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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 27r

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: 0.77.

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. 26v); this page is its right half.

The machine reads it as

  1. In quarto gradu, indigemus veloribus: abc aequ. h. a, b4 ct aequ. f. ab a C +C q
  2. ascendendum ergo est minimum ad aequationem octabi gradis: Sit ergo
  3. X + ea X + a X+ 1 X + 4a X + 5aX +6a X
  4. eabX +21abX + 3t abX +41 abX +51 abX
  5. +M abc +2 a bX 13cab 142 a6 X
  6. e
  7. Y2abex +31 abCX + 411 a bCX 151 abc X
  8. TEElaBck 133abX +43ab X
  9. 161 ab X
  10. 152ab X
  11. + 7 a X
  12. n
  13. + abx 132 abCX +qua bex
  14. MnaebeX +3314bcX
  15. h2abex
  16. 1 aq
  17. 7 a
  18. 61a
  19. = (2)614bC
  20. 52a
  21. 52ab
  22. 5245bE
  23. =suNbC
  24. SH1aB
  25. 430
  26. CA3 at6~
  27. 434
  28. 3c
  29. quabe
  30. 421a
  31. Tt214b
  32. 3314b
  33. a63
  34. absoluta multiplicatione prodibit aequatio in qua extabunt formae omnes octari
  35. omnium graduumusque ad octavum inclusive quae tollendae praeter abcx. a X a at
  36. quod ut fiat non suppetit satis arbitrariarum, nisi quoniam obs sunt arbitrariae numero
  37. 2. tot scilicet quot formae infra gradum octavum; in octavo aut formae autem
  38. sunt primo etiam 29. dende formae octavi gradus scilicet: a
  39. scilicet. a. ab. a V. a bc a b abc. a b b2C. a bc. a’bc b numero je
  40. quinqque
  41. id est in summa formae 39. Quae tollendae ordine omnes, temtis his abc. at.
  42. a bc ab quae si subtra hantur a 39 restant tollendae 3. Cum
  43. tamen formae sint tantum 3 arbitrariae 29. Sed in promtu, remedium est
  44. quia enim omnes termini octavi gradus reduci possunt ad simplices (scilicet
  45. ad. ab7) accedentibus inferioribus potentirs ipsius X. potentiis Ergo tolli poterunt
  46. reliquae formae, etiam sine arbitraris, satis ergo arbitrariarum habemus
  47. ad tollendum.
  48. aliae
  49. Si ergo omnes forma sint sublatae, restabit aequatio:
  50. abc X
  51. X re abc X + 8s a A+ ga
  52. + h a+b+
  53. aequ. 0. comparanda rquationi
  54. decte Xx GX + rX +s aequ. 0. etiam ad ad excitutae, quod fat multiplicando per
  55. XY 9N’+ rX1s
  56. arbitrariam formulam, X +x + lx + m. fiet:
  57. it k aequ. - 9.
  58. +l9 + KY aequ. 0 trgo Caqu.V.
  59. +14 - gr aque teu laqu. Y.
  60. denique M aequ. 2)
  61. Ergo Q abc aqu. 2Y (. q (+)) ae qu. fa
  62. =s9 + p - 45 aqu. 9abc
  63. Aliter XE C IX +YX
  64. s’aequ. darhab
  65. Eodemque modo et in altioribus quaesitae aequationes
  66. haberi possunt nam ex data a tolli potest
  67. ad. et superest tantum quaerenda a b+ in ultimo.
  68. Xex q txam
  69. ml etmgs nns
  70. +x itentex AlsX
  71. qr = qX
  72. X + R +EXHS
  73. X XKXLIX +M
  74. ex mai x
  75. +Ix ige rik HX
  76. ed quoulam
  77. rXX alq rtrXitSX
  78. A +q ArX +sut
  79. Xd + + teita tsa as abet + ga
  80. =habe

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 27r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0055?run=74