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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 39, page id 834940469:0047
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=47
# Source image: https://digitale-sammlungen.gwlb.de/content/834940469/jpgs/default/00000047.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.90
# 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.

Perici AB. C D, nempe Z, minor erie rerminatione serici AB,
CFP, nempe L; acque exhuius7 rerminario seriei AB, C, II.
nempe X, ae qualis esminori duarum mediarum arittimerice
concinue proxorrionalium inter A ec B, d idco . cademmi-
Ror est, quod demonstrare oporruit.
B R OP. XXV. EH EO R F M A.
TIdem Posiris; dico Z. leu secton
rem liyperbole minorenr esse
quam minor duarum mediarum
Seometrice continue proporcio
nalium inCer ASEB: INEeF A eC B
sic media geometrica C, d inter C
de Bmedia geomerrica FI, Icem in-
cer C _ Hmedia geomerricaM,
 incer Mc HImedia seomerrica
HI; continuerur que haec series ConvergenS AB, CTTI, M N, O
P, ec, in infinirum ve hac ejusterminatioZ. Latis paFCE CX
Praedictis C C esseincer le aequales, de ITimaiorem esse
quam D:acque ob hancracionem M media geomerrica in-
ter C: e TI inaior est quam E media geomerrica inter C d
D. Deinde Nmedia seomerrica inter M de FI maior estme-
dia harmonica incer casdem; de quoniam M maior est quam
F X FI quam D, erie media harmonica inFeF M de TI maiOr
quam F Media Harmonicaincer F Se D; proinde N media
SComerrica inter M CCCI maior orie quam F. eadem methro-
de veramque seriem in infinirum concinuando, lemper de-
monstratur terminumr quenlibet seriei AB, C D, minoremr
esse quam idem numero cerminus serici AB, C. FI; de igitur
terminracio seriei AB, CD nempe Z. minor erir quamtermi
raeioseriei AB; C=TT, nempe Z; acque ex truius oterminario
leri ei AB, CFFL. Peir X, aequalis est mivori duarum mediarum
Geometrice concinue proporeionalium inter Ae B; d idco
LCademrminor clt, quod demonstrare oporruic.
E.x dictismaniteltum est hanc approximationem exactio-
nem ese illa, in ancecedenti proxolicione, demonstrata, erit
(BICC