Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 186v

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: 0.79.

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. 187r); this page is its left half.

The machine reads it as

  1. Geueralissime:
  2. quod eodem redit.. si scriberemus:
  3. fy dae + g, X dys +
  4. ere
  5. Sit data aequatio (1) inter X et y.
  6. Scribamus arbitrariam Z ap. Sdx + g Xdus + h+ lx + dx + P td
  7. C cuau
  8. m+ pX + 4
  9. ete
  10. Ex aequ. 1. datur aequatio (3.) inter de. X. y. dy
  11. ex
  12. +syret +
  13. Exae. Assumetur aequatio inter . y. Z. vel quod eodem redit inter X et Z
  14. Inde fiet aequatio (5) qua habebitur dZ quibus substitutis
  15. x
  16. in aequ. 2. sublata erunts dque dx. dus, et fiet aequ. (6)
  17. ubi huabetur V pure et rationaliter per X. y. g. Denique ex aequ. 6
  18. tollantur literae X. V. ope aequationum 1 et 4. Habebitur
  19. aequ(7) in qua quae erit quaesita si v non ascendat ultra
  20. Quadrat Simplicem valorem.
  21. Quoniani autem hoc semper haud dubie procedet, ob duplices
  22. arbitrarias, videndum saltem, quomodo id prestetur compendiose
  23. Est et alia via sine Transformatione per additiones
  24. rationalitr
  25. ordinatarum: Datur quadratura figurae cujus aequatio est X Abxtequ
  26. itemque fid X + b X + Cxy+ dy + C aequ. 0.
  27. OnQuia enim omnes figurae Rationales quadrati possunt vel
  28. absolutae vel ex data circuli et Hyperbolae quadratura. Hinc
  29. + KX
  30. datur quadratura figurae, cujus aequatio est axx bxytexeus + f aqu. o
  31. cujus aequatio
  32. Datur et quadratura figurae
  33. 27+ h77 +1Z + my t n aequ. 0.
  34. Sit jauss. 93y + hyZ +- Cx + i Z + n aequ. 0.
  35. Fiat jam py + QB aequ. Z
  36. per aequ. 1. est
  37. y aequ axx + Cx + F
  38. (b X - e
  39. In aequ. 2 substituatur valor ipsius Z ex aequ. 3.
  40. frei +gyy + hqyo + l’y + mgv +n aequ. 0.
  41. aX
  42. py
  43. mpus
  44. +hgry
  45. liqu exaequr. fier:
  46. +per
  47. 29 ac X + 2g af X + 2gcf X +
  48. Ehp..
  49. 2hp
  50. +g c+.
  51. +lip
  52. 2 hp
  53. +hp
  54. 12 Pabx +a exxHC
  55. Inip
  56. +higr
  57. bc
  58. +lt.
  59. 2beX+C
  60. bx+ x +
  61. adequ n
  62. sbtticex
  63. +qm V +B
  64. +mt
  65. + qub vx + qmibexvt qme v +rbXk tu ibex n
  67. f
  68. a XX+C
  69. bx+ e
  70. taexx+tex et
  71. +ab Hb5 X +b5.
  72. in4V + n
  73. bx + e
  74. Im B+n
  75. +gA XXB
  76. abX + a e XX + CL X + e)
  77. + bc. fb5
  78. 53
  79. +
  80. toia
  81. ubi ut tollamus X: X.
  82. taciemus +g +hp aequ. 0
  83. e a ab aequa et siet.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 186v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0368?run=74