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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 44r

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: 0.84.

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. 43v); this page is its right half.

The machine reads it as

  1. ab equ. abx - 3abc
  2. - 3
  3. (4)
  4. aeb aequ. a X - a. ab equ. X - 2ab X = a 2ab aego X - aX - babe
  5. i
  6. = 3
  7. 27 = 2,3, 2 = 3 4)2 127 23, 2 -6
  8. 16
  9. 3a b aqu. N a babe. Auferantur a Sccrricem aequatio 3 ab aqu. 4 fiet: a b aequ a Xt pabta babe
  10. 118
  11. 27 - 3 - 6
  12. -9 + 18 +3 - 6
  13. sed Lm. Sed aequationem 6 etiam obtinuissemus si ab aequ. 1 duplicata
  14. subtraxissemus aquationem 2.
  15. Eodem modo si ab aequ. S auferatur aequatio + restabit a b aequ. aX- a. ut supra
  16. Unde patet Sufficere aequationes 1. 2. 3. 4. 5. cum enim sint quantitates
  17. na
  18. a X aX. ab X. a. a. a b tolli poterunt exempli caut
  19. duae a b. et ax. ita ut maneas tertia verbi gatia X aequ. a + habX 5 abc
  20. itaque rufficiunt nobis tres aequationes fundamentales: aeb qui
  21. b aqu. ab X - 3 abc. ab aequ aX - a. ab aequ. 33 - 2abX - a
  22. Unde fient: e +a X + habe aequ. a. et _ aqu. 3ab X +
  23. rantitptes
  24. equ abx -gbe
  25. Scilicet sex. et cum quatur ex illis restare necesse sit mininum quinque, quia
  26. eriderem
  27. C
  28. inveniri potest X per at. abcd. abc. ab Hinc aequationes utiles
  29. poterunt tantum esse ex. ita ut in ses tollantur ope 5 reliquarum:
  30. ae a. a ab. a bc
  31. aX aequ. a + a b. abc X aequ. 4 abcd + a bc
  32. aeb aequ. ax- a
  33. (abc aequ. abc X - 4 abcd.
  34. ta X aequ aequ. X - 3ab X aqu. a3
  35. 1b
  36. atc
  37. Ergo ab aequ. +a X +3a bcX - at
  38. Cat + a
  39. b a abx 1a + 2 ab 2 qu i a X + 2ab X - 1a- 1 ab - 2ab. 2ab
  40. Ergo
  41. cab.
  42. O1 a + 2ab)
  43. X a
  44. X - a)... ... . . aequ.
  45. a X aqu. a + ab.
  46. ab equ ax- at.
  47. + a X - 12 a
  48. - 12 ab.
  49. +(3) 1 abc.
  50. et
  51. a bx equ. ab + ab + a bc abcX rqu. abc bca
  52. aex- a abex (ubed
  53. ab aequ. a bX - 2abcX = (k b + g ab0d
  54. abc aqu. abcX (2 ibed et abe aequ, a bX - aX + at -() a seu abeaqu. ab x- ax
  55. abcX + a . 2ab 18)
  56. ser nqu. 4. 5. sit a bX aequ. aX 12abc X - a + )a b 8) abcd
  57. abXcque aX +, abCX= a b-8’abed ut ante
  58. et per aequ. 6,7. fit.
  59. er anam
  60. a1X aequ. a+ a b a bX aqu. ab+ ab bc ab X aqu. ab 1ab
  61. a bcXaequ abc +() abC +t bcd. abcdX aequ a bcd 1Habcde.
  62. si in aequ. 4 pro abcd dX () abode substituas ejus valorem ex aequ. 5. fiet:
  63. aebc + ae bC aequ aebc X = () abcd X + (15) abcde. Porro a bc bis haberi potest
  64. ex praecedentibus. Ergo fiet: abc + (2) a bc aequ O ae bcx - B) abcd X + (5) abcde
  65. et a b0 . + 2) a VC aequ D a beX = (3) ab cd X + (15) abcde
  66. et pono ex aqu. 3. fit abc aequ. a b X - a b Quem valorem substituendo
  67. in aequ. Sit a bc aequ a bcX = (3 abcd X + (5.) abcde ()a b X +bD Ca
  68. 10
  69. Porro ex aequ. 2. fit pro atb substituendo valorem ex aequ. 1. fit ab4+ (bcab a. ab
  70. atque ita habemus at. Ergo per aequ. 10. eti a bc. )a bcX -(5) abcd X + (30) abede - (4) abX
  71. ergo per aequo 9 etiam a bc Ergo per aequ. 6 etam a brg. Veruus quia,
  72. tum ab tum abcd bis invenire debemus, sac per consequens caeterat
  73. d
  74. quan formas hinc necesse est ut adhibeatur duplex valor opraecedenti
  75. formaru, ut ab, vel abe
  76. =habe X
  77. 12abcd 3a bc
  78. Pab XH() arraN
  79. +b. 96. abc.
  80. a
  81. abed

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 44r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0089?run=74