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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1217, page id 1815201908:1274
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.86
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pedum ex bali rectanguli B M O, _ altC MI R ad parallelexipedum
1217
QV AD R A Y V R AI H Y BE R BIOF X.
lub balircetangule LL a Commun alTudine IL I.
demonstrato.
DEmonstratum esta rectangulum LMN ad V R S rectangulum; quadruplica- at, 8. 
tam cius habere rationem, ouam ooncinet rectangulum BM O ad Y R P. rC- u
ctanoulum. sune ducem paralleleppeda (ib hiscc BAHBAS d CoMMHIM MMuaIne
MR incer se r Pranet baleS. Txitur Pacet propolcionis veritas.
Lo1ooiio eat.
Adem ROUFA manenEC:
Dico rationem parallelepipeat, quoa ex balu rectangula L. MI. L
ad parallelepipedum ex bals  ke3 coninete collesrationem parallelepi
pect super bali OM P per mulciplicarionem ad parallelexipedum (uper
baliteltanguli XR T, quocies rario haec per muleiplicationem contince
rationem pataltese pipet tuper bali rectangula B Mt O ad parallelepipe
dum, quod sic luper ba(i Y R F. rectangula, modo eadem alcitudo omnii
bus parallelepipedisin seruiat.
Demonstratio.
Dipedaautem, de quibusasimus, calem Corciuincur incer se racionem, quam bales
rectangulares super quibus crecta lunc, quoniam alcirudinibus conneminne ex hiypo-
chell. Patec idicur vericas aserrionis.
DEmonstracum estbrarionem rectan an LM L  ecaM VL 33. Coles 6159. dt
continere permulcipliedcionem rarionem rectansun OM P ad Ll L, Guaies in
hiaec racio continecrationem. BM O rectanguli ad rectangulum YR E, Patallele
LAOPOSITIO CXLI
X Scemaribus viiuersalibus quae incercipiuncur parallelis By, C 8
sconsticuancur ordines sex Agurarum, quarum cernae inscruiane hiy-
Perbola, alix vero circulo. Luma eton Patavoau Conekar
dem lacio parallelepipedorur comer rarionem parallelepipedorum
quae tiunc exrccanguls C in C a D in H.
dinila sic parallelis qua exhibeane rectangula quaterna ABC D, e
FPOTI. Secunda aurem AOUFA AIGNa LOTA LCCCA MIICa aBBAICME (ecta (IE
parallelis iildem Formancibus rectangula PIEL. MI _ NOPO: Terria
qua Constiruant rectansula 1E3 LV a XYZ.
denique in qua cernuntur parabolx coneaux secta lic ii Idem parallelis,
Dicoicaquerationem duorum patallele ecotum qua sam ex ltu
X rectangulum, e ex rectangulo S in Y ad duo parallelepipeda Orea ex
ductarectangulorum P in Z d t in X, cories continereracionem pa-
tallelexipedorum ex lin N, de ex rectangulo IE in O, ad parallelepipe-
da exductu rectanguli L. in P, ex M in 9 rectanoulam, quocies haec ea-
quae signuntur ex ductu planorum A in P. ee B in F, ad parallelepipeda
Demon-
 ae o   a