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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 947, page id 1815201908:1004
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G E OME TRLC A.
racionem datam. Se d postularer eriam praeseneis libri maceria parriri rarionem dacam
in parces xequales, que Facta mulciplicacione incer se exhibeanc rarionem quam com
bonunc. Sed cogormateriam illant ala cempus ditterre; cunt de Valctuo praeci
picare cogac quod prx mantblis habeo, ee imperium rrseac illorum quibus ob.
moxium mesccicrelisiola Protetio.
PR O POSILIOCLIX
A
DOnAnEUF dux CeriCS GUIGUE qUANEITAEUI I CONTIMUAta ratiOne
Dico rectangulum AF ad EK, auplicatam habere cius rationem
quam haber rectangulum BC, ad Dl rectangulum.
Demonsirati.
B, C, D, CiF, C, H, I,R.
ponacul, ectansala dd LR rario, elt duplicaca cacions BC reclansuli ad cc.
ctangulum D L. Ouod erac demonstrandum.
Eatangulum A F ad R R rectangulum composicam habet racionem exratione
Aad E, hoc es: duplicara racione B ad D, _ exracione F ad K, hoc eAt duplica- 2P
caratione C ad I. igicur cum rectanguli BC ad D Lrario ex ijidem racionibus co. huius
ROTOSINIO CLX
Inc dux serieserium contitua tM. A, B, C, 0, C1.
Dicorationem C. A duA In FatIONCMFD, OupCatam extribe-
reracionem cius quae letur per ductum rarionis B A in L. V.
Demonstratio.
LLAEDEF ad D, ita A ad H: d V
 ad D, ita A ad G. Torcurracio
C ad FT est aequalis b raTIOHI C A,
ductx in FD: ee racio B Ca qualis
est racioni B A. ducx in lationem
iivo
F D. sed racio C H duplicara estracionis B G, nam rario C FL componicor exracio.
nibus C A, AFI (hoC est ex construet. FD) quae duplicare lunc racionum CB, BC
hoc est FF, ex quibus componcut Laco C . Igicurrario C A ducta in F F. dupli-
ala o DA  i L. V. .
eO51210 CLX1.
abencium primam A.
Ine dux series continue proporconallum candem leu x qualem la
Dicorationem C A ad rationem C A habere eriplicatam proportio-
Remeius, quam habec rario B A ad rarionem F A: e racionem D A ad
racionem A eriplicatam habere proportionem eius quam habet rario
B A ad rationem F A. Acque ira deincepsin intinirum.
15+
Demon-
 e e e et sute at. atset ei  a p  ste e t el ente de e el at ute e e t     Ao a t   . 1 t t  ett  .  t A          p  pi