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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 175r

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: 0.73.

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

The machine reads it as

  1. BAB videtur hic
  2. una mechoius prohis Demonstratio et amplifieatio
  3. interpolassiogabus e
  4. emonstratoru Arithmeticae infinitorum
  5. martii 1656 scheda 2.
  6. pe -1
  7. e-1 a Wwallisianae
  8. repiehusa CA aa-X, = ex a A. a- X + e. R. A- X , du
  9. Sed faciendo ax proportionales ipsis X seu X Geometricae progressionis,
  10. qeti c-1
  11. fiet: W. A
  12. a- X
  13. e Cd
  14. + C. X. a - X
  15. Ergo generaliter
  16. si potentia si gradus si detur factum ex dignitate abscissae
  17. t refidai dignitate residui: et factum ex dignitate abscissae
  18. unitate aucta, e refidui unitute minum quae sit uno gradu
  19. altior, et dignitate residui, quae sit unilata in serio
  20. C
  21. vel contra
  22. tradu inferior ex se invicem pendent.
  23. C
  24. uno
  25. Et achus
  26. generalius quia dx possunt fieri proportionales ipsi
  27. W
  28. qetoao
  29. seu . pX, fiet d X. a -X = Co X. a - X +
  30. et cum β3 sit constans, utique patet generaliter
  31. s
  32. et a X mulcipticata per aea
  33. h- n+I
  34. as
  35. x
  36. a
  37. s
  38. ha
  39. 0
  40. e- 1+ V
  41. (3 X
  42. pendere,
  43. a
  44. ex A. a-x
  45. a
  46. u 10-1
  47. X. a - X
  48. ex se invicem
  49. multipticata per b C
  50. et per
  51. a sei sed nihil hinc novi, et omnia eodem
  52. v
  53. o
  54. cedeunt, et licet facias dx= constanti tamen semper
  55. idem prodibit thecrema
  56. A
  57. SX. E X Si- X A redantur ad 1 - x. Si - X seu ad L - si -x
  58. eX
  59. Sx
  60. ex
  61. Xe
  62. pendet ex, 1X. 1 -X Similiter Et porro reducitu
  63. quia bantur
  64. 1- 2X + X, L1 -X,: _ et X 1X. Ergo Mecim etum
  65. Ergo quia dantur: eet S1- X et +X. YI X dabitur et Y.
  66. 1
  67. s
  68. L ad
  69. +
  70. IXA
  71. d1-X
  72. Xe
  73. Et ita porro, et hinc tandem generalis habetur demonstratio FEeoremat
  74. XVX
  75. Wallisianorum. adeoque progrussus Tabula condi poterit generatis
  76. si id tres sint et fiet
  77. e co
  78. e
  79. d
  80. x d +mX n nApX. qu
  81. d abc = ab dc + ac db + bc da D)
  82. l+mX. HA PX. BCK V. rXC-
  83. 10-1
  84. +mx. G+X. ppCd. EX
  85. ea
  86. v
  87. +
  88. + n+ pX. g+rX. e inc

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 175r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0347?run=74