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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 145r

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: 0.81.

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. 146v); this page is its right half.

The machine reads it as

  1. homveoptota
  2. sit aequatio assumtitia transcendens, unde ducatur d tangentialis simplex
  3. 6 = l0 + IIX + InXI + 12 X + l2Xy L13 X, + (3or 31 X,2 32 Ny + 33X + 3. 33 X y L 3. X
  4. 40+ 41X 3
  5. = l gode + Iu oXxto A E. go XxAx + 2la A Ky qpa lil sop ly ) ( +. X. sp 3. lo a1 X gay + 2. la 1. 3 X ptx + li a. XAy 1 3. 13 1 X I
  6. ydy
  7. n ex
  8. ydus
  9. Im 1. a1
  10. ydx
  11. Xy
  12. Z.I2 ln. s 2B _ 13. 13. H
  13. 1. 21
  14. l30. 51 +3151 +31 5I 23251 32.51 3. 334 3. 32 51
  15. gelu
  16. )2
  17. 3251
  18. 3351
  19. Naer aequatio 2 conferatur cum aequabione generalis quas data (ut ipsa aeq. u inveniatur)
  20. (3 Sodrr9IXIG + SIXIx + Buxyax + 92 X ay + 82XZ +921 Xydy + 821 Xydx + 93 dy +93 X Ax
  21. Vax ydys
  22. a
  23. Vix
  24. Vdy
  25. ay
  26. Vax y’ay
  27. rgdx xisdus
  28. ubi praefigo cum differentialis dx vel dus) sequitur potentiam allior inferiorem, alias 8.
  29. nempe o 9npraefigo pro X ydy, quia x est superior potentia, et y inferior, habetur autem
  30. et tespiciende patet fore 921 = 3. 93. Caeterum in 8 et 9 ponatur latere 1. ita in S
  31. dia
  32. comparae 19q.
  33. comparatione omnium numerorum damtis praefixis Vivel 8velu, summae characterum sost fixarum
  34. idem conficiunt in eodem termino, vel indicant servadem legis homogenectum, quod calculi
  35. rectificationem adjuvat. Sed ut catculus sit tutior, ao hibeamus anteptraefixas, exprimentes novenarium residuum valoris
  36. pro 80. 91. 81. 811. 92.92. 921. 821, 93.83
  37. 191-481 = 1. - 2. 14. 40 2811+ 2.f2 = 411. 41 69 21 = 3393 subil 8rb. 191 4 81. 8139. Debgr. 182. 293, b69
  38. 241
  39. 11= 880-30. 51 : 40 = 191 - 111. 40 - 31. 51, : 41. Et ex 5q. 8 fit. 889. H - 30.51. 41 = 191. 40 - 111. 40 - 31. 40.5)
  40. fit 111 191.,40 - 31, 40. 51 = 889. 41 + 30. 51. 417: 40 111 (per X y) = 792 - 121. 40 -, 32.51, :41
  41. a
  42. et ex fit 1 = 191 - 481 + 2. 12. 40 et ex 5, 111 2 2.792 2811 +2. 12. 417: 41. Ex et B3 fi C 121 = 2811.797, 2.12. 41. 3251, :40
  43. Ex 1et B3 fit 12= 2,792-2811 - 191. 41 + 981. 919:, 2.40. 41 - 2, 41 cM p et 12 fit. 191. 40-31. 40. 51 -850. 41 130. 51 H- 191.90191 10; 240
  44. Ex A et 16 fit2 2811. 40-2,792. 403- 2.32. 40351 -2.191,40. 41 +2. 31, 40. 41. 51 + 2. 980. 41-2.30. 41. 511219140412 18,. 104
  45. 3: 2. 40t. Et aequando duos valores ipsius 12 ex 15 et 16. fint Z. 792. 40- X. 2811. 4072191. 48. 4 2. 451. 40. 412 2. 191 40. 41- 7. 31 40. 41. 5
  46. 1.880, 40. 41 + L. 30, 40. 91: 51 C2. 191. 40291442451. 48. 4) - 7. 191, 90 31 + 5, 21. 40. 1. 51 + L 880, 412. ( 20. gi. s 1 1). . 1 su.
  47. ita ex Eterminis dx, Xdy, Xdx, Xydx et xdus habuimus valores literarum 11, 111, 12, 12) et praekrea 69.19 A
  48. Ex X dx est 13 = 082 - 2. M. 41 - 32. 51, : 3. 40 = (ex X. 1∞) 683- 33. 51,: 3. 41 unde fit 12 = 3.682. 41 -3. 31, 41. 51
  49. 3.683. 40 + 3. 33,40.51 3: 6. 41
  50. 121 7 293 - 33.513 : 41 (ex Xytant XI) 1841 - 4683, 2. 33 5tj
