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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 88r

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. 89v); this page is its right half.

The machine reads it as

  1. Haec in scheda isla coepta atque affecta demum
  2. in scheda 12 jannar. 1684 absolvi
  3. i caebcet
  4. Ad tollendas ex aequationibus literas incognitas Methodum inveni generalem, in qua
  5. stane pene omnis calculi algebraici viscontinetur, incipiemus a pluribus aequationibus sed
  6. simplicibus, plurium literarum; utque in s datis ordinem aliquem observemus
  7. quo scilicet in quaesitis, ubi inventa erunt propessio appareat, ideo omnes coeffi
  8. pieutes primo aequationis sunt denarie supra denari secundae supra
  9. in vicenarium, tertiae supra tri enarium; rursus litera a coefsicientes suo denario
  10. vel vicenario vel tricenario addant unitatem, literae b coefficientes
  11. binarium et ita porro. Et ila stabunt aequationes
  12. 20 + 21 a + 22b ae qu. 0.
  13. 10+ 11 a + 12 b aequ. 0.
  14. ambae inneliplicentur per arbitrarias et componentur, tolli poterit litera una a
  15. et stubit 10l + 11 l a + 12lb aequ. 0. 20m + 21ma + 22 m b 49. 0. Quas duas
  16. equationes componendo, aeq 2fer +10 l + 11 l a + 121b 1
  17. 1 m um a 6, 2 2m b5
  18. et proinde, ut tollatur , fiet ul aequ et 22m
  19. g. 0.
  20. 13
  21. et faciendo laeqo 22
  22. et m aequ. 12 salis factum est. et fier: + - 10. 22 ∞, 11. 22a aeg. 0.
  23. + 11. IR +12. 21.
  24. Hinc jam habetur Methodus tollendi eandem literam in duabus aequationibus repertam
  25. multiplicatione scilicet per cucem Nempe sit quationes 10+ 11a + 12b 49. 0.
  26. et 20+21 a+22b a9. 0. Multiplicetur aequ. 1. b per 22, et aequ. 2 per 12 et
  27. subtrahatur una ab altera, sublata erit litera b. nempe stabit:
  28. + 10. 22 + 11. 22a aeq. 0.
  29. - 20. 12 D21. 12 a
  30. sint jam tres literae: aequationes et literae: 10 + 11 a + 12b + 13C690 et 20 + 21a rub 2 )
  31. et 30 + 31 a + 32b +33C aeq.0. prima multiplicatione per crucem tolli possete
  32. sed quia ea bis institui posset, satis est simul plures conjungere adEibitis
  33. literis arbitrariis, et fiel: 10l + ula 42lb + 13lc . )
  34. eut 131 + 23m + 33n aeq. d
  35. 20mtuma tum b + 23mC 4 ∞7. 0.
  36. 30n +31na +32n b +33n C
  37. et 12l + 22m + 32n Eg. 0 et
  38. Ed quia ita calculus aeque propemodum difficilis ac primus ideo salius erit resumere
  39. muthiplicatio nem per cuicem, et fe + 10. 23 + 11. 23 a + r4 3 b aeg. 0. 10. 351 1. 35 +12. 32b
  40. e et +20. 33+4. 33c
  41. c30.23- 3123 a
  42. +10, 12. 25. 33
  43. - 10. 13. 23, 32
  44. - 12. 13. 20.337
  45. 4 13. 13. 20, 3E
  46. =10. 12. 23. 33
  47. + 1. 13 22. 23
  48. + 12. 1323. 30
  49. = 13. 13, 22. 30.
  50. sed ita nondum
  51. homveoptotice.
  52. .23b
  53. 1
  54. L 1I. 13. 23. 32
  55. (= 12. 13. 21. 33
  56. =13, 13. 21.32
  57. =20. 13 - 21. 134 - 22. 4 b
  58. Ergo + 10. 28 0 1133
  59. 3. 13 - 91. 13a - 32. N67
  60. + +y. 23 9+2. 33
  61. -20. 13 32.0 C.
  62. = 1.33 ,12. 83
  63. 430. 13 - 22. 13
  64. = C+ n 23
  65. +31 - 22. B
  66. =13, l+23. 3em K7) Ex 5 et 6
  67. = 12. 33l - 22. 37M.
  68. 290
  69. et fiat l aego - 23. 31 et Magot 13. 52
  70. 110
  71. + 22. 33
  72. Et habebimus: n aequ. + 13. 23. 32 - +3. 23. 32
  73. 13. 22. 37 = 12. 23. 383
  74. Ergi ex aez 4. fier: - 10. 23. 32. 95
  75. apparet modus hactandi
  76. +. 10. 22- 33.33
  77. + 13. 20.32.33
  78. C 12. 20. 33.33
  79. literas omnes
  80. seu
  81. = H. 12. 335
  82. M0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 88r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0175?run=74