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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 31r

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: 0.85.

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

The machine reads it as

  1. Investigatio
  2. semidiametri circuli curvam, in proposito
  3. puncto osculantis, si pro ordinatis ad hibeantur convergentes
  4. ad certum punctum
  5. ad centrum radiorum p
  6. sit curva 16GC, e unde radii convergentes pC; quaeritur punctum
  7. Vcentrum circuli osculantis, adeoque Cv ejus radius semidiameter, sint
  8. elementa arcuum 1C2C, 2C3C unde ex 2C et 3C extremx per pendiculanite
  9. eductae concurrant in V. ex 2C in 4 prc perpendicularis 2C.L
  10. et ex V in P, C et P2C, perpendiculares ViZ, VIZ ex quibus V1Z secat
  11. Producta) PrC in d, et V2Z secat pic in β.
  12. patel obte e similiu In triangulo pharacteristico 261L+C
  13. EC iL 2C, a vicetur: 1C.L, dx. iL2C dy; et 1C2C, de et PC, X
  14. ob triangula 2C 1L1C, eV
  15. CZV similia fit CZ, Z
  16. sit CZ: CV: d dus: dc.
  17. Russus ob triangula Y V2Zd
  18. et P1Z5 similia sit d 2Z: d1Z: VZ
  19. PZ denique
  20. ob triangula P1Z8 et PI L 2C similia fit 1Zd: 1L 2C son dy:. pZ: p
  21. C.
  22. Ergo dZ diZ Tollendo _d1Z ex analogia 2 per analogium 3. fit
  23. L d2Z. PC: dy. P.
  24. eX
  25. Z. PZ seu S2Z: dys. VL
  26. C
  27. jam quia ed et srZ differeulinum hubent haberi possunt pro parallelis
  28. errore inde sidifferentia enmerit infinitres, si 12d et B2Z considerentur ut
  29. elementa arcuum centris p radiis pB, P, Z P2Z descriptorum, patet, sumi posse
  30. d2Z pro β1Z seu d2Z esse differentiam inter P1Z et p2Z adeoque
  31. d27 esse = d p=
  32. L
  33. 17)s
  34. iu
  35. dy. L: pC jam PZ = PC, 7 CZ. Ergo
  36. o)
  37. dez = d pC - dCZ jam d PC = x, et dC d cZ - d ay: de per 1
  38. quos valores substituendo in aeq. 9. fit d PZ = dX - CV a dy: ac dyVZ: p
  39. WZ= VE VZ: VC:: dx: de Ergo set
  40. per 7
  41. jam V d VZive
  42. et dy = XcO: a posito eo angut esse anguli etament seu alculationis circa
  43. 4
  44. elementum, nam ta ratio a; nam 1L2C seu dus sunt in ratione composita
  45. radiorum pC seux et argulorum 1CP2C Ergo dy: Bc = coia. Ergo denique
  46. E
  47. ex y 12. (3. 14 fit dx = eV d dy: de= dxxia d de et denius
  48. ax
  49. ju
  50. ai a ag. nc. aqo
  51. Ergo CV = dX: d dy: dc + Codx: a de
  52. jam ddue: de =

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 31r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0061?run=74