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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 123r

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: 0.77.

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. 124v); this page is its right half.

The machine reads it as

  1. curvie semiparabolicae
  2. Opera pretium videfur, quae de intervallis Tangentium parabolae a
  3. puncto in ejus applica axia altitudinis applicataeque aequalium a
  4. communi, ratiocinari coepimus, absolvere, nam si ad progressionem
  5. queundam simmiabilem reverari posset eorum series, curvae
  6. parabolicae rectam aequalem geometrice descriptam, ac proinde
  7. perbu
  8. Geometricam, non ut hactenus mechanicam tantum parabolae
  9. quadraturam haberemus. Esto altitudo parabolae AB. aequalis applicatae
  10. BC = a, DB = 2a ejus B. 4a. DBC = a. summa quadratorum
  11. Sa Et RqSa = DC. Triangulum DBC. = 2a a2 = a. dividatu
  12. per k5a, et productum duplcetur fiet 1a, RqSa 2=
  13. Ra -Ta2
  14. sa
  15. 4a 2a = BE. Intervalli Tangulis De.
  16. A75. A95.
  17. Assumatuo nuncalia altitudo minor quam
  18. a puncto B.
  19. nempe AF. cdjus ratio ad AB sit quaecunque (X, erit AF = (a). et Cumque rat
  20. quadrata applicatarum sint ut altitudines, et applicata prior BC.
  21. fuerit a. erit ejus quadratum a multiplicetur per fiet a
  22. c et R4 = = (a erit applicata FG. Ejgs F- addatur Y. kF: 4C
  23. H ~
  24. a eqe
  25. fet a 4a- aa + 4a a= a a + 4a cum bqus cit. (19 a a + sG
  26. Triangulum DHG erit 24 a, 2. = a) divit atm per HG
  27. 2
  28. a
  29. Rga
  30. pudidumqu duplicetmr fiet: a seput
  31. Bq + 4a
  32. RgaX
  33. (e90)
  34. gae
  35. e
  36. _agat Rg. da +
  37. Dividatur per HG productumque duplicetur, fiet: Aga
  38. 2a
  39. eq
  40. a
  41. = FI Cumque sit ut HR ad AB. ita FI ad BK
  42. Rga
  43. ita stabit regula proportunum HF- 2a dat HB = (a + 4) quid datit FD
  44. A9 a f4a
  45. a ea 1a
  46. L
  47. pq
  48. R92
  49. 2a
  50. Rga +4C =
  51. Rq a + 4
  52. (aa + a ) BK
  53. Rja +44
  54. Ergo si ratio altiludinum sit 1. Ratio intero allommeit.
  55. 24 aa+a. - 2 Rq. a + + a
  56. nas aqu +a Rsat R45
  57. si jam ponatur altitudo continue decrescere uniformiter, erit a= infinito e
  58. reliqua infinit - 1X infinit - 2X. infin. 3X. etc et si partes sint
  59. funtae erit esto potent esse a = 10 X. reliqua _9X. 8X. 7X etc.
  60. ergo rationes ea obunt: 3o Z = crgo 1o - a
  61. Erit ergo a. modo
  62. 1 10 etc. Nole sumum labissener ita inititur
  63. 1+ = + 1Z +1+ 2, +1+ Z etc
  64. 10d+ a
  65. 49 4 + 4
  66. 0a + a
  67. A4 +
  68. de
  69. 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 123r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0245?run=74