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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. 29

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. COM BTHAYTONES.
  2. aequatvE, ex eodem, summxe cellularum seriei 4, erianguli 6, nempe
  3. D Y F F F, scu cellula K, Seu 15. est aurem p ad R, re + ad 3, Icu re 4
  4. 2d 6-- 3. ex consect. 11. Tr. arith.
  5. Prop. 6.
  6. Si sine duo numeri quilibet quorum minor in majore com-
  7. binetur, sinc autem e alii duo hisproxime majores quo-
  8. rum minor in majore quoque combinerur, erune mul.
  9. cicudines combinationum inrer se, re hi ambo rleimi
  10. MMIeri.
  11. Sine duo quilibernumeri, 2, 4 alii vero his proxime majores, 3, 5;
  12. Dico mulcicudinem combinarionum numeri 2 in 4 esse ad mulcirudi-
  13. nem combinationum numeri 3 in 5, VE3, ad 5.
  14. Consect. 12 triane. arith. hanc continet ex sie demonstratur.
  15. Mulcicudo enim combinacionum ip(ius 2 in 4, aquacur, ex lemi.
  16. 5. Tummae cellularum seriei 2, crianguli 4, nempe p F L. 7 6, Peu cel-
  17. lula C, Cen 6; Mulricudo vero combinationum numeri z in 5, Xqua-
  18. cur, ex eodem, lumma cellularum seriei 3, crianguli 5, nempe A F B F C,
  19. Seu cellula F, Peu rO; F.K aurem C ad F, Vr 3ad5, Cx T2 consect. triang.
  20. arich.
  21. Lemma 6.
  22. Summa omnium cellularum basis criang. cuindlibet arich.
  23. mericirnicace minuta, equatur lumme omnium com-
  24. binacionum que feri pollune in numero qui proxine
  25. minor est quam exponens balis.
  26. Sicrriansulus quilibecarichmericus v. 8. quintus CHI u Dico lum.
  27. mam cellularum sux batis II F F Y C Y R F u, minus vnirare, set
  28. minus vnd ex extremis HI vel u aeguari summae omnium combina-
  29. tionum quae heri possune in numero 4 qui proxime minor est quam
  30. exponens basiS, 5. Id est. Dico summam cellularum R f C f F f FI.
  31. Supprimo enim extremam u, id eAt q Y 6 Y 4 F F, Ceu 15; Xquari
  32. mulcieudini combinacionum numeri r in 4 nempe 4; Plus muleieu.
  33. dine combinationum numeri 2 in 4, nempe 6; Plus muleicudine com-
  34. binarionum numeri z in 4, nempe 4; Plus mulcieudine combinatio-
  35. num nameri 4 in 4, nempe I. Quae quidem sunt omnes combinatio-
  36. nes quae fieri possunt in 4 superiores enim numeri, 5, 6, 7, ∞ c. non
  37. combinantur in numero 4: major enim numerus in minore non com-
  38. Binatur.
  39. Mulcicudo enim combinarionum numeri Z in 4, XGUaTUE, ex S. lem.
  40. cellula 2, balIS5, nempe R, seu 4. Mulcicudo vero combinationum

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. 29. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0079?run=74