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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 90r

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. 91v); this page is its right half.

The machine reads it as

  1. aea nontim depreh ind
  2. pontum deprescad
  3. (13)
  4. 2duatum incognitectum, quae in se non ducuntur
  5. y + eY - al + fX - 2
  6. Vy) = b y) + coy - al + fX - X
  7. (5) srrst tar (al - al) 1fX L X p o.
  8. X +4 + Xt + ax9 + fX - x 10
  9. e p = bY + co. Erg per (4. (5)
  10. eri = br = b + s + a. Ergo per. (9) (0)
  11. (14) Crj - bx9 - b + xt + a Ergope
  12. (17)
  13. (19
  14. XF, e + b xq + b - a. p 4.
  15. (
  16. bxq Xt b+ a - e.
  17. X Xtq + + + ag + f. ex 14. 12
  18. (5
  19. () ∞7r + 1. (So sta coy oristraeral
  20. 0 5H Xt (gr +) va
  21. X t
  22. jam quia Cp,- b7 + Cd ex plicando Y et Co,
  23. sit Ea Idem peane calculus
  24. serviet, ad si adsit terminus
  25. VX., est enim yXB X 4 + XI
  26. Unde divisis omnibus per X. i aequalioni
  27. Jungantur Aequationes 12 et 14
  28. es
  29. 12 acedet X9 + l. quae sane
  30. nihil turbant, valor enim ipsius
  31. Xg. puus, per meras datas in
  32. ventus, in ejus locum substitui
  33. potest, C. autem est data
  34. Habemus ergo Methodum
  35. Generalem exhibendi
  36. suc pere6) eo) (ai ne aq ( f aqudta
  37. Jungantur inter se aequationes 12. et 14.
  38. utraque ante conjunctionem per arbitrariam
  39. multiplicata:
  40. 1 P
  41. in Numeris. Aequationem
  42. quadraticam quamlibet
  43. quodcunque incognitatum,
  44. modo id fieri potest.
  45. Si unius in cognitae esst, semper
  46. sciri potest an fieri queat solutio
  47. per extractionem radicum, si
  48. βxFg + tβ + aqβ + f β- Aβ 7 0, Aequatio 12. per abbitrariam multiplicata
  49. eY + bx + b) = xtY = a) 10 Aequatio 14... . . . .
  50. (22) Cntq Xty + ly a te n-
  51. C) err. bV+ c
  52. Item per 14.
  53. + p X - f - aq - xt 4 ex ae9. 12.
  54. es b9+cd
  55. divisis omnibus per X
  56. per 14
  57. XEG p X - f - aq - + ex ag. 12.
  58. (22)
  59. quam libet
  60. 1 0
  61. 70
  62. (12) xtg , t + ag + f - x 1
  63. (2)
  64. C
  65. --
  66. duarum incognitarum colligo
  67. ex datis, semper in numeris possubi
  68. lem esse nisi ipse calculus praesens pluda
  69. quod escib aut fieri queat Ares in cognitae
  70. β X +g + bxgV f xt7 + tB F ag C X β + fβ + C) + b7) + aY 0
  71. aequiparabuntur
  72. Habemus arbitrarias =B. γ. X. t. q. Numero quinque
  73. unius exhis tribus
  74. F nec aliud jam quaeritur, quam ut inveniatur valor purus ipsius l
  75. Bo Et iptiu X. vel C2 vet 9., quem vlltr quem una tatitum
  76. Cn
  77. ex reliquis duabus ingrediatur.
  78. Caterum it ipa fieri quean com–
  79. dmodius, nec attollantur dinensiones efficiendum est ut sint duae quaedam ex his
  80. tribus, quae in se invicem non ueantur; quod ut obtineatur termini omnes
  81. E
  82. tnon nisi per arbitrarias assumtas multiplicati in ultima aequatione
  83. destruendi sunt, ponamus ergo:
  84. Enficr
  85. f ( 4 ex + b7 + ) 10.
  86. cY + b7 + a7
  87. et restabit aequatio:
  88. BX +4 + bxqV X + ) + t B + aq ( = x (3 pit 9 in qua si B. Epi
  89. Ponan n + 18 4, fiet
  90. frocus
  91. 3
  92. quia cognidae sunt
  93. Pagr + bX4Y q X + nd + noa (+ 2B , 6 (( age r agB rl
  94. 12
  95. e ita potenno onnia divili per X.
  96. (20)
  97. duabus.
  98. aetu destrnetur tam
  99. quam
  100. Ergo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 90r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0179?run=74