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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 209r

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: 0.81.

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. 210v); this page is its right half.

The machine reads it as

  1. Duae Aequationes vel Formulae 814 X + 13aX + 12 aa XX + 11 a X + 10 a 20 et
  2. 24 X4 + 23aX + 22 an xx + 21 a X + 2070 debent habere divisorem communem secundi gradus.
  3. Dividatu prior multiplicata per 24 per posteriorem multiplicatami per 14. Et divisor semper per
  4. resimum, dones residuns sit aequandus nihilo. ita enium attinus divitor qui est secundi guadis succedit
  5. as n s
  6. qunti i sepemi
  7. 414 24 X) + 13. 24 a X + 12. 24a aXX. + 11. 24 a X + 10. 24 a
  8. = 14. 24 = 14. 23 - 14. 22 - 14. 21 - 14. 20
  9. + A8 ax + 44 aaXX + 4+ ax + 4B a. Residuus per quem riditus 4X teque
  10. compendio 400. 33 4X + 00. 32 aa xp + ob 31
  11. multiplicatus per 43 et fiet
  12. 23 qu 29 a
  13. compondio scribita X + 2392 a
  14. 24. 43 24. 40. 43
  15. +24 45X + 23, 43ax + 22.43 L Xx + 21. qu a X + 20. 43 a s
  16. 24. 43 ax 1 29. DaxX + 24. 9 aex + 24. 40a)
  17. Erit residuus (ab 22. 43. 43 xx (+ 21. 93. 43 ax + 2012. 43 ga, a
  18. Qui dividere deblt dausorem paiem, mutsiplinetut i diriserpisepera
  19. dividatur diifor novissimus pe multiplicetur per 122. 43. 4
  20. A +22343.47 X.
  21. 22. 43. 43. B XX
  22. in hac divisione, ut residuus evanesiat
  23. =42. 2392. 415 +41. 2342. 45
  24. 24.470a X3 - 24. 41 43XX =24 40 aX
  25. Enga X + 24. grea px tug. giax + Entoa
  26. qremaex -qqx -qu. m a
  27. t Residuns novissimus per . 43: a3. Et pro nova divitione fret
  28. dividatur hcgar dirifor 43
  29. + 22. 4t. g2 9) aax + 22. 43. 43. 40 a fx
  30. a 132...
  31. + 20. 13. 93. 43 aa
  32. 44 2 X a a
  33. - 42. 2342.40
  34. Murtiplicatur prior aequatiius per 40, et posterior per 41 et st subtrahatur a priore posterior, scet
  35. et . 43. 1D . qrr esfe 0
  36. -42. 2342.401
  37. 2. 14Xa240 42042. 42 (42
  38. C80. 234243.
  39. a
  40. Engsia r, 1 . 9 p 20. 4) = 21. 40
  41. Seu 1. 20. = 10. 21
  42. 2 , 11. 20, 24 = +10. 21. 24
  43. sed quia etiam successisset novissima divisio sine residuo, si ordinassemus secundum a, et invertissemus
  44. Et sufficit haberi duas aequationes
  45. (+41. 2341. 43.) 40)
  46. et explicando 40 A1, fiet:
  47. nam altera quam ex destructione residui divisionis serundum X duximus, ad hanc reduci deveret
  48. 20. 4. 43 aa =0
  49. processum ideo, etiam pari jure fiet 13. 24 = 14. 28
  50. ipse autem communis divisor, nempe ultimus est
  51. ubi qui expliceter primum 2541, fiet
  52. +21. q
  53. =-4r. 23q2. 4
  54. oa
  55. seu t22. 41. 43. 43. 9
  56. - 20. 43. 43. 43
  57. = 23. 41. 42. 43
  58. 424. 41. 42. 42
  59. + 23, 40. 43. 43
  60. = 24. 40. 42. 43
  61. . - 91. 2342, 43
  62. + 21. 43. 43. 43
  63. = 22. 41. 43.43
  64. 22. 43, 40- +20. 43
  65. -42. 2342.40 - 40. 2342. 13
  66. +22. 40, 43. 43
  67. -23. 40, 42. 43
  68. 424. 40, 42. 42
  69. + 24. 41. 42. 43
  70. sed hac aequatione carere possumus
  71. 10. 90. 13. 43. 2342.
  72. inhric aequationibus serdatu
  73. quia, nil juvat, praestat aequatio non explicata
  74. nempe aeq. st in qua quaedam evanescunt. Ie
  75. im cralicetur aequ. 5i fiet
  76. et jlanc ex pli corquae sunt 40, H, e Z
  77. A. T2. S. B (N 12. 2.40. 43
  78. ie 40. L. F. B3. 242
  79. 940. 41. 42. 43. 2347)
  80. -20.20. 43 420. 40. 432. 23. 43
  81. +20. 22. 41. 153- 7. 20. 40. 43. 2442
  82. 20. 41. 42.4743. 93 - 40. 43. 24. n
  83. X. 42. 43244
  84. explicetur, prsus explicentur prembra quae easden habent non explicandas, et 420. 41 42. 43 (23. 43 + 24. 42), quod dabit
  85. Haec aequatio dividatur per 43 (et ut quam commonssime
  86. +20. 41. que - 13. 23, 24. + 14. 23. 23 4 12. 12. 24 - 14. 22. 24,
  87. 20. 42.42, f. 20 13 + 124),- 15 10 2a +1 420 23 + 11 22 24 - 1 21 22
  88. 2 hy aq. s sit
  89. + 20. 43. B. 93 ac
  90. 27433 a a
  91. rogd. 94. 43
  92. = 20. 43. 43, 43 a a X
  93. 4 40. 2392. 43...
  94. 421. 45. 43. B aX
  95. + 20. 43. 43.13
  96. +29. 40, 42. 43
  97. formelium et irtuatium
  98. 422. 48. 43.42 aXX
  99. 42. 2342..
  100. +21. 43. 43. 43 a X
  101. = 2. 43. 43. 43 aX
  102. 1+ 22. 43. 43 XX
  103. 13qu. 13. 9. 24. D B ri to. n2. 43. 24 42

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 209r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0413?run=74