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Leibniz-Handschriften zur Mathematik LH 35, 10, 13, fol. 13r

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: 0.89.

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. 6v); this page is its right half.

The machine reads it as

  1. em quia non valde difficilis est
  2. exequi placet, e primum quide
  3. si omnia sint in rodem plano
  4. ND sit Ap et _N) sit du erit
  5. ND sit du et D(V) augnentu
  6. DN m incrementum ipsius FN seu descenseus ponderis vocetur du
  7. et D(N) delinatio in latus seu crementum ipsius AF, voletur df
  8. ANL ef adeoque FN sit n, et AFFKF, fietque proinde
  9. + FN _ et d. AN = AF DNY) L FN. DN: _AN. Eodem
  10. equ d ANV
  11. modo d. BN ~ - BF. D(N) L FN. DN,: BN et d. CN = - YF. DNV) L FN. DN,: DCN
  12. possibilium minimum, id est debet esse nullum, seu fi
  13. oBF, D(G + FN. DN
  14. BN.
  15. = cF. 1) + Fv DX (5)
  16. . CN
  17. Patet enim si nulla sit ista quantitas ulto minorem fore quam alias
  18. sit ergo EAF. BN DCN + BF. AN. _CN + H. CF N. ABN (6) DN
  19. FN. B DBNHCN +GPA N ACN + H _ AN ABN
  20. seu sit: -E.AF: +GBF: BN+ CF: CN
  21. EIC FN EANA G. BN AH:
  22. (7) DN
  23. XN)
  24. D()
  25. si esst si E, G, H, forent aequales
  26. res redipet ad theorema a mesilulam
  27. de invenienda tangente curve
  28. Cujus in qua summae AN+BN+ C
  29. debent esse aequales
  30. quod si velum rem etiam exprimere per curvam, st concipi summu in rectangulis
  31. ub, rectis ei AN, BN, CN, in datas respondentes E, G, H factis
  32. am jungendo aequationem 2 et _7 reperietur d. AV: DX nam
  33. debere esse aqualem
  34. per 59. 7. tollatur De) ex aeq. 2. fiet:
  35. L. AN: FN. C.AN + G: DI + H: N
  36. DN
  37. Ergo L. AN - dBN
  38. 1
  39. =E. AF: AN + G. BF: BN + H. CF: N
  40. En
  41. FN FN = FN. BN-AX Quod est theorema elegans
  42. BY
  43. AN. BX
  44. Nempe differentia quibus trahuntur duae quaevis chordae est ad AN, BV
  45. AN
  46. DN
  47. conatuum
  48. conatum
  49. a pondere N (nempe d. AN d. BN) est ad oimponderis trahentis X
  50. (nempe ad DN) _ e in ratione composita radisd secantem (B)
  51. anguli majoris et differentiae secantium ad secantem anguli minoris (FNA
  52. Et differenli duorum cha conatuum quibus trahuntur paria aordarum sunt (d AN- dBN
  53. binae chorda
  54. sunt in ratione composita directa differentiarum inter chordas, et raciproca rectanus
  55. (BN - AN) et reciproca rectangulorum sub chordis. ponendo clavos chordarum
  56. Quod m Theorema etiam verum est, si pondus
  57. N per pendiculariter desceidere conetur seu regatur a crena perpendiculari
  58. in eodem horizonte.
  59. AX- Nq C: um:: EN. XB- AV 4: X B. AA ex aminandum an hoc verum
  60. a
  61. A N = s, A H
  62. AN= si
  63. et pro inde resistenti intit
  64. AF. D (V) + F N. DN
  65. .AN

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 13, fol. 13r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068166:0025?run=74