# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1023099829:0058 # Permalink to this reading: https://leibnizlegible.com/page/1023099829:0058?run=74 # Title: [Traite Du Triangle Arithmetique, Avec Quelques Autres Petits Traitez Sur La mesme Matiere] Traité Dv Triangle Arithmetiqve, Avec Qvelqves Avtres Petits Traitez Svr La mesme Matiere (shelfmark Nm-A 605) # Folio 8, page id 1023099829:0058 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=58 # Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000058.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine # Lines: 39 recognised, mean confidence 0.93 # 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. ANMERTCOEDM ORDTUrM exponens ordinis, 3, nempe, 360, Duotiens 25, est nu merus quaesitus. Nec difficilis demonstrario, eadem enim prortus construetione, in- venta est, ad Anem cractarus Triang. Prich. cellula quineae leriei per- pendicularis, cerria vero Periei parallelae; cujus cellulae numerus, idem est ac numerus quinrus ordinis cerrii, qui quaeritur. Porest aurem ex sic resolui idem problema. Productus numerorum qui praecedunt exponentem or- dinis, diuidat productum rocidem numerorum continuo- rum quorum primus sit radix, Quotiens est quaesitus. Sic in propolico exemplo, productus numerorum, 2, 2, qui praece- dune exponencem ordinis, 3, nempe, 2; diuidat productum coridem numerorum, 5, 6, quorum primus lic radix, 5, nempe, 30, Ouoriens, 25, eAt numeruS quaCIEUS. Nec differt haec constructio a praecedenre, nisi in hoc solo, quod in alcer a idem Ar de radice, quod hr in alrera de exponente ordinis. Perin- de ac hidem esser invenire, quincum numerum, ordinis rerrii, ac rer- cium numerum ordinis quinri, Ouod quidem verum esse iam osten- dimus. Hlinc aucem obicer colligere possumus arcanum numericum, cum enim ambo illi quorienres, 15, sine iidem, constar, dinilores esse inter Ce re diuidendos. Animaduerremus icaque. Si sint duo quilibet numeri: Productus omnium numerorum pri- mum ex ambobus propositis praecedentium, est ad productum rocidem numerorum quorum primus est secundus ex hisambobus, ut productus ex omnibus qui praecedunt secundum ex illis ambobus, ad productum toridem numerorum continuorum quorum primus est primus ex ijsam bobus proposiris. Flxc qui prosequererur, ex demonstrarer, et noui Forrassis rractatus maceriam reperirer, nunc aurem quia exrra rem nostram Lune (iC Pex simus. DE NVMERTOORVM ORDTNNM RESOLVPTONTF. Problema 2. Dacoameto, ae expoHee thi ordinis, invenire radicem. Pocest aurem sic enuntiari. ooCueIo, MdeMIreTaMLCBMMLAIaLIIMI MMMeTI Ordinus