# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/797370323:0450 # Permalink to this reading: https://leibnizlegible.com/page/797370323:0450?run=74 # Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53) # Folio 10, page id 797370323:0450 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=450 # Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000450.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine # Lines: 53 recognised, mean confidence 0.85 # 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. haotorhical Drincirles plies no Concradiction, ic Chould bo. Aill soins on in Mulciplyins; che Produce o all vrhich Mulciplications, and che sum ot all irhich Products, ould make a Number Preater chen any sinite onc, hor great soe ver, 1. e. 2n infinite Dumber. Litevile iES cercam thac berreen any riro given Terms an infinite Number, Ot Geometricat mean Proporrionals, can imply no Concradierion, tince e can alsion cheir sum; chus be. erixe = andoche sum of an intinice Num ber ot mean Proportionals, at the race OF 2 to1 is equal ro Ulnicy; and since the Sum is altienable, the Parts cop imply no C on eradiction; and universally becrixe =ando, there and an intinire Number oF mean Proporcionals, in che ratio ot a co1, wtiole Sum is- lo = and che meon Proporcionals chemselres, are C. Behides, che Wrhole abstract Geometry, depends uxon ehe Dollibilier oE infinicely greac, and smail Ouancicies, and che Truchs dilcorer d by Merhods, whichi depend uxon chele Sup. 0 375 20 de a posirions, Poli Wvhich 1 arc100 Ilelirarie quaincec necolels. chese chis A0IS VI Contrac 15 evider boch FX dels, anc ble; 10 Univerle hence, c De AilI F IS Thc cer lame rie ocher bac and vhe ehe Limit. vet a dice USs there mits, tor