim F. G7, F B, DC, iuncta AC occurrat F B in HI:
B Percle-
penta.
Porrionales.
C 33. Mitus.
842. huius.
cPerel
nen
Percon
SeoA B C parabole diameter AD, quam in D secet ordinatim linea
sC, act aeee pe  aneto C F, ducarur ex A linca AF (ccanS
Parabo.
A e quete   ate es . 1 . 1e s  t e     1 .      1 1 .  1   e e  1  e  .  e. 1 1    1  e  1 11 61.      e  t t  p