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Machine transcription of the Leibniz Nachlass

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 447

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: 0.83.

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The machine reads it as

  1. PFOD. CL XZZ. INELNLTORUM
  2. 5. Nempe summa duplicata seriei Primanorum, 0 F 2 a f 2b f 26, _c. Cu
  3. jus cerminus ulcimus 2. L, et numerus cerminorum H. L; exie 2l. BeL. PCOP. 2.
  4. 6. Summa criplicacae seriei Secundanorum, 0 f. 3 a 2 f 3 b f 302 _c. cujus ter.
  5. minus ulrimus 3 12 de numerus cerminorum L F; erit =3 12 1+
  6. PFOP. 20.
  7. 67 3V. per
  8. J. Summa Periei Fercianorum, 0 f a. + B3 + c. dec. eujus cerminus ulcimus 1,
  9. numerus cerminorum L. +. L; eric L p +. F 12. per Pcop. 40.
  10. teuumisinus summucum aepreguum, (pura = L 21 + F 3 1. + l. = = 3 1.
  11. +LF p + F E V.) nempe
  12. 24 P. 4 2414+ 24 1 + 24 1. + 12 1. + 121 4612 +61. + 611 +61.
  13. Gregati sextans
  14. st Aeereeaum ceiumillacum serierum; cuju s. 28.
  15. Ia + 613 = +F12 +61
  16. c
  17. cus h Ideoque -
  18. 24
  19. Cst numecus Frianguli triangularis cujus la.
  20. PRO P. CEXXX
  21. Theorema.
  22. Acus numeri Trianguli crianeularis ad ipsum numerum, estut P act
  23. a +613 + +r12 +6
  24. Adeoque, Dato latere Idabitur numerus Frianguli criansularis, puta
  25. a +613 + 2c13 +6
  26. Daro autem numero Frianculi criangularis non invenicur iplius lacus nisi resol.
  27. rendo hanc aequationem 24 n = 14. + 61 + F2t 2 + 61.
  28. P ROP. CLXXXI.
  29. um crcncts ue cin Theorema.
  30. is
  31. eries numerorum Frianguli criangularium, in praemisa Tabella-
  32. commode interpolari poterit; si iplorum numeris laterasibus, FOF
  33. interponantur medii Arichimerici, quot opus eAt, _ ex iis FOrMENEF
  34. numeri Trianguli criansulares, Der praecedentem.
  35. Pura laceribus interpolatis 3, E, +2, 2, 23, 3, 32, 4342, 5, 53, 6, _c. respondene
  36. numeri Frianguli criangulares 238, 2, 2338, 539 128, 15, 23728735,50728,70, 94 2373
  37. +26, _c. vel eriam 238, 1y 2663 5, 118, 15 728335, 528, 70, 726 7 +26, dc. Vel potiis
  38. 3d23 F, 335, 32 325, 3335, 3170,38. 126, ec.
  39. PROP. CLXXXTI
  40. Lemma.
  41. DRoPolicum sic inguirere, quam ad latus Cuum rationem AabCa
  42. lequencium serierum numeri Fisurati pura Frianguli prramida
  43. les, Prramidi erramidales, etc.
  44. Poster quidem hoc prastari eadem methodo qua ulus sum ad ProB. 176, _ 173,
  45. ope propolicionum ibidem memoraTUI REIDC PTOp. 2, 20, e 40, timul cum
  46. PTOP.

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 447. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0467?run=74