# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/797370323:0489 # Permalink to this reading: https://leibnizlegible.com/page/797370323:0489?run=74 # Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53) # Folio 49, page id 797370323:0489 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=489 # Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000489.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine # Lines: 55 recognised, mean confidence 0.74 # 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. e2 heometri. thesum ehe last There. chelalt, 00 1 -) From 1 1 +. 2 ile every recedine 15 ∞ 1, IS CXCEDE by che is obser- 1. 8 esc. et -= 27 AatUTat esc. Consinued c0 ∞0 B, BC cause there are more Perms in ehe Frt, chan in che second; che second dis veroins Falter, and at a grearer Hace chan he Erst, arrires aC C 1 lOOner, 1. c. atTeF a Perver Number oF Terms chan. che Fust. 30 likcevile, it che Series bC. 1 F 4 F 16 7 64, ec. Concinued 10 ∞0 n. chen every Term = is criple oF aII ehe SMI ofchie precedine Terms, and con sequendy ehe sum oF aII = ∞ 4; and univer(aII che Geometrical Propression besinins a1 end goins on continually c0co r. in che Ratio, Ot B EOM, VIZ. 1 + 1 = n 1. n 1t Oc. Erecy Term = 1 ISn=L CimeS, ChC Sum oF all che precedins, and becaule che la is ∞ 1 cheretore ehe Sum et all ehe precedine, is e ∞T B 1 nieum 1. 2nd consequencty ehe sum ot the lalt, atct oF alI che precedins, 15 ∞ x + 21 0o e =Cby che Rules oF Addition) ca LaBY, es FOr elle EWO Seriess F2 + F8, esc. cominued W I dd and