Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 12r

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. 13v); this page is its right half.

The machine reads it as

  1. Habemus solutionom hujus aequationis ilus = 10+ ny fit endrm y = Bsit s dx 10
  2. proponatur jam dy = 10 + 11y + 13 dy fict y = sd ( + 5. 13 ddus
  3. BSI
  4. sudx
  5. BSi
  6. itaque si 13: bs= sit constrns C fet y = bs, (10 ( 14 du 2, Ergo (3 13(b
  7. 5F
  8. SbS
  9. Ergo si 13: _ bs sit constans potest solvi aequatio dy = 10 + 1y + (3 ddy
  10. Efficic Tentemus hoc efficere. Sit aequatio data dy = 10 + 11y + 13 ddy
  11. fiat y = p pV et dy = dpv + pdx et ddy = ddp V + 2dp dv + podr. Et habemus
  12. dv = 1 dp v + pdx = 10 + 1pV + ddp V +, 2 dpdv + p ddV
  13. o
  14. seu de = 1e + _∞ dp = a p +d dp - dp 1 + 10 + P - ddV
  15. - ex
  16. P = 2,
  17. P- 2dp3 p- 2dp13
  18. +pV cempendio dv = 20 + 2 B + 23 dd v
  19. debet esse 23: bs constans. Faciamus p esse constantem et fiet
  20. 23 = 13 et bs2t = bt IPsa, ita nihil lucrati sumus sed si p si ab. - 0
  21. fit 23= 13P :, p - 2. 13dp et 21 = u1B - dp, :, p - 2 13 dp
  22. et quia 23: bt c constanti fiet d23 = 21 b = 21. 23:c
  23. et
  24. d23: 23 = 21 A: c ergo tantum opus, summari posse 21
  25. Merentietur 23 ipsius 23 valor, habebitur landem aeq. debe
  26. sed debet p esse. 4oxx + 4 1X + 42. ta enim dap = 0
  27. sit 23 = 13, 40XX + 134IX + 13. 42 unde habetur et d23 habetur et 21
  28. +40 Xx + A1X + 4 2
  29. 413. 40X - 3. 13. 41
  30. et deberet aeg. fier identica
  31. sed tunc debere determinatur relatio
  32. inter 1 et 13.
  33. aqualio 12g9 + 9de L 1209y + 12 ydy + 102 dydy est aequatio quae solici potest
  34. nam fiat y = bsp, et fit 120 f b5~ bs + 112 bP v b V + 102 vv bN (SV = 0
  35. adeoque 1 120 + 112V + 102 rV = 0 sit _ y=
  36. sit aequatio 100 + AIy + H2 + d 121 4y 112 dy + 22)y = 0
  37. fiat y = 6 Z+c0 et fiet 100ZZ - 2. 1007CD+ 100 coc + 111 (Z = Coc0) + 1212 Y 212Z COH 12IC0
  38. c0
  39. (Z () (dZ + d0) (ZYC) (dq dec) 12 dco - 2cod2)
  40. Ponamus esse 12 =0 fiet dy : y = Y( ( 120: 102) et log y = ( Y (= 120: 102)
  41. (SV.
  42. ra
  43. 1099 = N27 1209y + 102 dyddy = 0 fit 120bs bs = 102 v b b v, 12 vdro
  44. y = p SV dy = v (V ddy - vo bs + du Bsv
  45. y = fdx Z s
  46. sit aequatio
  47. 102 Vb W ( + 102 pb v 1B ( V = 0
  48. seu 120 + 102 V + 102 V dv
  49. sit aequatio y + 11 dy + 12 ddus + d 121 dydy + 122 dy ddy = 0
  50. fiet du = A2: Z unde habetur aequatio, in qua ipsius Z affectiones ubique
  51. aeque altae. unde faciendo Z- bso habetur aequalio in qua V et du
  52. 10g seu ( = logZ = y et Hinc methodus gentralis omnem
  53. aequationem differentio differentialem in qua abest unius
  54. literae terminus a affectto ordinaria, atteliendi ad diterentialem
  55. ddy: dd dav: dd7 = dvdv+ d2dZ,: deodeo. sit dv: deo = dt: t ddv = deo tdct- 1 at
  56. tandemque dcot dat = duo dtat, deodeo = ddZ dtdt + tt dq dZ aZ. facendo t = bs ellemus quidem
  57. e o ui c otanate atis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0023?run=74