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Leibniz-Handschriften zur Mathematik LH 35, 5, 23, fol. 25r

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 31v); this page is its right half.

The machine reads it as

  1. es
  2. erit cinuli
  3. Y. tangente BT +, Carcus AB, abe aequ. F- t + L
  4. srruat
  5. rite
  6. -t
  7. 3I Spt 7Y
  8. Sit Hyperbola HP, cujus centrum C. demonstratum est alias
  9. abscissis CE, CF, FG existentibus progressionis
  10. Gometricae, seu ut numeros, tunc quadlinea
  11. P, E8, FR, GH, fore progressionis Arithmeticae
  12. sit CE aequ EP aequ Y. et A EF vel ED sit X
  13. et E9 seus
  14. r-X
  15. rex
  16. erdx erit logaritEmus Hy perbolicus de Y- X seu de CD
  17. rax
  18. et dx
  19. Y+x
  20. erit logarithmus Hyperbolicus de Y,4X seu de CF
  21. er ex 4 rrdx
  22. seu 8 r-X
  23. seu 2sa
  24. dirLXX
  25. 1V dx
  26. rrxX
  27. r+X
  28. erit log. Hyp. de
  29. er de est log. de r+ +S-1 d
  30. ret sa
  31. D er- XX
  32. 2+X
  33. erit logarithmus. Hyperbolicus de Vrr- XX
  34. quantitates, tunc ita procederemus:
  35. rrdt est log. de r- Fs- 1
  36. Y-t.-1
  37. -
  38. Ergo
  39. rrdt fuet log. de rr+ +
  40. 2Srrtet
  41. et serat foret log. de
  42. 2t et
  43. arcus AB
  44. Vrr+tt
  45. secante C7
  46. Unde sequeretur dplos arcus fore secantium logarithmis proportionales
  47. et possent inveniri quotcunque mediae proportionales sola sectione arcus
  48. in partes aequales. Quod verum esse, non ausim credere. invitarefutatur
  49. CB CA, CY, r. C55. SV, (-Y
  50. TV: SV: CB: B5
  51. et Z aequA: DE noqu. m C. ergo IV seu BT: s:: Y: Issa rY. et B, aequ Ys: fs H. Est autem
  52. erit DN vel F9 aequ , seu DNago et F9 aequ.
  53. YZX
  54. r-x)
  55. Est autem DP aequ. (rrdx et EQ aequ. Cerda.
  56. Urgo De seu
  57. et DQ
  58. dc
  59. quemadmodum alias demonstravi BF
  60. seu ut Logarilhmos.
  61. uod si liceret honc calculandi modum transferre ad imaginarias
  62. s
  63. CT aequo CB + B72. Ergo CT aequ. rY + rrss: ss- rr seu ex aeqo 2rr1s- F
  64. -r
  65. unde manifestum est CT non esse mediam proportionalem inter ret
  66. quod fanen fieri deveret, si eat cuus ille haberet in migmaris locum g
  67. Be appellato
  68. Radioseistente
  69. eu a aqu. s

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 23, fol. 25r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068041:0049?run=73