# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1032977698:0307
# Permalink to this reading: https://leibnizlegible.com/page/1032977698:0307?run=74
# 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 285, page id 1032977698:0307
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=307
# Source image: https://digitale-sammlungen.gwlb.de/content/1032977698/jpgs/default/00000307.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.89
# 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.

501
CAP. VIII.
Analosis Infinitorum.
Corol. T. Cum DH ac WV Y leu omnia e aUE dX sInE
aequalia, ex hypothesi, (I+ Tcu TD sic altignabilis, d
vero seu summa ipsarum dx, auc 2, constet numero inti-
nicelimarum finiro, eric juxta lemm. hujus I. Z infinicesi
ma; quam ob causam e h ac b, (cum casdem, non plures
salcem, numero insinicesimas, ac Z, ex constructione
Contineant) paricer Fucura sune infiniresimae; unde
per lemma 10. termini B~, ZX E bc nihilo fene xqua
Les, remanebitque ye = +x; quamobrem, cum ex equa
tione prima sic y e= ta, erit a= X; unde idem, quod
Schol. hujus TI. Corol. II. crictum Fule, denuo sequieur:
nimirum, si omniae seu dx Cune xequalia, omnia a seu dy Fore
equalta, quin _ extera, illic loci permethodum inductio
niscradica, hinclexirime collisi poNtunE.
Corol. TI. Si verorum Z, cum B, cum b, constent nu-
mero infinitesimarum infinito, erune singulae harum juxta
lemm. IV. hujus, ex quancitarum altignabilium genere:
quare nullus in xgnarione secunda rerminus eranelcit, a
hoc (ol0 in Catu, POstis, nECirpra, ax aqualibas, intes
ipla dy interceder differentia; allumedquea majori ip(des
exIF a - = =
e bc
e  B. L 1 +Z
Cujus disserentixe propriecares accurarius incasanti pa-
tec iplam eNe natuTa TUa quancirarem infinitesimam, seu Fer
mino Leibniciano, differencialem, neuriquam rero infinite-
simae insinicesimam, aur differentio disserentialem; quOd LAMEM.
Si Calculos differentialis quanciraribuspure disterencialibus
suxta celeb. Leibmnium applicari debegc, requiri videtur.
Niti alio luri credibile CA) prortus Fundamento sua de
duxerie Vircrudicissimus.
Schol. III. Sedulo discrimen hoc accendendum rectat,
num infinicesimxe, si una pluressimul considerandae veniane,
numero sine siniex, nuin vero intiniex, cum hac quidene
cauteld accurare adhibiea plurimae objectiones, quibuscal
culusquiliber infinicesimalis urseri alioquin ridetur, (pon
ce dispareant; neplecta rero, nOn exipua quanaoque
 MaCCANE.