Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 8, 9, fol. 5r

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: 0.79.

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

The machine reads it as

  1. seplem fr. 1690
  2. Ope
  3. de Quadraturis ad alias reducendis
  4. Anralyseos
  5. Omne mea calculi infinitorum, reducitur quadratura proposita
  6. ad alias variis modis. Ex. g. sit (X sat bx de fit
  7. sit , sa+ bx = v fit sexdx. jam sexdx + (xxdo = _B XX
  8. jam do = bdx: V
  9. Ergo
  10. bX sa+ bx ax + Sib XXdx: Vat bX = XX SatbX
  11. Ergo si datur una Quadratura datur et altera. sit atbx- eca
  12. fiet dx = deo: b. et X = d cd: b = a: b et XA 2a
  13. et XX = a coco: bb - 2aco: bd + a 4: bb. Ergo ex D. fit
  14. bb in scoc du -(2a0 deo +(adco. datur ergo D, adeoque et C
  15. as.
  16. icua
  17. in genere
  18. similiter sesset
  19. fiet D=
  20. si 8
  21. Sed
  22. sco
  23. X Iae +bx ax = O faci (eet =
  24. e
  25. X V x
  26. (X dv. et C+5 = xet v. itaque generaliter
  27. SX Vae+bx dx reducitur ad
  28. a + bX = c ad
  29. et+ = F: 2
  30. Zb X dx. VaerbX, seu faciendo
  31. 22
  32. P e-1- 1.2
  33. c da dio + cd
  34. deo etc.
  35. semperque finitus est numerus, si e sit integer. Quod si e sit fractus
  36. verus verb. gr. eo ipso pro dit series infinita quo quadratura
  37. Circuli Hyperbolae aut Ellipsebs; idemque est pro fractionibus aliis
  38. quibuscurque est autem
  39. Cvet1 -1. 2 = Coe2-1.2. et ila porro
  40. e+ 2- 1:2
  41. Itaque quadratura curvae Cujus ordinata est X Sa +bX, reducitur id hanc
  42. redeseriem:
  43. B
  44. et 2- 1:2
  45. Cd
  46. e+2- 1:2
  47. et 1-1. 2
  48. Cd
  49. e+1 = 1: 2
  50. +
  51. C - 1.2
  52. C0
  53. - 1- 1. 2
  54. = Cd
  55. 0
  56. e- 132 C- 1 = 1:2
  57. ∞- 2- 1: 2
  58. + Cd
  59. ∞ -2 - 1:2 et
  60. quod servit ad interpolationes Wallisianas demonstrandas, et reddendas generales
  61. patetque simul quod in casu fractrum fracti valoris ipsius e, mo et irra-
  62. tionalis re redtuca ad quadratur A Cariam dividendo enim
  63. totam anen per esis d
  64. Et dividendo totam seriem per cos patet
  65. hinc dari methodum incundi per quadraturas summam seiet talis
  66. cd
  67. 1 1.2
  68. = Cd
  69. (+ 1+IL
  70. 1.2
  71. (+1: 2
  72. at
  73. C0
  74. C = 1. 2
  75. = 1- 1. 2
  76. Cd
  77. e - 1- 1: 2
  78. +
  79. 2 - 1. 2
  80. Ce
  81. ek
  82. ea 2 = 1: 2.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 9, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068104:0009?run=73