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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 115r

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: 0.88.

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

The machine reads it as

  1. e LG: GE: CL: CE. (L: BF.: 9: 1
  2. pa 3 sex C+ = 4BF (pE, aeq3) sau 4bi
  3. seu Ct = G. Z X LG: CL. TH: HC. ia
  4. HCHC. q. FB. es, ZB (per let 5) = rrar X
  5. tHC= yxfr GX sad THA BY AT
  6. eAT X -TB = 1+ Y - rYX = A4. Eg
  7. TH = r-I. IAY- rYX. Ergo ex, G et I
  8. fit LG LG. C seu (perb) 92. C= C17
  9. ETH: HC id est per u et GE: CE epit
  10. e+ r rV: gY. Est autem GE= b- FG
  11. e rE st et FG = CC,:Y et
  12. TF = Z - AT = Z - 1+r- pX = ZC. Ex
  13. Ergo ex 18 per 19 et 20 fil G8= b- Z.Y + i Fr. VX: V
  14. C=Ex CG agatur CM normalis in M adt
  15. FE Erit AE = v - BC = v - r= IX= ME
  16. et CEqu= MEqu + BFqu. Ergo fit
  17. CEqu. = vv - 2r - 1 VX + r-1. r= (XX +
  18. 22= 2XZ + XX seu CEqu vou
  19. V -2. =I VX + rr - 2YXX 1 ZZ. 1x
  20. Ergo ex 17 per 21 et 24, fiet
  21. I 1+r =rr: qqer= vr -Z+ tK NXXX,
  22. Ero vv - ZV. VXF rY - 2VXX - 2XZ +23
  23. Atque hc tantum quidem ex unico
  24. puncto duci potest. Sed _ quoniam
  25. duobus punctis proximis C et (C) non
  26. tantum maneat puncta adeoque B et B
  27. non tantum manent puncta A et B
  28. adeo rectae AFZ et FE, V. sed
  29. etiam manet AC+ CE constans
  30. seu aequalis A(C) + ( (C) E; ideo
  31. BE vocetur AC + CE = C. seu fiet
  32. Ov- ZY = IBX + rY - 2YXX = 2X Z+ 23
  33. EC = 2gX + 99XX.. itaope
  34. quia autem duae ad sunt variabiles
  35. nempe X er Y, (quae Y etiam latet in
  36. hinc si differentiemus ae99. 25 et 27, habebim
  37. epdx: ar bis in differentiali ipsius 25
  38. in differentiali ipsius 27, unde tollento ex
  39. his duabus differentialibus prodit nova aequatu
  40. ordinaria, quam conjungendo
  41. t 26, tolli
  42. loterit
  43. 1
  44. ipsius 23
  45. idem fiet
  46. ope aegg. 23 et 4
  47. ante differentiationem
  48. tollas X, restabit equ fiet aequatio in qua
  49. bla bariabilis erit _Y, unde differentia
  50. evanescet dr, et fiet aequatio in qua
  51. erunt X, F, Y, V, Z
  52. erginee in qua t
  53. cujus op
  54. in qua sotae ordinario
  55. quo juncta cum gg. 25 et 26, tol
  56. itaque tolli potest c
  57. videm abest X
  58. be aequationis disperentiandae, et en
  59. utroque ante
  60. crfferentialis
  61. modo procedas, supersunt veciabiles Y
  62. v. Nob
  63. indeterminatae X Y
  64. , est autem C arca
  65. er si malie
  66. urvae data demtus vel minutus
  67. in i
  68. data est curva E(E)
  69. nem in rectam
  70. hinc
  71. tus extensu
  72. soluta. Et aliter
  73. habuiffumus Relationem inter
  74. habuissemus et arcus longitudinem
  75. curvae C(C)
  76. ladeoquet
  77. adinarie haberentur
  78. cum tamen debeaut haberi e quad
  79. granscendenter, itaque nec ista via tam
  80. lansibiris, per cur
  81. lineas datas CL
  82. rectas vel curvas) quaesitae in dati anguli
  83. dit dua
  84. loco occurrentes;
  85. edit saut
  86. eoleum i
  87. ne potuit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 115r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0229?run=74