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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 95, page id 1815201908:0152
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=152
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.77
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

San.
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nest
Prinus
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nalo.
iIK
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AC; A
rd
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GEOML =RIC X.
PROGRESSIOMVM GEOMETRTCARVI
L a
O
S F
Terminum culuscunque proeressionis in infinitum continuata desienat
L LdtLe Laa
IFuerit magnicudo AB, ad magnicudinem B K, vemagnicudo B C ad
Omagnicudinem CK.
Dicoproporrionem AB ad BC, sinc termino continuati actu pollé
incramagnicudinem AKE, ica venum quam ad IL perveniatur.
Demonstratio.
FTacenim ve AB ad BC, hC B C ad F. quiaisitur AB eA ad B R, veB C ad C K,
cric alcernando ve AB ad BC; id est ve BC ad L, lic BK 2d CR: ex rurtum
alcernando, veBC ad BK, licP ad CR: quare cum B C ex daeis, minor (IC, quam
BK; Cric eriam L, minor quam C R: poreric ergO IpAL, ex C K Cumiaqualis CD:
crancautem A B, BC, L, ires concinuae proporcionales; ergo _ AB, BC, CD treS
Cunt continux. Fiat iam his cribus magnicudinibus continue proporcionalibus AB,
BC, CD, quarra proporrionalis concinua M: quoniam isicur paulo ance ostendi cAe
BK ad BC v CK est ad L; live C D, eric dimidendo ex inverrendo, BCadCR,
Ve CD ad DK: eodem plane discurlu octendam, M esse minorem ipsa DR, quo
ance L Octendi eite minorem ipsa CK: porerir ergo ipsMI, ex D K abscindi D F xquia
lis. Sunc igitur quaruor magnicudines AB, BC, C D, D F. concinux proportionales:
Reque ica demonstrabimus proportionem AB ad B C, inera lineam A R fINC TEF-
mino posse actu concmuaris ita re nunquam ad K petuemiaeur. Ouod erac demon-
ArandUI.
R OPOSITIO. LXZVI
IFUCTICMIASHILaO A B, ad magnicudinem B K, remagnicudoB C, ad
dmagnicudinem C Is; e proporrio AB ad B C, concinuetur in magni-
cudine AK; per plures Terminos CD, DF, E F, _C.
Dicoctiam CD, Tore ad DK, et D F. ad F. H, de sic deinceps, vt AB
eAt ad BK e BC ad C K, _c.
Demonstratio.
sic CD, ad VR. non alicer oltendemus ve CD ad DR, SC cA0 D E Ad ER3 aF
que ica deinceps in intinicum. Quod erar demonstrandum.
Vandoquidem AB est 2d BK, BE BC ad CK, eric alcetnando AB ad BC
Lhoc est ex datis BC ad CB  K al CR: de rurlum alcernando ac inver-
rendo K B ad BC, vei R C ad C c Macnao seecendo, bee aCR,
P R O