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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 19, page id 1032977698:0041
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=41
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.79
# 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.

nis
is
est
nH
1d
5
red
ce
Ai
n
ri
1It
O
111
0
est
3
il duc eia at aa  suc
Exiguo, sed in quantirare, cujus ulcerior diminurio actu
concinuo sine Rne perapitur, consictere.
Ouibuspercepcis analysiinfinitorum in Geomerriâ Cne
lapluspericulo ucemur; cum nihil hic in concinui divisbi
licarem, e incommensurabilium asuminerriam, quibus
Scopulis altisa Indivisibilium Mech odus nautrasium pastura
videbatur, commissum BIE.
I. Pollene de plura, ex prosrettionis infinire proprie-
care, circa numeros intiniros demonstrari: Verb: er: Si in
monadicorum proprestione singulicermini, seuunitares,
ducancur in secerminatam quandam quanriraremr
eric, si cerminotum quoriras aue mulcicudo sic =m, summa
hujusproprestionis m. In omni enim proxrestione 
qualium, cerminorum agsreparum quodlibee equaturret-
mino unico in quoricarem terminorum respectiram ducto.
quod sacisnorum est.
VTT. Pacechinem numerum simpliciter infinieum ChenC
cum roco, quioritur ex proprectione infniris quidem, sed
merisumicaribus constanci) per quamsibet quanritarem 
mulciplicatum auc dirisum, extibere numerum alius se-
n
neris infinicum im aue; quiad primum in decerminatam
tiaberrarionem, uE L ad unicarem, aur urunicas ad l.
YITI. Ouin _ hinc apparec, quodvis infinicum pm.
ce summam propressionis equatiump, cujus rerminorum
quoricasinAnica est seu L m; estenim,
Pm = p. + P + P F D F p. D sie continuo ad sque cessatione pereen-
do. JuxaW. 6.
E. Nec opusest, superioribus intellectis hoc etacuni
adruere: omne scilicee infinicum insuo penere, aualy-
rico esterri, per quancirarem decerminabilem in n seu
numerum infinitum ductam; siC, Dm, RI, ym, am,
deC. Tunr singulx, sed sui generis, inRHIEX quAHEIEateS.
2. Exquibus consequicur, tore quaneicarem enjusti-
be