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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 57r

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: 0.85.

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. 58v); this page is its right half.

The machine reads it as

  1. Melius in alia scheda
  2. Aequatio datdy: du (+ my +ngus t prsfek 3:, 9 Hry ttyysy Aet= equatio quaesita
  3. differentialions liberata sit 0 at bytcgy + eu+ etc quae differentiata duubit
  4. =24. d30 +23, 431 + e2 d32F y Bg lx, da + ydb + yydc + ye etc a 0+ 1bG k29) + 3Cyy + 4f Y+ et =3 -0
  5. ed
  6. 1. 15. 31 72. 142 +3,13 33+. 12. 34 +5. 11. 35116 = 25. d30 424. a31 + 23cera l3 3 a u dx 4 + dyt =0 seu dh: dx = 4: t = + = C: D. seu 2d = tC. seu fiet
  7. Il
  8. lemyangus rete ibys F2cGt3 eyy ret otryt lyy tete, da t yssot yyde + yderen
  9. 1be+ Edyt 3egys + 4ffy +5gl y
  10. +Am tem +hem 1+fm
  11. Sit aequatio data - dy: dx = 1 = 10 FH y + 12gy +13y retC, :, 20. + 219 + 23 yyt23y ek = 2 - 0. 7
  12. Sit aequatio quaesit 0= 3 = 30 +, 31y. +32yy +33y + etc. quae differentiata dabit
  13. 0= 4 = dx (d30 + y d31 F gy d32 +y d33 t etc) + dy (c31 + 2. 32y+ 3. 33yy +4. 39y t etc
  14. seu 0 = 5 = dx = + dyC unde - dy: dx = 5 = 2 it = 6 = C: D. seu C3t - 4
  15. 1. 10. 31) +2. 10. 32Y + 3. 10. 33 yy + 4. 1034y t ete . 20430. + 30d3y + 20 d3 ryy + 2o 43Gre
  16. +1. 11. 31 2. 11. 32
  17. 1 3. 11. 33
  18. a 1. 12, 315
  19. v1
  20. 2. 12. 32
  21. 1. 13. 31
  22. YZ1. 430. 21 431 21432
  23. determinantur
  24. ubi 10, 11, 12 etc, 20, 21, 22, ete
  25. sit 10=0 et sit 30 constans seu d30 0 fiet:
  26. dx, 11. 11. 31,
  27. dx; J. 12 31 + 2. 11. 32,
  28. 31 + 2. 17. 32 + 3. 11. 33
  29. 22d30 22 d31
  30. 30, 31, 324 etc d ex X
  31. g
  32. =10 = 20 a3I
  33. =11 = 20 d32 + 21 d 30dx
  34. =12 = 30 33 + (21 d34 + 22 d31) ex
  35. et
  36. etc
  37. 23 d30
  38. dX, li. 18. 31 + et c3. 32
  39. Et s e habetur solutio. Nam pe quia generaliter possumus
  40. solvere hanc aquationem. Z+. dque hv, +i dv + K dX o posito h, i, k
  41. dari per X, hinc h solvi possunt aequationes 10, 11, 12, etc. Nam per ag +0
  42. sit dsts dxi n ex. 14. 20 et habetur per 31 Hinc porro per
  43. aequu sit Nam in aequ. 7 termini ultimi utrobique evanestunt ob 10 =0, et d30 =0
  44. uati
  45. sed 31 ex = d31 fit dX 1. 11. 31 = 20 d31 seu dx, 1. 11: 20 = d31: 31 quod
  46. in raquat sed dermini pengise
  47. aequatia
  48. haberi potest per Cogarithmos. Termini an depenultimi aequati, dant:
  49. dx, 1. 12. 31 + 2. 11. 33 = 1 20 432dX + 21 d 31 dx seu dx, 1.12. 31 +2. 1. 32 = 11 = 20 d32+ 21 d Vd
  50. se ubi eum 31 jam habeatur fiet +1. 12 3,1 edx + 2d. 32 dx = 20 d32 quod perinde est
  51. ac si pro 32 ponendo V, et pro Z. I1 ponendo h, et pro 1. 13. 31 - 1. 21 431 ponendo K et pro-20
  52. similiter inventis jam
  53. 1. 21. 431
  54. a Kdx +hodx F idv ∞0
  55. 31 et 32 inveniri potest 33 per aequ. 12. simili methodo. Nam aequandi
  56. ponendo; scripsissemus
  57. comparando Terminos ter quartos perantepenultimos, fiet q 11. 3F +E
  58. dx) (1. 1. 71. + 2. 12. 32 + 3. 11. 33 = 22 d3i dx + 2 d3e +, 20 433de C et pro od. 33 dX
  59. ponendo d33, fiet fol. 13. 31 + 2. 12. 32) dx - H 3. 11. 33dx f 2- 20 d33 =0
  60. ∞1. 22d3100. 21 432
  61. quae ide ope pujus 33 habeni potest ad modum Aequationis. 13
  62. Itaque ad omnes Aequationes Tancentiales rationihes solve
  63. membra.
  64. determinandas tantum dispiciendum an possint. tolli terini in quibus
  65. est qua per unam tantum ordinatam afficiuntur quae
  66. comprehenduntur hoc membro: dx t Idx posito ID da determinari
  67. sid
  68. quomodocunque non per non aliam indeterminatam quam a
  69. a sit A
  70. X = 200 + 201Z:, 30021301
  71. Et ubi 100 101, 102, etc sunt intre sed 200, 201, 300 30l ad hibentur ad tollendum, terminum
  72. ergo sit 10 = 100 + 101 X + 182 XX + 103 X + etc
  73. terminum 93. quanquae 301 possit poni 0. ita in aeq. du aequatione data seu 1, quae
  74. erat 102 -dus3 dx = 10 4 1y+yy + etC 7: 120 + (21 y +22yy+ et C. in
  75. in 10 de primetur X ab X ad X Z a 7) ad 2Z. Sed eodem modo faciendo
  76. pur
  77. et p destruetur ubi rursus
  78. F.8 +.. 8 et faciendo =. 600 + 601: 300l 470
  79. rursus Z = 400 + 401, :, 5008+501; destrub
  80. at selal inbetiur soiauta ritius srmentire cotantur mil prues seruagus et 13)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 57r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0113?run=74