Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[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, fol. 25

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.93.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. C OM BTHA TTOHES.
  2. Primo, quod ex le parce, in primo trianculo eam proxortionem con-
  3. rinoere Summa enim cellularum rnicxe sux Perieinem pe numerus pri-
  4. mae cellulae C idestrnicas, aequatur mulcieudini combinationum ex-
  5. ponenris seriei, in exponenre crianguli, hi enim exponences lune vni-
  6. taces. Vnicas vero in rnicare rnico modo ex lemm. 2. huins combinacur.
  7. Secundo, Si ea proportio in aliquo trianculo contincat; Id est si sum-
  8. ma cellularum vuiuseujuscunque seriei trianculi cujusdam, aequetur
  9. mulcirudini combinationum exponentis seriei in exponente trianeuli
  10. Dico ex eandem proportionem in trianculo proxime sequenti contin-
  11. gere.
  12. Flis astumpris, Facile ostenderur in lingulis eriangulis eam proporrio-
  13. nem concingere, conrinsir enim in primo, ex primo assumpro immo
  14. de manifecta quoque ipta elt in secundo criangulo, ergo ex secundo
  15. assumpro e in sequenri rriangulo contingie, quare de in lequenci dein
  16. inAnitum.
  17. Tocum ergonesorium in secundi assumpri demonstratione consistie,
  18. quod ita expedieeur.
  19. Sic criangulus quilibet v. 8. Terrius in quo supponitur HXC PFOPOE-
  20. eio, id est, Cummam cellularum seriei prima C F0 f x aequari mul-
  21. ticudini combinarionum numeri, I exponentis seriei in nUmeTO, 3.
  22. exponente triancali. Summam vero cellularum secundae seriei e +
  23. aequari mulcicudini combinarionum numeri 2 exponentis seriei in nu-
  24. mero z exponente rrianculi, summam vero cellularum terriae seriei,
  25. nempe cellulam, A, aequari combinationibus numeri z exponentis
  26. Seriei in 3 exponente trianculi Dico et eandem proportionem con-
  27. cingere ex in lequenci criangulo quario, id est, Cummam cellularum v.
  28. 8. Secundae Periei e Y i F B, aquari mulcieudini combinarionum nu-
  29. meri 2 exponentis seriei in numero 4 exponente trianeuli.
  30. Frenim o Y L. aequacur multieudini combinarionum numeri 2 in 3
  31. ex hyposh. Cellula vero B Xquaeur ex reneratione trianeuli arith. cel
  32. lulis C + ∞ F ∞ hae vero cellulae aequantur ex Byp. mulricudini com-
  33. binationum numeri F in 3. Frgo cellulae o f. L F O aequancur mulcieu.
  34. dini combinationum numeri 2 in 3 plus multicudine combinationum
  35. numeri r in 3, hae aurem mulcieudines eequaneur ex quario lemmate
  36. hacius mulcicudini combinarionum numeri 2 in 4. Eroo lumma cellu-
  37. lacum e Y il F O aequatur mulciendini combinationum numeri 2 in
  38. 4. Q. F. D.
  39. Idem Lemma 5. Problematice enuntiatum.
  40. Daris duobus numeris inxqualibus invenire in triansul.
  41. arith. Quoc modis minor in majore combinetur.
  42. Propolici line duo numeri r. 8. 4 ex 6, oporret reperire in criangulo
  43. arich. quoc modis 4 combinetur in 6.

Cite

[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, fol. 25. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0075?run=74