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Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 10r

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: 0.78.

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The machine reads it as

  1. Examinemus Calculo solationem problematis de figura in quam
  2. c
  3. se pondere proprio carvat funis.
  4. S
  5. Ca veccece
  6. ranscementem dy=aax: Exx-aa
  7. 2
  8. Invenimas autem Aequationem
  9. Aequatio autem praestanda est
  10. y Sax +du: (Nax +dus = y - X dy: dx.
  11. seu fiet.
  12. Fyraxrdu (Sapidus V- (sax tau el der dx
  13. X dy: ax
  14. en (y Faxadus) (Fax edis dyst y dxray) - udx +ay X dy: dx(= ssatus dus son. dus
  15. a
  16. jatum ayx per I est dy: dx = a: 1XX - aa. adeoque fiet
  17. e
  18. seu vax nau dy. dx = =Sranaau d ay. dx
  19. 4x
  20. d dy: dx = axdx: _ (.2) Xx- aa adeoque per . , ex A~9. 5 peretu
  21. co = (-1.2 Cd dc) fit EF +a a: SXK aa = = XadX. XX- aa ExK-aa seu
  22. 1.2
  23. 23: 2
  24. sit C0 = Xx - aa. de
  25. fiet d 1.rxa na
  26. sex aa d
  27. e
  28. et a a: LXX= aa
  29. red
  30. ap
  31. sublato communi divissre irnationali fit. ( sit Hrixa
  32. = = (, 2 2 a X AX: XX. 04 Yer aa
  33. ex +que = X dx: XX- aa. Adeoque Ax idy dx. Xx. ( nr a
  34. seu 1 + dy idr = XX: PI xX a4
  35. seu 1 + aa. XKG XX. 1 XX aa.
  36. seu 1 + aa: xx aa = XX. B( ex aa
  37. C
  38. ergo subest error inralculo
  39. eu XX aa +aa XX
  40. XX aa P) XX aa
  41. Vdx + du a: (XX -aa = - ( Sax +du a XaX: XX - aa 1XY-aa seu divisione facta
  42. L (10)
  43. adeoque er aequ. 5. ex n 6 et 7. fit:
  44. eu Yax +dy - x (Sdx +du X: Ex aa. sive Sit dy. de =- sot lyX. n a
  45. lesen pro du: ax ponendovalorem ex aeq. 6 fit 1+ dy: du = X: rxx- aa. Ergo ex 10 et I1 fiet
  46. (11)
  47. 1=-Fax +dg: sex aa seu Exx aa _-Ssaxraus. cujus differen
  48. 1
  49. tialis est: Dx dx : Ixx -aa = - Sdx + dus seu XXdx: XX aa = dx + dy. seu
  50. (14)
  51. XX: XX =aa = 1 + du: dx quod succedit test enim ipsissima aequatio 11
  52. (16)
  53. Itaque habemus solutionem desiteratam
  54. si velimus a dx: exx-aa invenire rationaliter sic licebit procedere. Sumatur
  55. XX aa = (X ZXC DC00 et X = co:2 + aa: 2C0. fit adeoque YXX- aa = X
  56. Ergo isiet denique
  57. dx = deo: 2 - aa dco: 20000 sen =coco- aa . ticoco
  58. A dx aa: YxK- aa = cocoto coco -aa duo: 2c0co aa: aa = 4c000: 10 =- d0 : o
  59. +aa: 2C0 W: L= aa loco: rd
  60. Ergosetdentr
  61. quae pendet ex quadratura hyperbolae. Itaque problema est solutum. Nam
  62. qdordinatae hujus curvae ad tangentem verticis su basius, sunt lagarithmi ipsarum co
  63. 1 L
  64. paxem
  65. seu ipsarum X = Xxaaa posito X ese abscissas seu AB

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068056:0019?run=73