# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1023099829:0082 # Permalink to this reading: https://leibnizlegible.com/page/1023099829:0082?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 32, page id 1023099829:0082 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=82 # Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000082.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine # Lines: 40 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. CO M BIN ATIOHES. Numerus progressionis duplae quae ab vnitate sumit ex- ordium cuius exponens proxime major est quam numerus datus, satisfaciee problemati, modo onitate minuatur. Sicnumerus dacus r. g. 5. quaericur summa omnium combinationum guxe in 5 heri postime. Numerus sextus progressionis duplae quae ab rnicare incipie nempe 32 rnicare minurus nempe zF laristacie, ex lem. 6. ergo posumeheri 3C CombinatioMeS IM MUMCTO 5. Problema 2. Datis duobus numeris inequalibus, invenire quor modis minor in majore combinceur. Absque trianculo arith, ICoc est proprie ultimum Problema tractatus trianc. arith. quod sic resolvo. Productus numerorum qui praecedunt differentiam da- torum onitate auctam, dividat productum cocidemnume- rorum continuorum quorum primus sit minor datorum onitare auctus, quotiens est quaesitus. Sine dari numeri 2, 6; Oporrer invenire quormodis 2 combinetur in 6. Alsumatur eorum differentia 4 quae rnicare aucta est 5. Tam asTuman- cur omnes numeri qui praecedune iplum 5, nempe, 2, 2, 3, 4, Guorum productus sic 24. Allumantur coridem numeri concinui quorum pri- uS (EZ, nempe proxime major quam 2 qui minor est ex ambobus datis, nempe, 3, 4, 5, 6, quorum productus 360, dinidatur per praece- denrem productum 24. Ouoriens i5 eAnumerus quae lIcUS. Tta venu- merus 2, combinetur in 6, modis 25 differentibus. Nec difficilis demonstracio. Si enim quaeratur in criangulo arichme- cico quocmodis 2 combinerur in 6, altumenda est cellula 3, ba(IS7, ex lemm. 5, nempe cellula E, e iplius numerus exponet mulricudinem combinarionum numeri 2. in 6. Vraurem inveniacur numerus cellulae Ecuins radix est 5, ec exponens seriei z, oporter ex probl. triane arith. ve productus numerorum qui praecedunte, dividat productum toti- dem numerorum continuorum quorum primus sit 3, e quoriens erit numerus cellula E, Sed idem dinilor, ac idem dividendus in constru- etionehuius propolitus est, quare de cundem quorienrem Corrira est di- vilio, ergo in hâc constructione repertus est numerus cellulxe E, quare e exponens mulcicudinis combinarionum numeri 2 in 6, quae qua- REBATUE. O. B. F.F. D. Monitum