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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 20, page id 1032977698:0042
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# Lines: 37 recognised, mean confidence 0.86
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eC
L F N VI AI A
ver generisintinicam sem ad determinaramr, ut insiniresi.
mam adnihilum eomerricum, et e converso; est enim
quarca proporcionalis,
emm quae inre geomerrica pronon
quanto est habenda juZFA L CMM. 10.
ZI. Quare _ quicquid per insiniresimam mulciplicq
cum, per infinicum aliquod dividicur, nihilo aequiraler:
ZII. HIinc B aequationis expolicae cerminos quoldam
infinirum aliquod mulciplicaverie, aliique sine ex merje
decerminabilibus quanticaribus composiri; omnes rermini
infinico vacui ex aequarione porerune, nihilorum ad instar
rejici; sumro enim in pro numero infiniro sc myy +1,
=pX x + mrx + num.
Dicofore myy =mextnum. Onde dirisis permerie
gy = rx + nn: rejectiscerminis P X X X ly, tanquam in-
Anicum non continentibus.
Demonstr. Cum enim, existente uE SuPEa, ly =F myy
=PX +MFX +mun. eric, bis Facta divisione per m,
 = PX X = r X L nn)
m
nim m m im m unde, per Lemma 10. rejectis
rejiciendis, ac ductis omnibusin m, remanebir aequatio,
γy =iYX = nN, 4. C: d.
XITI. Fodemmodo probabicur ex qualibet requatione
omnesterminosper infinirum aliguod dirisos, caereris om
niinfiniro sive mulciplicanti sire diridenti immunibus, tu-
copollerejici, coraenim eguatione per m divitâ, hisoli
cerminijuxca Lemmaro. nihili ad instar consideratipore.
FEIC.
ZTV. Tum E cerminos per intinicum mulciplicatos,
rurlumque per intinirum divitos, pro decerminabilibus
m
habendos, est enim = l
9m
Hlaec antem ale olatibo