  51. Ergo ex et 23 fit 2, 293- 2. 33. 51 = 1821 - .683-2. 33. 51 fit 2. 293 +6∞3 = 192)
  52. aequando duos valores ipsius 12 ex 16 et 21 fiet , 8. 191, 40 cu . Bii. 10. g2. 51 - 680. 412, . 30, 4. 51- frigi 30. 2l is e
  53. (26)
  54. 082. 46. 4]- 32: 40. 4151 - 683,407+ 33. 40.5)
  55. Et aequaddo duos valores 121 ex aeq. 17
  56. et 22fit. f 811. 40 H - f79C q. 2t f. 3i go. n. 51 f. 191 40. 11 4 f. 31. g0 4(. 31 + L. 58D. ~ - + 38 4(51t L. 191 46. 4 - f. 481 40 9, b) 1 18,
  57. Itaque invenimus valo Itaque ex decem comparationibus invenimus valores literarum
  58. quaesitarum 11, 1I, 12, 12Y 1t _ (9. 7.) _ III (aeq1o) ret (qC
  59. quaesitarum V, 11, 12, 121, 13. et determinaves datae ad comparandum per aeque, 6 et 25.
  60. et denique supersunt adhuc aequationes tres, nempe 18, 26, 27 in quibus non amplius
  61. Extant literae u, 11, 12, 121, 13. et ope harum trium aequationum resoli adimpletione,
  62. habemus adhuc literas affecta 3 30,41, 4 30, 3) 3233, 40, 41 0x quibus tamen
  63. (ue
  64. valent tantum quatuor. Utins pro inveniendis de, 31, 32, 33. considerndo 40,
  65. sinfinge4041, ambae literae in eribus residuis aequationibus destrnentur et ex aeg. 1 fiet: 2792 428H gng1- 41. 51
  66. porro est in nost a potestate salva gegervitate caccere ut sib 40=i
  67. Etiqita in aeq. 15 e vanescili.
  68. nec datur ejus valor, sed aeg. 15 et 18 e0 redeunt, ut sit 4= 2. 792 - 28113: 481- 191. Inventu ergo1, absolute jam
  69. 440 + 30s
  70. restant aequationes 26 et 27. in quibus s jam hibitas 40 et 41 relunquemus sine explicatione, ne examina
  71. r ex per abjectionem novenarii, et numeros homogeneitatis indices turbentur. Quaeramus igitur quantitates
  72. on endo aegq. 2b et 27. destruentur mutuo quae duobus punctis signavimus et fiet 2811. 46. 1- 79230. 41
  73. 082. 30. 41 - 683. 40 + 293. 40 et fit 41: 40 = 683 - 293,:,092+792- 2811
  74. jungendo un aequationes 28, 29, 31, habetur nova determinatio et sit 682+192 - 2811. E792- 291 = 683. 293. 4 81 - 191
  75. Resdat adhuc una aequatio cujus ope quaeratur si placet, 32 set siec 32 = to81. 48. 91 -4 P. 51. 30 + 4091. 3131 + 40 3 51. 33
  76. 13.40
  77. equ querit i vulac 2 cpsidea 082. 45 4 - 683. 4 1880 N 491 4
  78. quia 40 = 1. ideo in valore ipsius 32 avanescet 191. 40. 414 191. 40. 91
  79. 8o 1g1. 40. 41
  80. +Y890. 413
  81. A.. +191.40. 41
  82. 481. qua
  83. 403.41. 51
  84. conjungendo determinationes seu aqu. b, 25, 32. ex 6 et 25
  85. fit 2.692 +3. 683=31821. Ergo ex ag.32 fit 082 +792. 2811. 1. 192- 3. 281 3. 1821- 7. 6921 . 481 -19
  86. aequationes 49, 32, 35. non servant examen uam pendent exassumtione aequationis 28. caetercese
  87. eadem formam habiturae
  88. afficit jam hic calcalus pro aequatione data, qua uti quam tentare debemus ita t
  89. 9 seocerit instrem calcutus, aliique elici camones si pontmu 121, 13, 33 esse 0. et ita natum aeq. 2. mntriplicemus per 10 471Y
  90. ermare, ut praestentur aequationes 6, 25, et 32
  91. ad vindem vuadium exattetur qui atae mnro us d paa. on ta dintite veteritines moestgenus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 145r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0287?run=74