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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 162, page id 1815201908:0219
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=219
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
# Lines: 29 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

 e m  1
PROERESSIOHL.
PR OPOSITIO CEXXIII
Ara CE ve tupra cuborum Ceries. Oporret exhibere superkiciem om-
nibus superticiebus omnium cuborum progrestionis dacae aequale.
Demonstracio.
150. hums , TaC LTCCLAHSAM P FXGF aequale progrestioni quadratorum AN, BN, eCc.
cum F I sexcupla hac linex PII. Dico rectangulum FI esse id quod queritur.
Cum superficies singulorum cuborum conster sex quadraris aequalibus, manifectum
est omnes scriei cubica supertcies consticui ex sex seriebus quadeatorum A M, B N.
_C. aequi rectangulum FIF ex constructione seriei quadratorum AM, BD eA X.
quale. Ersolex rectangula FH, hoc eAt ex construct. rectangulum F I, consticuet
omnes serier cubiex dacae superticies. Fecimus ergo quod perebaeur.
PR OPOSITIO CLZXIN.
Aca sic cuborum prodressio sibi muruo insistentium, consticuens
toreliduas baltaa uperficies, nempe BKICHC, BONE MV
de reliquas omnes in intinicum limul Cumpras, quadraro primi cubi x qua-
les este.
ctontario.
Psladem cubica.
Elacenim seriei rarionis primae A F ad cerriam F. O aqualis V Z; lup ex qua in
alcicudine AEI hacrectangulum Za, Cumpeaque V X equali, A FY ducatur ad
Rectangulum a L. per 79. liuusxquatur leriei quadratorum AC, CL, F P, ec.
hoc est (quoniam cuborum plana omnia tunt quadeata aequalii) leriei quadracorum
AB. HD. OF. dC. ergo cum a X ex conser. quadraco AB aequalo lic, cric reli.
Quum BZ reliquae quadrarorum scrici ND, OF, ec. xequale. Acqui series qua-
dracorum
V a parallela ZB, qua abrenat suaca La asate Guaca +V.
 u u et s  a qul t e u u itt ut  et e   pui a ti i ut   pi e e   pen  e   1  a   e  e  pe e s  . p l.