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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 55r

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: 0.84.

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. 56v); this page is its right half.

The machine reads it as

  1. C= 2 =O: D
  2. sit aqualio data -dy: dx = 1 = 10 ruy + 1yy+ 3y CtC: 20tuytngy rasse
  3. ote quaesita 0 =3 = 30 + 31y + 3299+33 + 34 y etc, quae differentiata dabit.
  4. 0=4 = dx (430 +y 43, + yy d32 + p 433 + etC) + dy (1.31 +2. 32y+ 3. 33yy + 4. 3477 etc) = 5- dx 4 dyt
  5. unde - dy: dx = 6 = 4. t 27=O: D adeoque Ot = 8 = D2 Atq adeo fiet.
  6. . 10. 31 + 2. 10.32y + 3. 10.33yy + 4, 10.347+ etc = 9= 20 130. dyy + 20d3ryy + 20 d 3y tet
  7. +1. H1. 31
  8. 2. I1. 32
  9. 3. 11. 330
  10. 2. 12.32
  11. 21 430 21. d31 21.432
  12. Haec aequatio aliquam est identia 22 30 22. d31
  13. 23. 430
  14. sed regulariter hoc postulandum non est
  15. itaque coincidentietur potius alteri aequationi, factae ex ductu quaesitae e in artitrariam, formulam
  16. 1. 13,31
  17. quae sit 4 +a2y + 43yy + 44 + etc. Unde fiet productum
  18. Lu
  19. 30. 41 + 30. 42)
  20. odro
  21. F31 41
  22. +30. 43gy + 30. 44y7 + et =10 =0 et prodeunt aequationes
  23. 2. 10. 32+ 41. 31
  24. 1. 11. 31 47. 30
  25. coltii
  26. 1e 3,102) = 3l. 1
  27. 2. 11. 32-
  28. 1. 12131
  29. ponamus aiquationem datam esse
  30. 29 430
  31. coincidentiantes quae scquantur
  32. plitatobus 10, e 11, 12, 13 C 14, 15, etc. et
  33. sed et et ex issis 24 2t, 22, 23, 24 ete habere solum 20 et 21
  34. edrete
  35. prodibu aequationes A1. 30 = 2d30, 41. 31 + 42. 30 = 20 d31
  36. eu ordinet habere slum lite
  37. 13. 31 +48, 33 + 42. 32 + 43. 31 + 44. 30 = 20433 +22431. Sed placet ordine exponer
  38. 41. 32 +42. 31 +43. 30 = 20. 432 + 22430
  39. 141. 30, .3
  40. on
  41. 2. 13, 32491. 34
  42. 41. 32 1.13. 31 +4133
  43. 20456
  44. 3.t . quus
  45. videamus jam qua
  46. ratione res possit
  47. finiri, ut quam
  48. 4+, sit 0 et 30 sit constans et
  49. prima aequatio habetur, A1 sit constars et erit (d30. 30 -71Fdp. 20 si jam 42 sit 0. fiet
  50. 30 et
  51. vidanus an licent fatere =0 quis qu
  52. loganthimi eorum
  53. differant constente N sit 43, et 94 et 20 et fie in
  54. n+ = 38. vel certe habebitur dotem vodo, ut in summando
  55. 41 32 aequ. 20d32 + edjon Aihoo seu 20. 4g2 aequ. 20 d3c + 41. 22 30, et haberi
  56. 3, 35, 36, etc =, et
  57. potest 32. ex dende B. 31 441. 33 = 20 d33 + 22d3) et habetur 33.
  58. 43 44 3144 45. 46 etc. ilidem esse 0. Et ex aequti Et Maeter ultimam aequationem
  59. ponamus in hoq caso non assurgi ultra
  60. 35 feur 33 G
  61. et adeo esse
  62. h.B3. 33, = 22433 seu (d73: 33 3 sdx. 13: 22
  63. et habetur 33 absolute. Aequatio genultima dabit 2. 13. 32 +42. 33 =22 d32. ubi 33
  64. nil turbat. Sed aeq. antepenultima est l. 13. 31 + ( 41. 33. + E2. 32d32 - 2 (13, 33) 32 qu. 20d33 te2 c 31
  65. nulla prodibit alia Ex ex ipsa siet
  66. fi, 22. 13. 20.32 + 42. 20. 852 22. 41. 32 H22. 42. 31 + 43 = 22. 22. 41. 30. Et exk aeg. 4
  67. seu antesenult. fiet 20. 13. 31F 20. 33. 41 + 20. 42. 32 aequ)20 d33 + 22. 41. 31 + 22. 42. 30
  68. sed video nos pro 6 649. habere 30, 31, 32, 33, 40, 41, 42, Quod subicit. Ex perutli Tertia aeq.
  69. ia aequi
  70. Ex 1. Aer. 4r = 2t 20d30: 30 et 20 d30. 31 + 42. 30 = 20. 30d31 et 42 = 20. 30d31 -20. 31 d30; 30
  71. seu pen antep eagltima fit 241. 32+ 20. 47. 3) aeg. 2 20 d32 4 22. 91. 3 ex
  72. Exaeq. 3 est, 20. 30132 4 30, 31. 20. 30d31 - 31. 20. 31. 430 = 20. 38d32 + 22. 30d30
  73. supersunt adunc duae aeget. pro 30, 31, 32 nam 33 per ultimam habetur. Et haum cum sint
  74. et d32: dHC et d si possemus aequatione
  75. Tollamus omnes
  76. iacnit disfe entules rationesduae d3i: de
  77. ote te cetu aetise tentus sen tt
  78. Et ita porro
  79. minimum ascendamue
  80. 1. 10.31
  81. 4. 16. 34 Y +1133
  82. 3. 11. 33 42. 3
  83. 2, 12, 32
  84. l 13. 31 44.30

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 55r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0109?run=74