Leibniz Legible

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. 449

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: 0.80.

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The machine reads it as

  1. PFOD. CL XXXII. INFLNLTORUM.
  2. Propolicum sic inquicere, Ouam habeac racionem series finica Ouartanorum, (ab
  3. Oinchoaca,) ad seriem coridem maximo A qualium.
  4. T. Character numeri Priansuli criangularis, ( per PrOV. 180: ) est
  5. 21 +61 + xr 1 + 61. Et Frianeuli prcamidalis F 10H + 351 + 505 f 211
  6. DEF PrOB. 182.
  7. O2 f 03 f 0+0
  8. a +6a + 4 482
  9. 24) B F 6b3 +
  10. ct +6c3 f 226 4 60
  11. 14 f 613 F FF 12 = 61
  12. 1. f 101. + 35 1. + 5012 4 241. Aer eeacum.
  13. 120
  14. 20 a Aivs 1OM
  15. 2. EHt aurem, (ue Paxius
  16. dictum, est,) numerus Fisura-
  17. cus unius gradus ( in praelenes
  18. tabella) aggregatum omnium
  19. Praecedentium in gradu sibi
  20. proximo: Adeoque numerus
  21. Friansuli Prramidalis, clt a8.
  22. Pregacum Friansuli criangula
  23. rium. itt e
  24. 3. Ec propterea, sumpris la-
  25. teribus 2, 2, 3, ecc. vel (eorum
  26. I0cO) an B,C, _c. (quorum maximum dicatur B,) e Formanis inde numeris Frian-
  27. Sulicriansularibus; tlorum axeregatum exie numerus Frianguli pyramidalis ejul
  28. dem laceris, nempe F101 = 35 13 + 50 V f 24. l.- ∞ ∞3pen0 ciy 1a 3u1i
  29. +. Summa aucem seriei 0 = 6 a + 6B + 6c _c. eA (per PrOP. 2.)
  30. 2+67
  31. 5. Summa seriei 0 = TZ a2 = rF B2 = FY C2 _C. est (Der PrOP. 20.)
  32. E 1X22+
  33. 6
  34. 2x p = 2213 + 211, 21 1. + 121- 221 +338 +721
  35. 6. Summa seriei 0 + 6 a3 + 6B3 f 603 _c. est (. per Drop. 40.)
  36. 26P + =6p -612 + 51, 67 +61 612 4 121 +61
  37. . Ea creo lummae in unam collectae tune
  38. 51 +61, 221 + 331 + +11, 622 + 1213 + 67 9 1 + 4013. 60 f291
  39. 8. Si igitur ex riginciquadcuplo corius agoresari, auteratur summa irium serierum.
  40. Nempe A ex 5) 13 = 1014 + 3513+5012 + 24. 1.
  41. autcratur 6) 912. + 4013 +6012 + 291.
  42. Hoc est, Si ex 30) 813 +601 + 2701- + 3001 +. 244. L
  43. auteracur 30) + 45 11 + 2001 + 3001 + 2151.
  44. Panebir summa
  45. Seriei quarrae, 9uae 30) 615 = 15)4 = 1013 + 001 = +1.
  46. Mst Quarranorum e
  47. Hoc ectus
  48. HOC ett, = p+
  49. 30
  50. 613+67
  51. +01+05
  52. 1+ 3 p + + 2p 1+
  53. Oux est ixicur summa seriei Ouarianorum cujus cerminus ultimus est J. nu.
  54. merus terminorum I F. L.
  55. Vel; s Pro numero terminorum J F F, substienatur m et propterea series
  56. aequalium m I; eric serieo Quarcavorum = m 12 F 3m 13 = 5 m 12 = 2 m I. (A
  57. nempe cerminus primus (it o, sccundus r:) vet V , 3m 12, m 1. m1a
  58. L.
  59. 261 361 301
  60. ec. ad
  61. Addica.
  62. O. Adeoque

Cite

[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. 449. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0469?run=74