# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068002:0024 # Permalink to this reading: https://leibnizlegible.com/page/00068002:0024?run=73 # Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5 # Folio 12v, page id 00068002:0024 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 13r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068002&page=24 # Source image: https://digitale-sammlungen.gwlb.de/content/00068002/jpgs/default/00000024.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 36 lines, status machine # Lines: 36 recognised, mean confidence 0.95 # 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. hoc Modus autem construendis construendi d numeros duplex est unus per continuam additionem. Nam ex unitatibus sumtis inde ab initio conflantur naturales, ex naturalibus triangulares, ex triangularibus pyramidales, et ita porro. Alter per continuam multiplicatio nem; et hic cum sit a Tabula independens, a viris egregiis a Fermatio Pascalio, et aliis jam traditus ita habet. sit gradus e combinatorius e, erit ambinatio sed quem ad unam expressionem pro omnibus ita redegi: sit gradus Exponens combinationis e. Ita ut pro nullionibus, omfinationem Beanum C Sec 2, 3, etc. dic Cvinem Dico enionem fore e, e - 1 , P - 2, e - 3, C - 3. ete usque ad = (C- 1) seu usu ad 1 1. 2. 3. 4. 5. ete usque ad e N Hinc per singulas eundo 1 nio = e 2nio = C, e-1 hnio, C, C -1, C-2 . 2.3 1. 2 (enio) etc est igitur enio seu combinatio, productum numerorum inde ab e, exponenle combinationis descendendo, divisur per productum In his autem numeris ut obiter dicam ad instar Trianguli Arithmetici quod dedit Blasius Pascalius vir ingeniosissimus observavi Harmonia Triangulum Harmo. nicum. Nempe ut in Triangulo Pascaliano, id sunt rasin dant Harmonici basin dant Aritametia arithmetici replicati. ita in meo sunt Harmonici replica replicantur Harmonici. Triangulum Arithmeticam totidem numerorum inde ab unitate ascendendo, ita ut ascentet finiatur in e, descensensus in 1. que alter in principio alterius 15 Triangulum Harmonicum