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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 254r

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.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 255v); this page is its right half.

The machine reads it as

  1. sit Parabola ACC, cujus vertex A, axis AB
  2. ordinatim ad axem applicata BC sit AB, X
  3. et BC, y et latus rectum a, fiet
  4. raX = yy;
  5. GtCB: BP = dy: dy
  6. et 2adx = 2ydy seu dx: dy = y: a. jam CB est y
  7. ergo BP est a. Ergo si sumatur AO, aequalis ipsi a
  8. dimidio lateri recto, erit e centrum circuli parabolam
  9. oscutantis. Cujus dimid Et A visecando A0 in F, erit
  10. F focus parabolae
  11. videamus jam quae sit differentia inter Curvam
  12. Circularem descriptam excentro O radio AO, vel a
  13. et parabolam cujus latus rectum est ra. ita scilicet
  14. ut latus rectum parabolae et diameter circuli
  15. coincidant sit corculica quato 2a Centro igitur
  16. seuAt
  17. radio A OA describatur AE arcus circuli et sit BE
  18. ordinata, fet D, et fiet vD = 2aX - XX. Ergo
  19. chard Ergo BEqu vb + XX seu BEqu + ABqu = 2aX
  20. seu = AE qu. Ergo AE = 2aX. idas id
  21. itaque _ AE chorda, aequatur ipsi BC ordinatae
  22. parabolae
  23. si jam EAE ponatur esse portio circuli
  24. talis, cujus chorda EE aequetur distantiae
  25. foci AF; rem ad calculos redigamus
  26. sit aS AO, 1000000 et AF 500000, et
  27. useu BE, 25000B vit AE seu fiet
  28. seu 25, 1000 jam 2 fiet BE = a
  29. quia BE est BE est =a seu B, hoc loco est a
  30. fiet Aaa = 2aX - XX. seu XX - 2ax + aa = aa- aa
  31. Doeb Xa, 18 E( EB, et 2aX = aa, 13. Ergo
  32. y seu trax ∞. a, B2 B jan 3 = 1. 732050 et
  33. jam 13 = 1.73205080 et X
  34. 53 erit = 056602540
  35. erc et AB seu X, erit O. 13397460, a
  36. seu fiet X - a = 8 = = d Y15. A et
  37. et X = a + LaVis = a, 1 + 3. 872. Ergo AB = a, 1 = 0. 968-
  38. seu AB = AO, ∞. ∞2 8. 032.
  39. Ergo differentia inter
  40. b
  41. B5 ∞B 10
  42. 10064 = 0.252 = A2 = Bct
  43. et BC se inter, 0. 25 et 9.252 est 80
  44. 3t a Xx si sit BE.
  45. c
  46. 0
  47. E
  48. Ve
  49. e
  50. 10 fraiet X
  51. 5916
  52. 25Of 12
  53. =a +a 35 L a
  54. et AB = 84. AO
  55. 6000 et AE = 84.31
  56. 5000
  57. 916
  58. 34
  59. 14 (21
  60. 1004(250
  61. 50
  62. 0000
  63. 90000 = 2. 84, 30 = BC
  64. = BC- 502
  65. 5012515
  66. Ak I 6 X 72(301
  67. 2
  68. 300
  69. 300
  70. = +
  71. XX - 2ax taa = aa = L aa
  72. 1.000
  73. 0. 968
  74. 0. 032
  75. (01032
  76. ermo disferentia
  77. inter BE et BC est
  78. 1teo so
  79. 0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 254r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0503?run=74