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Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 49r

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: 0.83.

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The machine reads it as

  1. De Transcendentius differentundo Tollibilibus et quod si oneuggaatur; nn aeq. diferentiam omnia
  2. queant postremo ad aeg. differeatiali cacoatem, quae debet
  3. esse
  4. a si quantilis st transcenieas
  5. a pater et hinc rediici posse via ad unicam tatem Euusaepdent ( 30+ 3y 50+ 51Y rf9y = 0
  6. dy. dx 10+ Ny +1299,. 20 + ay + 227y.
  7. sit
  8. LM +N = 0 si N = G VX fiet LN- des
  9. N = _(2) yiX fiet a X Z y (3) g.X + dx (4) qX seu dy P+ dx Q = dy (X) + du N)
  10. dy: dx = 628 A: B
  11. porio iso
  12. M C p set M lg L E log p Ergo M(d L 1L sa B. B pe)d P. L.
  13. et
  14. +L, d L. jam d L = M. L dL + sol: L d
  15. -
  16. Ergo fiet dP M
  17. jam dL = dy () + ax (L) et aM = ay () + d dx (I). Ergo ex aegq. 2, 5, 67
  18. (ettdus P = dx Z + M. L Rdy + M L Sdx 1 fdL et F dy + side. L. Wax
  19. fiet 04 dy (N) + dx (N) + M L (L) du + M. L= (LDAx + (AL: L (M dy + saL: L (MD ax
  20. 0
  21. et ex gert.fiec (V) + M. L = L) + (aL: L(M) A + (D + M. L= 1y + (a L: L (n D B =
  22. seu ma: L (A D
  23. et fiet: (L): L dy + (Di L ex (+ A(()) dy + A_, (X). D dx + (N) (2) dy + (N) () ax
  24. m = = N: L. hic ob
  25. L
  26. 1X
  27. a = () ay +CY)
  28. Ad (X) = (. (1).)dy +C
  29. a(XD = (1 (ND) (1
  30. L((2)) (((1)3.) ayr VL. C1).
  31. et ita seo rro
  32. 2 (L) dy rt) ax=
  33. L
  34. + B(1(XD.) dyt B ((X B. I) ex + (X Y (B dy + (A B BD ex
  35. FM. N( SA ((L).) dytA (C CL). B dx + (L) (1) dy +(1) (N) ax ( 2) A
  36. CB(1((LD) dy +B(. ((+ D. ) ax =+ (L MB) dy (LAB) ax (()B
  37. =G)A + (DB. L () L. M. (1) ay L MYEX L LK (M) Ly t LN C M B dx
  38. = M N(L) dy= MN(LDdX
  39. (N) AENDBOnNiEeB(A C Cn ).) dy + A C. C9). D ax + (M) () ay t B ) () dx
  40. LB (1 (n).) dy +B ((. C n J. ) ax (1) () ay Xl) By ax
  41. A (1) =+ B(CMY
  42. Ex, hac 6qualione collendo dy. dx per cag. 1
  43. ut prodeat aequad identica
  44. debent oia talia esse
  45. ler exhis patet suffecisse si statum ab initio ad solventam aequ. 1.
  46. di ad hibuissemus non aryu. 2. sed aeg. I1 scrbendo (dL: L + SI=0
  47. quia in arg. 1. nes in effectu eo redacta est reduci pe, posito
  48. si, M, ( esse ordinarias, non ita et () (M) etc. sunt odinario
  49. adeoque ora in ory. U demto (dL: L. Ergo abt aequatio quaesita,
  50. solvi pt per aeq. quae sit saL: L + 61 =0. simplicarem
  51. utique quam 2. et genegaliter, si differentremus aegu.
  52. aaequadem 2. et differentialem conjungamus cum orqu. 1
  53. datu, contrnuando semper demue rem o unicam trausien
  54. dentalem resid ad aequadem reducemus in qua oes transce
  55. dentales differentiando collibiles (nempe
  56. sevales nempe sunt Tetragoniftdcae, vel Exptonen
  57. tiales supersunt praeter unicam. ergo semper
  58. res reduci pb ad unicam Transcendentatem
  59. sollibliem differentiando.
  60. incisio, non esse posibile
  61. mitem
  62. differentiates
  63. Unde jam suspicari
  64. 2
  65. sit omnes aquades
  66. implicatae, seu tangentium inversae
  67. per socas Tetragonistica vel Exponentiales colanti
  68. Cogitandum ergo de genere novo exprimendi apto
  69. saltem ad constructiones
  70. edi
  71. fratio

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 49r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068051:0097?run=73