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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 409, page id 1815201908:0466
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n
PIA RCACBSOMLIAS
109
ad HE, quia vero, Y G, IF (id est IP) _ LIF proPOrtionaleS TuNE, VE FFF ad L L. L A2. Bulas
cuncu, ad LI. rria cum PC id est P C, SCCUCAM CMMI TCFEIA, IGIEUE VE A D ad DIF;
esit ad Ii cis Ociod etacdemonstranduni.
Occurrariam diameror FF C rectae A B in L iner2 paFaBOIaCMLIBICUEVEA IL 2d
siuc IE: Pema ad sccundam, sic TII cum IF vel IF, id cA HIF, penna cum le-
AD, HC HTP at B D; id oA 3dIYY, _ rE AD ad TTD; sic FTI ad TF, sed ve HITad B ibid
Sirver AD ad DTI, liC FIV MM Al L. C+
TE primaad secundam (quia HIL, Ifi. TC oPoates IAC) hC Hl. ett ad L C fpr
Est HXC Arehmedis prop. 4. Ae quadracura ParabolL aliter demonsteaca.
eressionit
etd = b. 2FL 3y 01303 Corollarium.
Tlic segulciir lincam AIL A LO, PatIOHE HberC duplicatam eius quam ha-
ABeC HFi 2d F C: cum enim sinE COncinUIR proportionaleS HLL, LL, C+ L, CHL dLX 9B
Arabolam AB C cirins diaM CFOFB L, CMCMIE AbLI B IIIVA VL, qua
haius
1. DCPr
rtiniu
ratioHL ait LO, duplicacarationis HII ad PL, id cst. TTF ad F G.
20BOS
divisa in F _ G, ve BF; BG; BF I ROPOrtionales, demitrantur
diamerri FH, CI, F. A dictat ex A ad BD ordinacim linca AC, qua
F FF CI rectus secer in Y d L a8a per  ea CM occurren
EI, Ct diarpeeris in M _t set i
Dicorationem L.M a   Lao 1, alt 1NL.
23gemil
it cit
oloctis.
l osacto.
leti
d:dI
LuZerC
cacaitihabecratloneni; L O A OII (CuM L F, FO, LEIS proportionales RInE) e +2 huius.
id es per pexcedencem F _t ad M FT; Similicer & K C+ ad CrI, duplicacam haber
eius quam habec RN ad N F, isicur e ratio LMadMHE, duplicaca est tacionis
K N ad NI. Ouod crac demonstrandum.
= et2d22t E1
IIdCM DOMEI ANCACML HINCA A B LCCANS F L lineam InO.
LDicoMHLL F rectangulum esse equale rectanoulo AIL FO.
Demonstratio.
Voniam BF, BO, B P linex continux proporrionales sunc, diamétri quoqué
LFH, OT, E A in concintia (uNEE an 3IOZ IA. LVALC FacIO AP 2d F FL, id est L. F adF F  17.
EFI, duplicaca est rationis AP ad CI, id est R C+ ad G+T; sed L F 2d F FF, duoli- huins.
romam talioL alCaaapiCaca cierarionis L. M 2a MHL, quam Li L ad
LFO, CFIEVET, M adMTT, SICF P ad FO: quare rectangulum MIILiFi aequale
estrectansulo M L F O. Quod erut demonstrandum.
FEE
PR O
6 oOrag
111
eaeoec