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Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 8r

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: 0.82.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.

The machine reads it as

  1. de est sucessus
  2. 10 Novembi. 1703
  3. Multis dentatis transformationibus faciibus, quibus tolleretur litera
  4. parameter ex aequatione langentiali; plerasque omnes comperi repugnare
  5. naturae: Una tamen novissime in mentem venit, quam nondum refutavius ea
  6. ob rei momentum examinanda est. Alibi ostendi tant Aequatione
  7. Jangentiali dari ag. dx ex y. a, et x: a, posito X et y esse cordinatas
  8. et a parametrum. sit jam y: a = deo: do et sit x: a = (2d0) Sddv:dZ. ubi
  9. pono lco esse constantem. Ex 1 fit dy: a = (4to) ddx deo: dodo et dx. a = (5to) ddv: dZ
  10. erit dd dy: dx = (6to) dZ deo dodo, sit jam aequatio data du: du (o) extgu,: ac
  11. quam explicando per 6, 2, 1 fiet rdco qu sade + deo deo seu Sddo 2 szdco- duodeo)
  12. seu adv 60) deo ddze
  13. avdo
  14. dcodv ddZe = 2 (d Z da = deo des) ddv.. jam est in nostra potestate assumere
  15. 2 dv S Zdco - deo d co)
  16. i F valorem ipsius da, quem permittunt Leges homogeneorum infinitesimales, et compendii
  17. 2d0 do Y(dZ de -deo deo)
  18. seu dav-
  19. = Causa esto dzdeo - deo dco = deo deo ddz ddz: ddvddr fiet dz - deo = deo duzaldz: ddv dd
  20. seu dz dav ddv = deo ddv ddv + deo ddZ ddZ, sive de = (13) dZ ddvdiv: + ddz ddZ
  21. 2x Ergoes aeq. 11. fet seu 2 2 dudo ddv razdio -deo dec) = t Zdcodvaz ddz - 2 dZe (d 2deo - d codeo) aldus
  22. : E. F fiet favav dco sadz) = 15) cedvaz laZ - 2 dz deoscleo feli faz: ddo) Et pro deo: ddo in hac
  23. aequatione substituendo valorem ex aequ. 15 fiet + 2dvav = (6) dudz - 2 dz ddque (dZ ddv:, ddvdlro + duz daz)
  24. e Et sive +Lavdv (ddv ddv + ddq la Z) + e d Z lZ dd Z ddv = (17) duaZ (ddv ddo + dd z dd 2
  25. = E sive fred (avaz = 2dv dv) (ddvado + ddz dd Z) = (17) 2 d Z dZ ddz ddv
  26. A
  27. 1 + 1(-
  28. dudz L 2dodo
  29. unde redu
  30. qE+ adz da zue 8) (d Z - 1= ldvaz f.do 1v) ddzi
  31. (2dody+ dodo (2) (avaz + 2d0 do)
  32. d2 dZ + Ae2- adv + 4 dud Zu avdo d7d7)
  33. dudz +. 2 dudv
  34. 4 2
  35. 4
  36. x ce ducr
  37. jam constat regula generali, fone a
  38. d Cdv: dx
  39. Datur ergo ddo ex do
  40. et sit compendio dav: ddz 2 rel (av: d2)
  41. dCdv: dZ)
  42. rel (du)-
  43. Res ergo quantum judicari potest redocta est ad quadraburas
  44. E Sed quia calculus polixior assumumue exe videamus an liceat exemplum
  45. rax + ab = gy. fit adx = ydy et _a:y - dy: dx = 2X + b,: y
  46. et a dx + b Xdx = ydy et y: (a +bX) = du: dus seu
  47. adhibere facilius:
  48. ey = a + b x, dx: dus jam (a + Bx) X = yy - ax seu a + b X = yy - ax, :X
  49. FErgo y. = (yy - aX,: X) dx: dy seu Xydy = gy a dy:dx = yy -ax,: xy ita b quod
  50. :2aX + XX b XX = yy
  51. notandum tollitur ex calculo. idem est si ex ope aequs. 1 et 2, voluisseruns tollere B
  52. D. NNam b: a = yy - 2ax, : x() = ydye = a dx,: (dx et fiet
  53. 4y - (2a = ydy = a) seu ut aute yy- ax = dy utrete seu yy - a x =7
  54. de 2Y 201X - 2x dx = X do
  55. av = ax,: xa = dv: 2dX sv. X): (3 v. X) - 2 (= f. X))
  56. sit ea log X + plog b: a) =L (Gy: ax) :, (yy: ax) - 2 =log2y - 2) dco: 1 - 2a Blo 1C0 - a)
  57. a a dx. x = ee
  58. pone yy = av fiet
  59. dv: dx = 2(∞ = X) - 2
  60. log(y 2) log, coeo qdta se XX B -c d log eo -24) seu
  61. gy- ax: xu = ag: de _ sit Y: a = alv. do idx et X: a = Sddv: d2 fiet 1
  62. yg - 24 seu Xxb: a = gy -2ax e ut oportebat
  63. et fit X log. X B
  64. sed nostra methodo pova
  65. dyidx = (dco ddp: duav
  66. (ado: de seu dyidx = duo dZ: dodx
  67. duo deodu en
  68. devJ: dque = = deo da acodco aZ + dv)ddv des dco du (dcodio daz L
  69. y: dx = (aZ. d) sdav.
  70. s fx): Sddv: di)
  71. -(dco: dv): Sadv: dz
  72. se 2 - a =
  73. sitsudd ddo Ecar. aa; lodvurc dud. d)a +dav: da Cardinadx tavadus: C (mo ralur.
  74. Ao . Zd. (Z + 2 d7a v dd vaaq= d Z dZ ddo dv = d vazue dd2 dav +. 4 a b ddv sdZ
  75. du = dx ddz seu log d
  76. et (i deaqe ddo ddo fa
  77. hypotuem nam ita fo
  78. ib=drao ddo i 1. ded sdaidoteo 1. omnita ab d
  79. dedo.
  80. 1t .
  81. llodcoZtdd
  82. lcd. Se
  83. dode Ado) : 2) (deo deo de + dx.
  84. povissinque vatore
  85. n Et exirubendo
  86. iseu ado C20)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0015?run=73