# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/797370323:0485 # Permalink to this reading: https://leibnizlegible.com/page/797370323:0485?run=74 # Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53) # Folio 45, page id 797370323:0485 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=485 # Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000485.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine # Lines: 52 recognised, mean confidence 0.77 # 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. lb2 F1 1 19 lanocher may be 31122 3 X 23 and eIt dins, inc infinite AlLThen bjection AOnS, 2-1 SrWohotels luwrhiche and yet cheir 3D Matural IC cheix Sums are suppos d equal, or in a given Ratio eo lone anocher; For Exemple, hom the Series 1 4 2 + 3 + 4 + 5 + 6, 6c. conrinued to ∞. Could be equal. 10 ∞ (112 7 e 2 2 ∞ Eec. concinued rill ehe Number oEche Perms become equal to ∞ 1. TIOW 1. F 2 ] 4 + 8 = 16, 8C. concinued to ∞. Thould be equal 10 2 + 2 32, = 2, +, erc. concinued eill che Num- bec ot Terms be equal 10 e 1. HtoW che Sum ot 1 + 2 F 4 F 8, Gc. concinued e0 r. Chould be bur chechurd pare of chesum Of,1, + 5 1 Y 5:ec. concinved 10 Sinee all che pares ot che Frst crro Rquations are unequal, and che pares oE che chird, have no such Proporrion, ascheir Sumsare supposdrohare. In Ansverto chele, lec us Consider, r. chac chere an infinite Num ber oF Seriess, trhole sums may actually infinite, belou an infinite Number ot Uni- cies, asell as abore ir; For Fxemple, 25 aboretan infinice Number of Unicies, chere isan infinice Number ot eros, of chrees et etstra Sns. adri ustonosibas FOM