# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/797370323:0037 # Permalink to this reading: https://leibnizlegible.com/page/797370323:0037?run=74 # Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53) # Folio - , page id 797370323:0037 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=37 # Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000037.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine # Lines: 60 recognised, mean confidence 0.88 # 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. and a d one re- ny sucto of. that D. 6 r great insists in D. 8 P. G D. LF P. 13 En D. 15 at Ideas, the De- D: 16 Properties hers that D. 10 Contents. 89. That Finices and Infinites are Disparata and of quite different Natures and Properties, P. 20 S. 20. That it is impossible ever. for us to under- stand or comprehend, the positive Nature and Properties of Intnites, P. 22 S IT. The Diviscon of Infinites into those hose intinitely small Parts are all unequal, and those hose intinirely smalt Parts are all equal, D. 26 A nem Arichmetick of Infinites, D. 29 S T2. An Illustration of this Arithmetick in seve- rat Problems abont Arichimetical Proportionals, their Sums, Differences, and the Number ef ihe Terms, P 30 13. The same illustrated in several Problems about Duantities coins on in a Geometrical Pro- portion continued, their Sums, Ratios and the number oftheir Terms. 3 IBid. The Method of findine un infinite number of different Geometricat Progressions, whose Sums may be egual, P 32 d T4. The same illustrated in Geometricat Pro- cressions ascendins, vith a Method of findins the intinice ly smallequal part ofsuch, and of findina different ones, rohose sums may be equal, D. 35 S 18. The same illustrated in the Ouadratures of Lxterior Hy Perboloids, with a Method of find ne an intiritels smalt equal part, ef some l’or- tions of the areas ofthese Lieures, D. 3Ed IBid. Severat Difficulties that mieht be broneh acainst these Inferences, ansivered and elear d. Y