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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 18r

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: 0.83.

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. 19v); this page is its right half.

The machine reads it as

  1. X +9X + Y aqu. 0.
  2. X = 34bX - a aequ. 0 posito, X aequ. a + b,
  3. ponamus: ab aqu - 4. et a + b aqu. = Y et per 4. ab aqu = hinc
  4. 1
  5. 6) + 93
  6. per aqu. 5. 6. fiet: a + r a = g aequ. 0. Nam - b aqu 2743 per 6. et b ao +Y + a per 5
  7. Erip duos valores aqu. 8. et 9. aequando fiet: a + ra - 2 aqu. 0.
  8. 17 (10)
  9. Scribamus
  10. primum ejus loco: f + r f .s. aequ. 0. ponendo, f aequ. a. et Saqo +
  11. fiet f + rf + F aequ S+ 7. et f + Z aqu. + 15 + . seu f aequ. - 2 + Y4 +
  12. 5)
  13. Pogro aequatio Ergo per 11. ot 14 erit a aqu. 3- Z + V2 + vel etum
  14. auts A aqu. -2 - Y 4 + = adeoque a + b aequ. Y- Z + Yqu a + Y- = - Y 4 + 2
  15. Verum notandum est aequationis 11 ad huc alias dari padices praeter Yf.
  16. Ivela
  17. Nam si a ∞f dicitatur per a- Ys. prodibit a f a Nam si dividatur
  18. a-
  19. a+ af + Ypi
  20. +a -Yf
  21. per a = Yf prodibit a + aY + Y s quo probari potest multiplicando
  22. ergo si a - f aequ. 0. dividas per a - f. quotiens etiam erit 0. adeoque
  23. habebimus aquationem a + f a + Y5 aequ. 0 Quam aequationem
  24. extrahendo, fiet: a aequ - Ys + 2s- Y5 + Ys
  25. Sic
  26. sive a aequ = + f.3 f. Qui valor duplici modo explicari
  27. potest, etiamsi f non varietur, et quia f etiam duplici modo exprimi
  28. vel b
  29. potest, hinc a vel b quadruplici modo exprimetur, imo quia ipse duplex
  30. valot f. etiam significat a vel l. Hiur habemus valores
  31. ex sequentes:
  32. et
  33. aequ.
  34. aequ
  35. aequ. - + 57 -3, 5--
  36. aequ. - + + Y-3,
  37. aequ.
  38. -2 - 1. 3, Y.
  39. 2
  40. aequ. = + - 1. 3, 3. ~ - Y
  41. Ergo a+b aeqo L+M. quod coincidit sum, seu Y. 2 14
  42. a seu - 54
  43. N
  44. aequ P+ R seu -
  45. agu N+ P seu 14 , Y- Z + Yq +
  46. aqu. er H. seu 1 (3, Y. Y + Y8+
  47. 4
  48. X + q. X + Y aequ. 0 R= qR - Y aequ. 0
  49. suspecta haec
  50. inquisitio quia
  51. video plerasque combinatio
  52. nes non procedere
  53. 2
  54. haec itaque diligentius
  55. excutiend
  56. G
  57. R aequ Yf
  58. +X + 4X aequ.0. dividatur per X 2R fiet X + RX + R aqu. 0
  59. e - 9f
  60. 2
  61. Ratio cur istae radices
  62. procedant traecandeta
  63. e quia cum ab aqu. 4
  64. extartda issumtae
  65. aor - 1
  66. 10
  67. 1b9
  68. +gr
  69. iia omnes
  70. combinationes
  71. ex valorum
  72. aut L+ N.
  73. L+ p. 8c.
  74. dant
  75. +
  76. hinc investiganda ratio
  77. et accurate inspiciendum est
  78. negotium valiorum ejus deu
  79. aequationis
  80. valorum
  81. en
  82. radicum
  83. amlignarum
  84. Estt enim res
  85. Subfilissima
  86. eroribu
  87. xposita
  88. 1a a1 at
  89. LH 36, H A, 1.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 18r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0037?run=74