Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 A 37, fol. 2v

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: 0.86.

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. 3r); this page is its left half.

The machine reads it as

  1. siguorum tantum pegula determinanda, superest Et hic quidem video
  2. cum sucimas didisa est ut paates atosomax pares, oppositum esse signera eru meutri
  3. naequalium graduum
  4. membri in quo summa notarum gradua
  5. in quodivisa est in empares
  6. Si fuissent aequationes duae XLMFIXHIOX =0 et 2F 2X = ofvet
  7. ne mutare signa opus sit 22 + 21X + 20XX = 0 fiet 12, 20. 20 + 11. 2021 = 10. 21. 21 seu
  8. + 11. 20. 21 2∞0
  9. Hs sunia congrunt prioribus, nisi quod pondum deprehendo motam
  10. G regulam communem signoum
  11. poteramus et per gradus ante sublationem literae omnimodam, uti depressione
  12. ad Gradum inferiorem Sit 12 + 1X +10X = 0 et 21+ 20X = 0 multiplcando
  13. illud per 20, hoc per 10x fiet + 1g.20 + 1t. 20X (F 102OX) =0 et multiplicando utrobique
  14. -10. 21. = 10. 20 53
  15. illic per 21, hoc per 12, fiet : (n. 21) + 1. 21X + 10. 21 X = seu 111. 21, 4 10, 21X = 0
  16. quae duae aequationes sibi imvicem respondent per inversionem Termicorum, vertendo
  17. sed n manet.
  18. quod si Eas rursus inter
  19. se sungaraus fit 10_ (1. 12. E1. 20) = 210., fl. 21. 2) (F 10. 1p. 20. ED + p. 1. 20. 21 - (. 12. 20. 20
  20. 10 in 12, et 20 in 21 et X in 1
  21. Signorum regula nondum salis apparet, video ubi sunt quadrata, ibi esse
  22. sigulum conhariim ei, ubi non suit quadrata, sed tamen in gradu primo, nulla
  23. sunt quadrata, et tamen est signorum mutation itaque glntiatius aliquid concspi quiet.
  24. An semper est mutatio de gratu g signi de gradu in gradum ut a 10 ad 11, vel a 20 ,
  25. 20 ad 2) Et simeter ab 11 ad 12, et ab 21 ad 22
  26. 412. 12. 20. 20
  27. tum urbat tamen
  28. 0: B 13 + 1 X + 1X + 10X o= 21 + 20X seu x= - 21: 20. 2t fint 13, 20 - 12. 20. 21 + 11 20. 31 - 10. 21 =0
  29. Sed pergamus ad gradum ontium:
  30. Et diminuendo ordine aequationes 13. 20 +12. 20X + 11. 20 X (1 10. 20 X
  31. -10, 31 X - 10. 20X
  32. =11. 20. 21. 2) =0 se + 10. 2. 8.21
  33. EI 11. X 13, 20. 20 + 12. 20. 20X A1. 20.20X) = + 12. 20. 20. 2)
  34. o= 13taX+UX + X
  35. Ex 1 et 2. + 13. 20 + 11020X + 11. 20X=0
  36. = 11. 20. 21. - 11, 20.20..)
  37. =10. 21. 21 +19. 20, 21.
  38. 0 = 22+ 21X + 20X
  39. ex ret 3 fit 11 20i 10 2. G
  40. Ex 2el3 fit _ N or 13. 20 c (F 13, 20. 22) + 12. 20
  41. 10, 22. 22. - 10, 21. 22.
  42. = 13, 20. 22, - 13, 20.21. - 13, 20.20.
  43. Ex det 4 fil p 1. 21. 2LXE +. 10 21 21. 2r X
  44. 413 20. 203 13. 20 20 32D.
  45. a
  46. o= l3 +IX + IIX +10X
  47. 10. 21. 13 = 10. 12.
  48. + 13, 20. 21 +13. 20. 20
  49. Ego landem ex 4 et 5. fint.
  50. 10. dB. 2.21. 2222
  51. 10. 14 30 22L 2
  52. +10. 13, 20. 26. 2222
  53. + 1. 12, 20. 20, 22. X2
  54. = (12. 13, 20. 20, 20. 72
  55. + 10. 13. 29. 21, 21. 21
  56. =11. 13, 2020. 22. 2
  57. 4 13. 13. 20, 20,20. 21
  58. (410. 10. 21. 21, 22. 22
  59. +11. 11. 26. 20, 22. 22
  60. 113. 13. 20, 20. 20. 20
  61. =(10. 11. 28, 21. 22. 22
  62. +(210. 13, 20, 20. 21. 22
  63. 22. 11. 1320,20, 20.22
  64. + 13. 13, 20, 20.20
  65. videtur in calculo peccatum esse.
  66. Nam aequ. 1. multiplicetur per form. unius gradus prodibunt quinque termini. multi
  67. sunt 4. sed literae ex formula uniue gradus sunt 2, ex formula 2 graduum sunt 3, Ergo sunt literae 5
  68. aeg. E sit gradus n. ducatur aequ. 1.
  69. nt eti hugohoc Cate. Ergo fit e= naI, al g - men +1
  70. Maltiplicetur aq. 1. per formulam gradus , erunt termini et 3H
  71. Ergo literae debent esse
  72. Ar A aequalio-
  73. plicetur aeq. 2. per orm 2 graduum; prodibunt termini quinque. Ex quibus tollendi quatuor, ergo aequationes sublatitiae
  74. fiet e =1 et 9= 2
  75. + 10. 1021. 21. 22322
  76. = 10. 18. 20, 31, 22. 22
  77. + 10, 17. 20, 20. 21. 22
  78. +1. 12. 10. 20. 22, 2
  79. =12. 13, 20, 20, 20. 2
  80. +13. 13. 2420. 20. 2
  81. 410. 10. 21. 21, 22.22
  82. 10. 12. 205 21. 21. 22
  83. =10. 13, 26. 21. 21. 26
  84. HI. 12. 20. 10. 21. 22
  85. = 11. 13, 28, 20, 21, 21
  86. = 10. 10. 26, 22, 22. 22
  87. + 2 (410. 12. 35. 20. u. 21
  88. (+ 10. 12, 20. 20. 21
  89. = 12. 12. 20. 20. 20. 2
  90. +12, 13. 25. 20. 20. 21
  91. mulliplicetur aeq. 2 per sem. form. gradus g. euul termini 912 +91 = C+ 3+1 fit g - et 1
  92. o= 22 + 21 X + 20 X
  93. nes sublatitiae etunt ex omnibus terminis uno demto, ergo erunt e+ 3
  94. 1+ 3+1 sed eago eodem literae sunt 1+1 + et 1 = et 1+ 1 + C + 1 = 2C + 3 Ergo De + 3 = (et 3 + 1
  95. in formutam gradus e, prodibit famula terminorum m+ eti ducatur aequ. 2. in form. gradus g. fiet
  96. quod sufficit perdratiter.
  97. prodibit ae quata terminoum n +9 +1. debet esse m+0+1 = n + 9+1 Ergo fit 9 = m - n + C
  98. Generaliter aeq. 1. sit padus m

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 37, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068250:0004?run=74