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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 141r

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: 0.75.

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. 140v); this page is its right half.

The machine reads it as

  1. curvae generatricis, est illud in quo se datae curvae
  2. perpendiculares secant.
  3. van y.
  4. IVLPNF
  5. 2V- N (y)
  6. _
  7. SiP
  8. (P)
  9. A 82P
  10. si si1V. P = 2V. PB ppB(p
  11. 22
  12. Ergo 1P - P dp = dx. Si B, Si P - , B2 F
  13. et loco (y) (P fiet:
  14. 5
  15. ∞+ dy
  16. P+ ax
  17. Z A Sip- dp + dx
  18. jam S, P aequ. . ergo fiet
  19. vel multiplicando per erucem.
  20. 127
  21. 2V2PH(p
  22. 1V2V dx
  23. r7
  24. 1V. P - 2V2 P, .V2V+ 1 P P
  25. (y) A V + dus.
  26. y
  27. 3 + dus
  28. B Sip- dx + x
  29. p + dp
  30. A P2- xt ax
  31. pZ dus - dpy + dx y A ap Z)
  32. fiet.
  33. sie si jam faciamus ex dp dx id enim
  34. aliquando ob arbitrariarum assumtionem fieri potest:
  35. ax. sine y aequ
  36. fiet du
  37. sin faciamus
  38. de
  39. sed missis assumtionibus arbihariis fier:
  40. licet
  41. d 2)-dus pZ H V ax - ap.
  42. Z y, dx- dx
  43. y 1
  44. ap y - dy p
  45. datur et Dq aequ 9. et Q1V aequ. X.
  46. VSp Vp - 5 P.
  47. 1Z
  48. dx-ax y2
  49. dps dyp
  50. 5 aequ QV - V5
  51. Ergo QS p X - p + PE aequ BY
  52. et fiet: X - 2Xp + 2X p Z + p - 2p Z + pr 2
  53. du + ady-dy aqu. d
  54. Nota BB
  55. et dp p dy, dy y ds u
  56. IX
  57. P
  58. quae postulat quadratarum hyperbolae
  59. seu
  60. en
  61. ursus jungatur. DB quae est data et sit aequ. d.
  62. Ix
  63. du
  64. 2 F 9 +24743
  65. . seu p H y dus
  66. dx
  67. jam ds dus adque-dx
  68. fiet dx p dy + vdau - ydx
  69. do
  70. du I
  71. dei
  72. l
  73. du dx + y daus - y dux
  74. substitutisque vatoribus dx. p in ipsorum locum in da duabus H
  75. aequationibus quibus valor ipsius Z explimitur, tolbi, tolli poterunt
  76. Z et p. et solum supererunt X. y. de dgys. yadx. adqus.
  77. compendii causa ponamus g+o, rrsus se quad + sit quad oqo B. P si
  78. seu Z+
  79. cus rebe cigieus centro
  80. b
  81. u
  82. sed spunet
  83. ipsi
  84. BN
  85. DF
  86. D9+SB
  87. cx a x
  88. SB
  89. 1pa P p
  90. Si P

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 141r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0283?run=74