Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis, fol. 796

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: 0.81.

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

The machine reads it as

  1. L O M M E R C I U M
  2. cundis lineares, E, 2, 3, 33c. ex comcinua monadieorum addicione ortos, 1 F L = 1
  3. ecc. tertiis criansulares, 1, 3, 6, dc. ex concinua addicione lincarium L- F 2 + 3
  4. eC. quarcis pyramidales, c, 4, 10, sec. ex concinua additione ceiangularium,
  5. 2 + 3 + 6dc. L.F sic demeeps.) Vel cciam, (I prO L, B = 2, B - 21, dC. Clacua-
  6. muS L, 2, X, dec. Crit u = 1+ = L, X = + 1 = 1, y = 1 ~ = u, 2 = 1 y = X dec.
  7. nempe constat quilibet ex praecedencium uleimo in s ducto, dempro penulcimo.
  8. Vel denigue (nam de haec tortan delienacio placebic porius nonnullis) si numerus
  9. expolicus sic verbi pracia 3; tier eadem series ad hanc tormam; (Vid. F. pist. 14. 1
  10. 3 in 9: 2X31X33 X 315 X 335X 3183, _C.
  11. Sic expotico n = 2, tier Pexies
  12. 2 in 1: 2251 4 53~ 5B 5. X 5 iti, c.
  13. Ubi connitis raclicum prima de lecunda (un prius) reliquae ea ratione contlimuin.
  14. tur, uc tractionum leguencium DmmeratOF aequec ubique denominatOrem TILIIM
  15. dempio denOinatOrE prONImE prXCedeNCE; DENOMINAIOT AULEM RGUeE nUMEraIO.
  16. rem cermini proxime praecedencis in impropriam tractionem reducti.
  17. Hlac aurem ni lacis superque susliciant praelenei nerocio expediendo; criam hoc
  18. licet adjicere. Inrenca hujusmodi serie qualiber, quae numero cuiris non quadra-
  19. EO, DuTan = 2, conveniac; hrabentur ltacim series quae conreniane, ejuldem nu
  20. meri per quemris quadracum mulciplo, puca n m, nempe dividendo seriem radieum
  21. sam invencam per illius quadtraci radicem m: HoC pacto;
  22. 2, in Q: 2X5+X58X533X 538ZX 5, 183, eC.
  23. B, in : 2X51 X 58X533 X 5 1 7 X 5, 163 C
  24. 28, in 1: 4 X331 X 3337 X 33 1135, C.
  25. 32, In 1: 3X331X3337X331155, ec.
  26. 50, in 9: 24.X F97+ X 297136, _c.
  27. 72, in 9: 2x 33+X 333 X3313), dec.
  28. 38, in 8: 1021191 X L9 , 13b. CC.
  29. 128, in G: 5FX
  30. 262, In G: 154OX
  31. 200, in 9: 7X 297 1X29713b, dc.
  32. 242, in 9: 1260X
  33. 288, in 9: 1 x 331 3334 4 3311 i, dc.
  34. THoc est.
  35. 18,
  36. 1O:
  37. in O
  38. 32,
  39. nO
  40. 2
  41. 50, in 9.
  42. 10.
  43. 98, in 9.
  44. 128, in 9
  45. 162, in O
  46. 200, in O.
  47. 242, in
  48. 12,70, 408, 2378, 13860 8c
  49. 4020. c
  50. 6,35, 204, 1189, 6930. ec
  51. 136,
  52. 102,
  53. 3465. _c.
  54. dc
  55. 31
  56. 286, .
  57. +
  58. 18
  59. D. c.
  60. 1980. ec.
  61. 13+. ec.
  62. 1366. ac.
  63. 7260. _c.
  64. 155. c.
  65. TIB videre est, nunc lMSO hunc alternos, nunc certium quemque leriet nu-
  66. merum, vel etiam quarcum, quincum, esc. diritionishujusce capacem cAe. PL Simi-
  67. licer de aliis numeris pueteandum crit.
  68. Sed nec incommodum erie monere, quod de supra innuimus, (quanquam d DIX
  69. senei necocio alienum,) li i expolica qualtione, pioaceia ulateea
  70. scito quovis numero quadrato, puta L: Teries quactraiorum quos jam inrelIs, du-
  71. Cenda ellene in dacum illum quadracum e; (live, quod cancete atel quacla
  72. corum radices ducenca estene in L) exempli BcacIa. Ouoniam, expolio numero

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis, fol. 796. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851708439:0820?run=74