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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 124r

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. 123v); this page is its right half.

The machine reads it as

  1. Unde intelligi potest res mirabilis, appliculam altitudinus
  2. quilibet assignabili minoris esse mediam proportionalem inter altitu
  3. dinem qualibet dabili minerem, et eam, in qua a applicata basi
  4. quae applicatae suae aequalis est. seu quadratum applicatae esse aequale
  5. rectangulo altitudinis applicalae suae aequalis cum altitudine minima.
  6. Hinc data e altitudine applicatae suae aequali, c. erit
  7. d = C. et b =
  8. Rg4.
  9. Ergo intervalla tangentium ita stabunt:
  10. 36
  11. R42 a + 1. = Bg12 +a
  12. hg1ofa
  13. latus currae, minus qualibet nca asigatit
  14. Quod si jam sint Triangula infinita, quorum basis sit β.
  15. altitudines intervalla tangentium, Triangula ipsa erunt.
  16. 3c ( 4c(
  17. SC B
  18. etc. Quorum infinita simul
  19. 2+ a _43 + 144+ a N4 + sumta, aequantur;
  20. x
  21. Segmento parabolico, seu residuo semiparabolae Triangulo inscripto
  22. adem to quod si ergo praboli Rectangulum Parabolae incircumscriptum
  23. sit 3. et parabola 2. et Triangulum inscriptum 3 erit
  24. seg mertum Parabolicum 2 - 3 seu 4 - = = Ac
  25. proinde si semiparabolae altitudo et et applicata sit c. cum
  26. Rectangulum futurum sit c. et rarabola et Triangulum
  27. et Parabola 2C erit segmentum 2C c - 4c 3C
  28. Ergo C- erit omnibus illis Triangulis simul sumtis, dividatur
  29. utraque aequationis pars per c. Erit E=
  30. si tamen B. maximum horum se
  31. ultinum (nam ininfinitum progredi
  32. alioqum licet) definiatur.
  33. EA
  34. a
  35. +dC
  36. Rtea
  37. et.
  38. c are
  39. ha 4c
  40. 14 +1 146+L
  41. t
  42. 8+ a 3 2+4 Egsta
  43. ota
  44. et

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 124r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0247?run=74