Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 7r

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.

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. 8v); this page is its right half.

The machine reads it as

  1. 10 + 11 X aequ. N.
  2. Maji 84.
  3. 20 +21X aequ. N. multiplicando per crucem et
  4. a se invicem subtrahendo, fit: F H10. 21 + 11. 2IX aequ. N. seu + 10. 21 aequ. N
  5. 20. 11 = 11. 21 X
  6. d-C
  7. 20 + 21X+ aequ. N.
  8. 10. 2
  9. 10+11 X + 12 x aqu. N.
  10. 10. 21 + 11. 21 X + 12. E1 X aequ. N. seu 10. 21 + 11. 21 X aequ. N. ubi fingento 12 aeg. N redit aequ. 1.
  11. 2. 20
  12. = 12. 20X - 12. 21 X
  13. jam ex Aequatione 5 et Z ad imitationem aequationum et L ex hibentium aequationem 3.
  14. prodibit aequatio 6. nam pro 10 et 11 in aequ. 3. substituetur 10. 21. et +11. 21 ad
  15. fingent 12 aequ
  16. 12. 20
  17. 10 + 1X + 12X + 13 X aq. N 20 +21 X aequ. N. fiet: 10. 21 + 11. 21 X + 1. 21X aqu. N.
  18. - 13. 20X
  19. jam ut aequationes 4 et 2 dant aequationem s, ita aequation B et 2 dabutnitae quationem 9. si in
  20. et per aequ. 0 etit baequ. - 13. 13. 20. 21 + 12. 13. 20.22 - 10. 13. 2022, 1012. 21. 23 ̸ 11. 12. 20.22 1213 2522og ui aequatione 4 pro 10, 11, 12. ponatur 10.21, 11. 21 +12. 21, et fiet:
  21. 13. 20
  22. 10.21. 21 + 11. 21. 21 X aequ. _ N. ubi fingendo 13 aequ. N. redit aequ. 5.
  23. = 12. 20. 21
  24. Jam ex aequ. 9 et 2 fiori debet aequ. 10. uti ex aequ. l et 2 fit aeq. 3. Ergo in ag. 3.
  25. + 13, 20. 20.
  26. loco 10 et 11. ponendo 10. 21. 21 et 11. 21.21 = 12. 20.21 + 13. 20. 20. fiet
  27. C(10)
  28. F 10, 21. 21. 21 - 11. 20.21. 21 + 12. 20.20.21 = 13. 20. 20.20 aequ. N. ubi rursus
  29. fingendo 13 aequ. N. redit aequatio
  30. Hinis habetur Progressus in infinitum hoc modo.
  31. Datum Commune: 20 + 21 X
  32. Datum fpeciule
  33. 10+ n X
  34. IOF UXFLEX
  35. 10. 2X
  36. irero
  37. (1s
  38. Hinc habetur progressus in infinitum hoc modo: Datum commune 20+2IX.
  39. data specialia
  40. 104 I1X
  41. 10+ WX + 12X
  42. 10+ 1X +1X +
  43. 10guX + 12X + 13X
  44. et ( ec,
  45. Quaesita
  46. 10. 21 +11 21X
  47. 10.21 + 11. 21X + 12.
  48. 20..
  49. 10. 21 + I1 2X + 12IX + 133X
  50. (17) etc
  51. non
  52. ubi multae apparent Harmoniae. Formantur enim ex se invicem aequationes
  53. ejusdem gradis, seu connexae lineis trans versalibus. Ita ex 10. 21 +11. 21 X fit 10.21 2 + 11. 21 21X si
  54. ullam multiplices per 21 Cet adjicias terminum 13. 20. 20 X ob gradum altiorem. +13 20no
  55. item ex aliquo nembio, fit nembrum altius affectum, ut ex +10. 21. 21 - 11. 20. 21 + 1220. 20. fit:
  56. 11. 21. 21 X = 12. 20. 21 X + 13, 20. 20X si tantum pro 16, 11, 12, scribas I1X, 12X, 13X.
  57. ex qua sumtae sunt, indicantes, ut: 10.21. 2t- co l0. 21. 2, - 1120. 2, + l2. 20. 20
  58. ubi in qualibet parte habetur l. 2. 2 Notae autem dextrae a gradu sumtae equatior
  59. sumtae a gradu literae incognitae in aequatione originaria, in quolibet membro
  60. semper conficiunt eandem summam, ita 0. 1.1 et 10.1 et 2.0.0. semper
  61. simul conficiulit 2.
  62. Io
  63. dhedu imatnda
  64. quaesita:
  65. iodeq +MMIX
  66. . 21. 21
  67. +13. 20, 20
  68. 410. 2 2 u. XX A. X uX
  69. ia roo.
  70. et
  71. i
  72. 202020.
  73. 110. vneii humaruiX: 40 aut at 21
  74. nno
  75. Mronore
  76. et
  77. ontuti
  78. ono
  79. 21X
  80. +10
  81. +10021
  82. Lb

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 7r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068241:0013?run=74