# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1032977698:0050
# Permalink to this reading: https://leibnizlegible.com/page/1032977698:0050?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 28, page id 1032977698:0050
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=50
# Source image: https://digitale-sammlungen.gwlb.de/content/1032977698/jpgs/default/00000050.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
# Lines: 31 recognised, mean confidence 0.87
# 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.

28
nalusis Infinitorum.
LAP. l
OuAECRC CKS, 7, 3 yy = 2 y X F k = X N: 3NX +
2y x + l=gy.. r: y. Ondereducta xquatione ob
tinebitur aequatio ad TaNGCNECM: 3y L 2 y y X
ky X∞ y F 3X X t + 2 y Xt Fl+ = y9+
Tlinc X in aequatione 5. 7, Femanenti prO a
iptum, pro e ipsum s reponendum ese con-
stat; simulque Fruditissimi Barovii methodus in
aperio polica est.
9. Nlotarirelim, omnes currarum aequatio
nes duplici terminorum senere componi; quon
rum primum (seclusis ab hac consideratione
guantitatibus l, k, 5, gux pro cogniristraben-
cur) vel Colis x aut y, carumque porestatibus
constat: ucy, ky, x, l x. quos terminos in PO-
lerum simplices nominabimus: Alterum aurem
terminorum genus ex ipsis, x iny ductis conAa-
cum est, UCy X X, yy X. eCHOSPTOPtETCA mix-
F0s aICCIIS.
10. Tum ex obserrare licet, ex singulis a-
quationis Curra terminis simplicibus, Tingulos
tantum huic Cerrientes aequationi terminos oriri.
Cum enim poteltates iplarum y ec x, PerTa.
dices, y = a EC x = e, IuXIa S. 5. exprimenda vc-
niane, Polita iplarum y aur x porettare maxi-
ma, (uc in xquationibus vulso ordinandis fieri
(Olet) Proprimo potestatis termino, Colus se-
cundus remanebic; primo siquidem per 5. 6,
C