Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[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. 24

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.

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The machine reads it as

  1. GOMBIHATIONESS
  2. Ex combinarionibus duarum in quatuor, nempe AB, AC, AD
  3. BC, BD, C D, quaedam Cune in quibus ipla licrera, A, vSUEPaTUE, ve
  4. istae AB, AC, AD; quaedam qua ipsa A carene ve iltae, BC, BD,
  5. CD.
  6. Porro, combinariones illae, BC, BD, CD, duarum in quaruor
  7. A, B, C, D, quae ipso A carenE, constanc ex residuis tribus, B, C, D.
  8. Tune ergo combinationes duarum in tribus B, C, D, ioieur combina-
  9. tiones duarum in tribus B, C, D, Cune quoque combinationes duan
  10. rum in quatuor A, B, C, D, nempe illae quae carene iplo A.
  11. IIla vero combinationes AB, AC, A D, duarum in quatuor A, B,
  12. C, D, in quibus a rsurpatur, E iplo A spolientur, relinguene res-
  13. duas lirreras, B, C, D, qua Cunc ex tribus licreris B, C, D, luncque
  14. combinationes unius licrerae in tribus, B, C, D, igicur combinario
  15. nes vaius liccerae in tribus B, C, D, nempe B, C, D, aCcirO A, eA-
  16. CInnE AB, AC, AD, quae constieuune combinariones duarum lirre-
  17. rarum in quatuor A, B, C, D, in quibus, A, vCUIEPaTuE.
  18. Peicur combinationes duarum liccerarum in quaruor A, B, C, D.
  19. Formancur partim ex combinationibus vnius in tribus, B, C, D, Par
  20. rim ex combinarionibus duarum in tribus, B, C, D; Ouare mulcieu-
  21. do primarum aquarur multicudini reliquarum, 9. F. D.
  22. Eodem prortus modo in reliquis ostendetur exemplis verbi graria
  23. eoc elle combin. numeri
  24. quoc lune comb. numeri
  25. 29 in 40
  26. 29 in 39
  27. x insuper quorlune comb. numeri 28 in 39.
  28. Ouacuor enim numeri, 28, 29, 39, 40, condirionem requisiram ha-
  29. bene.
  30. Sic eor lune comb. numeri
  31. _C.
  32. quoc lune comb. numeri
  33. 16 in se
  34. 26 i1 55
  35. acinsuper quorlune comb. numeri 15 in 55.
  36. Lemma 5.
  37. In omni criangulo Arith. summa cellularum seriei cujusti.
  38. bec, aequatur mulcicudini combinarionum exponenris
  39. Ceriei, in exponente erianguli.
  40. Sic criangulus quiliber v. 8. quartus, C D n. Dico summam cel-
  41. lularum seriei cujuluis v. 8. Secunda a Y L F B aequari mulricudini
  42. combinationum numeri 2, exponentis secundae seriei in numero 4
  43. exponente quarti triangli.
  44. Sic Dico lummam cellularum Periei v. 8. quinca crianguli v. 8. octaui
  45. aequari mulcicudini combinarionum numeri, 5 in HUmCrO 8, RC.
  46. Ouamuis infinici sine huius proxolirionis calus, lunc enim infiniri
  47. erianguli, breuirer ramen demonstrabo, poliris duobus assumpris.
  48. Primo
  49. 4

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. 24. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0074?run=74