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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 61r

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: 0.78.

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The machine reads it as

  1. X + bxX +aCX a quand. quadrato. sit X: = 10ZZ + 11 aZ + 12aa, :, 202037 + 2127 aZ 2
  2. fiet 10333 +3.10. 1071 a Z + 3, 10. 10, 12aa Z XX: an = 18. 102 + 2. 10. 12, +7. 10. 127 aa , : 20. 20L + redt Dmet
  3. 12. 12a 42. 11. 13aZ + 1ast. 11 ZYaa 22yaa
  4. 43. 10. I1. H1. a4 24 + 6. 10. 11. 12aZ +3. 10. 12. 12a2
  5. bioi ae +2lso a Z + 2b. 0. 1220 aa 74 + 1. 11 a3 Z3+ 3. 11. II. 12a Ly 2 + 3 1. 1a Z+ 1 a
  6. 1b. HH. 26.-
  7. 72s10. 10. 8. 4 +( so. 11. 20. 2
  8. l.C.1928. +. 610. 2822
  9. F b. PB. 18. 22
  10. 46C. 102d.
  11. F1. C. 11. 20 +4C. H. 2812
  12. = 1C12. 20
  13. +2b. 11. 1220 423 4II. 11. 20.42
  14. t4b. 18. 12720. 2. a 3 + 4b. 1. 122. . + 2b. 13. 13.2029
  15. +2b. 11. 11.5
  16. 42b. 13. I1. 22
  17. +4C, 10. 20. 23
  18. +6c. I1. 20.U
  19. +2b. 10.12)2 + 2b. 1.2. 2E t, L 2 2
  20. 1b. H. H
  21. 4 lC. 10. 22
  22. +46, 12 20. 22 F6C, 12. 28.29 24C. 12. 10.17
  23. Z
  24. O+301361
  25. + 4c. 11. 20. 2 +1. b, 11.2
  26. ut destruntur 76
  27. 10a + . 10. 20] + B20c =0
  28. seu 10.10aa + 10a. 206 + = 20b6 = =. 20 bb - 26 ac
  29. 1.3 3
  30. 206241626247+
  31. et fiet 10a- f20 2.2052020, - b + ((1b - 4 ac) seu 10 a = 20. 20f, compendio
  32. tis ut destrmatur 20 B, et 3
  33. similiter (12a = 2d. 24, -b - + (bb - 4ac) seu 12a = 22. 22g compendio
  34. 19 12 = 20C, a
  35. 18. 12 = 20. 22 dC
  36. 2
  37. 10+ 12 = 20. 20 c. a
  38. Ut destmatur 95, fiel 3 3. 20. 1 f+ 2. 20 1bf 4 26. asfb + 9 26 ntc + 113C
  39. Ergo fiit 20. 22 = 3. X. 1155 + 2. 1b f +UC, :, 2. ffb + 4 fe
  40. 2. 11. 22 b9+ 1. 1b. 22t,
  41. Ut destruatur Z fiet 3. H. vss + 2. 2f 223. 20b99 + X 11 2 Y 4. 2 1BC = 0
  42. seu 2D. 22 = 3. 11gg + 2. 11 b9 + 11b, :, 299 + 4gC
  43. e 1
  44. 14 64 1
  45. 15 10105
  46. quos duos valores aquando destruitur u, nec obtinemus quaesitum
  47. nisi in certa lege datorum si sit 2f+ 2b5 +C = 39g + 2b9 +C
  48. 2f+ 4fc
  49. 299b + 4gc
  50. cujus aequationis solutio una est ut sit g-f, seagif - 1. sed sunt datur
  51. altuc alius vulor (3 2 gg6) + 265299b + C 2990 =(399556) + 2bg 2fb + c 266
  52. fit
  53. +3f4gc (F 2bf49c) + c498
  54. 6
  55. 43994 fc (+ 269459+ c 4fc
  56. a
  57. 4ffg BC - bp) + 4599 (bb - 3c) + 2bi (gg - H) + cC (9 - f) = 0
  58. seu (bb - 30) 45g (g- 5) + 2bc (gg- ff) 4cc (g- f) =0
  59. seu
  60. O
  61. (bb - 35) 8f9 + (2bc (9+5) + (4CC _ - 0 et fot g- 4bcf + 2cC
  62. Et quia _ f = - b + Y (bb - ac) et g = - b - + (bb- ac) quaeritur Bcf - gbbs. BC
  63. Crelationis
  64. transsonatione)
  65. an his valoribus subsitutis, qtum aliqua rao obtineri possit haec aequato inter frtge
  66. sed vix puto
  67. 4 1 1.5,18. 15010. 5. 1
  68. 6 15 26 15

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 61r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0121?run=74