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

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. 210r); this page is its left half.

The machine reads it as

  1. 10 a + na X 1 tanx 1 17Y + 1X et 20 a 1 2t aX ManXX 1 23 aX + 24
  2. communem. is sit a 3ad +31 a X + 32X X
  3. debent habere divisorem
  4. D Dividatur 20X + 2 ax3 + 22 aaXX + 23aX +24 a per 10XX+ Maxtnaa
  5. t proditit 20 1oxx + 31aX +g2 33 + 34 at. et si sucedit divisio fit 33 = 0 et 34 - 0
  6. 10
  7. 10XX + MaX f12aa
  8. fit 10.20 + 10. 20 10. 31 L 10m - 11. X - 10. 32 - 10. 2 - 11. 31 +n. 30 10.35 = ,0. 25 - 1132 + 12. 31 131 = 10. 24 - 1. 3 + 12 3t -.
  9. est autem 37 ∞0 et 37 20 fiit 1052y - 11. 32 +12.3120 et 10. 24 + 12.32 =20 x, fit 32 = - 10.24: 12 et 3
  10. rt 31 = , 10. 12. 23(61 0. lt. 24; : 12. 12
  11. = 10. 22 -1. 31 + 12.30(3:10
  12. Ex 1, 2, 3, firt 30 = 20 31 = 10. 21 - 11. 20, : 10 et 32 = 10. 10. 22 = 10. 11. 21 f 11. 11. 20 + 10112. 20, : 10. 10
  13. 32 = 10. 24: 12
  14. et fiet tandem: 10. 12. 12. 21 - 11. 12. 12. 20 = - 10. 10. 12.23 (10. 10. 1.24 Ft 10. 10. 12. 22 - 10. 11. 12. 21 + 11. 11. 12. 20 +10. 1215 20 = 13. 14
  15. Ex Ad3 fit..
  16. 31 = - 1 12. 23 - 10. 1. 247: 1212
  17. +10. 12. 12. 21 410. 10. 11.24 =0
  18. +12. 10.10. 23
  19. 12. 12. 11. 20
  20. 1oxX Fuax tiaal
  21. IOXP + 1ax + naa
  22. 20X +aX +2aaXX +23aX +24 a
  23. (10 xx + 11 ax + 12 4a)
  24. gecap- aum
  25. = 10. 1. 21) = 10. 12. 217
  26. +y. ll. 207 + 11. 12. 20
  27. 010
  28. 1010
  29. = 10. 10. 11. 227
  30. +10. I1. 12.20
  31. + 10. 11. 11. 21
  32. = I1. 11. H. 20)
  33. 103
  34. +13. = 24 = 10. 11. 12. 21 20 miror in his duabus aequa-
  35. + 10 12. 72 120
  36. 4 H. H. 125
  37. tionibus nonprourilagem
  38. 121 - 11. 20 ax + 10. 10.22 - 10. 12.20 + 11. 11. 20
  39. 20 xX +
  40. = 10. 10.n 2
  41. +10, 12. 12. 20
  42. 410. 11. 12. 2
  43. =II. 11. 12.20
  44. 103
  45. 10. 10
  46. fiet
  47. 10. 41. 21
  48. 213. 23 - 10.10. 11. 22 = 10. 1012. 21 + 10. 11. 12. 20 = 0
  49. + 10. H1. 11. 21 =H1. H. 11. 20
  50. et 1824 - 10. 10. 12. 22 f 19. 11. 12. 2 + 10, 12.12.20 =0
  51. = II. 1I. 12.20
  52. -10. 12. 20 = 102 14 = 10. 24 - 10. 10. 12. 21 + 10. 11. 12. 20
  53. Hinc 10. 10. 220
  54. = 10. 11. 21
  55. +11. 1. 20 seu 11
  56. D 11. 12, 23 - 10. 12. 12. 21
  57. seu oen eite dietus scunt res
  58. paec aequatio servet legem justitiae
  59. Hic valor substituatur in aequatione e paulo ante posita fct vel potius in
