# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1032977698:0189 # Permalink to this reading: https://leibnizlegible.com/page/1032977698:0189?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 167, page id 1032977698:0189 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=189 # Source image: https://digitale-sammlungen.gwlb.de/content/1032977698/jpgs/default/00000189.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine # Lines: 28 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. C AP. II. Analysis Infinitorum. omnia fp L Omnia Z = fZ Cx 5. 23. IaM Cx currilineorum AGP, AYP natura CAd = b item u a, unde suffectis in aequatione he= 20 + f inventis valoribus erit B = b + d; quare f2 rectansulo per x interceptam expreso etiam h per eandem x expriietur. LX. GF. CIE fZ = VerXX + rx, AatquC f= X, _C Z = Yr, + rX, CrIt b = X, ∞ d = 2 Y + 2 X; unde ablata asymmetria emercet currilinci AZ P relationem desisnans aquatio, 47 + 22 Yr X + 9r X ∞ = 4 r hh + 4 X Bh. 5. 40. Ouod ( fsc Z, quolibet modo, hoc cs in relatione ad quaAibet lincaS FUM FCC- 125, Tum CUrrAS, expPIaNtUE, tamen h de- terminabitur; modo subtansentes bec d c05- nitx LinE, utipatet. 5. 4I. Animadrersu dignum videtur, A CUr- vilineum guaesitum per omnia he designetur, hoc cA fi O3 seu h ad A sCu X tanquam interceptam ordinata fuerit, ipsius h valorem insiter adaequari subnormali OV CurVE A, 23, P; cujustac est proprietas, ut existente ipsius applicata 9, 22, = 8, (IE PErPetHIO Z = 23 rocata enim hujus subtangenti . 2L, =m, e subrormali QV: 4, exteris ut Cupra