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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
# Folio 18, page id 1032977698:0040
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.92
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N
Scholium Generale.
Om nullus existat numerus, qui inter proxressionis
Arichmericae: X, 2, 3,4. eec. terminoslocumnon in-
veniat; Anculiq: hujus prooressioniscermini peneren-
cur expropressionis monadlex respectivisaperceacis; pu
merum quemliber, sub specie sunimae proprectionis unira
cum, considerari polse hoc ipsopater. Onde sequences.
_ alicujus in hisce momenei, numerorum proprietaces
emereune; nimirum.
I. Obiunicatum hxcpropressio subsistit, iptarum appre-
eacum numerum constiruie determinabilem, ac per monadi-
corum proprestionem cerro rermino cellanrem denorgn.
Sutm; verb: gr. 2 = 1. + 13 3  1 + 1 + 1, _C,
TI. Ubi vero nunquam subsistendo progredieur, e in mutri
rudinem rerminorum omni dererminabili majorem alsurpie
haec propressio, aggrepatum unitatum numerum constiruie
omni dato majorem: m, hac de causa per proeressionem mo-
nadicorum nunquam delinenrem exprimendum; veluE
m= 1 + Y + Y X r XC d sic concinuo absque cesarione perzendo.
TYT. Cerro rermino subsistens monadicorum proprestio,
adeoque numerus decerminabilis aliquot prosresionis unuates;
nunguam desinenspropressio seu numerus omni decermina-
Bilimaior omnes bujus progressionis unicaces comtinet.
YV. Numeri omni daco majoris essencialis propriecas.
aeratio formalis in perperuo accrerionis actu consistie,
subsistendo enim numerum decerminabilem cfficeret
(NO T.
V. Ouare, Siguantiras determinaca b dividarne pexriu.
merum omni daromajorem, seu continuo crelcentem, mo
eric tractio
in quantiras continuo decrescens; HRVeNEE
enimnumertrore, ac denominatore sine tine aucto, dimi-
nuceur sine Rie Fractio.
Onde insiniresimarum natura clarius illuceseie, parees
que iplas, non in dererminato quodam indivisibili, uc uc
exisuO