  60. 10.10. 24 - 12. 12. 20
  61. Ejus ope tollatur n, fiet 11 =
  62. 1010. 12. r2. 21. 21 - 10, 10. 12. 12. 21 21 f 16. 24 - 1p,10. 2. 22 4 10. 12. M. 20
  63. 12. 20
  64. 4. 12, 12, 20. 20 4. 12.12, 20.20
  65. 10. 12. 21 + f(10. 10. 12. 12. 21. 21 = 4. 10. 10.10. 1. 20. 24 - 4. 10. 10. 12. 12. 2. 22 + 4. 10. 12. 12. 12. 20. 20)
  66. illa quaeratur _ est 1. 11 = 10. 12. 2L 11 +
  67. 12.20
  68. Unde fit: 2. 10. 10. 12. 12. 20. 23 - (2)10. 12. 12. 12. 20, 2 = 10, 10.10. 12. 2. 24= 10. 12. 12. h. 202D, + (V. 1. 24 - 12. 12. 20) Y (1010 et)
  69. e
  70. mo
  71. 2. 12. 20
  72. et fiot 11 =
  73. = 10.10.12. 22. 10. 244. P. 1031. 22. 10. 12. 20. 24 -. 18.12 22. 157.28 + 19, 12. 21. 10.10. 12. 23, 1070.24 L10. 12. 21. 1010. 12.
  74. +10. 24, 110. 24 = (2) 103. 24. 70. 10. 12. 12. 20. 24 (+ 103. 24. 12. 20. 10.)
  75. (t10. 12. 21 ( (9. 12. 12 21.12. 12. 207 = 10. 12. 21. 10. 1212. 21.10. 10. 1 =0
  76. H = 12. 20. 1816. 1. 25 fp. 20. 10. 12. 29. 29 - 1 (1 2. 20. 172
  77. (+10. 12. 12 2010.24)-(2) 10. 12p2 20. 10. 12. 20. 24. L. 10. 12. 12. 20. 11.10
  78. 2 42 1. 24 - F 10. 12. 10. 24. - 18. 1. 22. 24 +2. 162 15. 20 2. 24 + , (, 1 23. 24 -10. R. 2
  79. WV
  80. 4 14
  81. 20
  82. +18. 7 21. 13. 20 = v. 12. 25. 26
  83. Hic inter 12 et 10 non obserratur lex homogeneorum justatiae, deest sed in teliquis excepto tomino, nam deest 23. 24, quod mitor
  84. =13. 125. 22. 20
  85. pro 10, 11, 12; 20, 21, 22, 23, 24
  86. = 18. 12. 25. 24 Unde habetur 22 rationalites
  87. d = V. 18. 203 = 102. 12. 26.24
  88. Et divisis omnibus per 10. feliciter prodit aequatio in quae servatur ex justitiae pon
  89. 9= +106.243 - 18. 12. 20. 4, -10,12. 1. 24 + 2.103.13.20. n24 + 18,. 12. 21. 27. 24
  90. + 10. 15. 2. 23. 20 = 18. 123. 23.20
  91. itaque si sit 20X + Y ax3+ 22 a X + 23 aX + 24 a divisibilis per 10XX + 1ax + naa.
  92. +12, 203 = 18. 127. 20. 24 -10. 135. 22. 20
  93. habemus aequationes unam O. quae dat valorem rationalem ipsius II, siune 22
  94. D1. quae dat valorem rationalem ipsius 22 sine I1
  95. atmm esset lex sustitiae si
  96. dt non esset aequatio
  97. alteram vero
  98. plnuntu lo enim respon dentium is in priore manet endem aequatio, sed in posteriore
  99. steque d) servab legem institiae formularem.
  100. etiam eadem formulat
  101. s

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 209v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0414?run=74