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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 81v

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: 0.86.

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The machine reads it as

  1. Sed quia ope aequalionim biliteralium differentcalcum simplicium
  2. solularum, solvi pd aequatio in qua βB, Bdβ, B, ds3, et B. Hinc in altiortus
  3. non nocebit reductio ad hanc aequationem
  4. sint bres aequationes pro literis Y, D C explicetur, V per β y +Z
  5. a
  6. et co per V4 Z ly + 2, habetur aequs in quibus 31Z 2
  7. ope aeq. 1 et 2 tollatur du, et ope aequ. 3 et 2 tollatur du; habentur, buae aequationes
  8. sed ta non hicebit ex hris formare binas quae sunt etiam sine y. Itaque praestat
  9. sic facere, ut ex 1 et 2 multiplicatis per arbitiariast compositis tollantur
  10. simul y et dy. idemque fiat per aequ. et 2 et d Possuuit eliam
  11. omnes bres conjungi multiplicatae per nver arbitrarias diverso modo.
  12. sed videtur sufficere prior modus.
  13. pro quatuor aequationibus dalis, et quatuor Eteris, posset quaevis
  14. litera explicari per y artiharius multiplicatam cum addita. inde
  15. multi plitants aequationes per arbitranias componeatur, ita ut fiaut tres aequationes
  16. novae in quarum qualibet absint tam y quam dy.
  17. Quod oplumae fiet si componantur 1.2, et 2.3, et 3.4 aqq.
  18. sic pro quinque aequatio nibus componentur 1.2, 23, 3. 4, 45. Et,
  19. cearex pat essatione
  20. oecatione
  21. sit A 10y + 1x dy + 42o v + ndu + 120Z + 121 dz + 130V + 131 dv. + 100 dx =0
  22. Videndum an non opus
  23. 210y + 211 dy CbC + 220Z+ 22 dz + 2∞ V + 27 dv + 200 lx 3
  24. 310y + 311 dy + 320Z 7311 dZ+ 370V + 331 dv L 300 dx = -
  25. Fiaul bres combinationes pta, ut in terniones itam ut in prima aeq. 1. solum multiplaetur
  26. per a, caeterae duae per f et g; in secunda ternione at2 mulsiplicatur per a.
  27. ina 84. 3, multiplicetur per a caeterae
  28. s quadzentemus remin una ubi si succedit
  29. succedet in ouibus 10a0+ et in qualibet ternionum sollantur simul votar
  30. pet 2, per singulae per l, et m,
  31. Tenlemus rem in una aquubifternione, ubi si succedit succedet in omnibus
  32. 110a y + 11 a dy + 120 aX F 12 ad Z F (30aV + 131 adv + 100 adx _
  33. 20fy +21fdy + 220 fZ + 22( fdz + 230fV + 231 f 1 + 200f dx =0
  34. 31og y +3119dy +32092+ 3219 d2 + 3309v + 331 gav 4 300gdx
  35. fac o Ad tollendam B, fit 1304 + 280f + 330g = 0 et f - 4 B 130a + 330g, : 230
  36. Ad tollendam de fit 131 a + 231f +331 g =0 et s - f = (31 a + 3319, : 231
  37. quos duos ipsius = f valores aequando fit 130. 231 a + 330. 231 g = 131. 230 a + 331. 2309 unde fit
  38. italib
  39. a = a, 130. 731 = 131. 230se, +230371 23t 330 et pari jure spermutalis Qet 3 i ) f = a, 130. 331 - 131. 330
  40. Eodem mondo invenientur _ h et K, pemntando linitiale cuni 2 initiali
  41. e
  42. e
  43. .
  44. K = a,
  45. et m
  46. 230. 331 - 231,339
  47. H id est fit h = a, 230. 131 - 231. 130
  48. 130. 331 = 131. 330
  49. = a, 330. ∞1 - 331. 230
  50. 230. 131 = 231. 130
  51. et prodibunt tres aequationes bi literae
  52. 110 a y + Ma dy + 120 a7 + 121 a d7 = 100 adx 9
  53. 210 fy +2115 dy + 220 f7 +221 f de + 200fdx
  54. 310 9y +3119 dy + 32092 +321 942+ 300ga
  55. M =
  56. 230. 331 - 231. 330
  57. 330. 131 =331. 130
  58. 10 a y + n1 A dy + 120h2+ 121 h dzue + 100h dx 2
  59. 210 a y + 211 a dy F220a Z + 221 a dz + 200 a dx ( = 0
  60. 310 R7 + 311 Ky + 320 K2+ 321 K dZ + 300 K dxd
  61. 10 ly + 1B Ldy + 120 lZ + 12) l dz + 100 l dx
  62. 20my + 211 m dy + 2e0 MZ+ 221 m dz + 200n dx C = c
  63. o ag +31 a Byfgoa ZF 3ut a l 4100 a ap
  64. a, 330. 131 - 331. 130
  65. 131. 271 - 131. 230
  66. (t2. 3: E
  67. lec3. 1 34
  68. 4
  69. 234
  70. vel potius2
  71. in relqquis attioribus
  72. 1a pali 12
  73. 330. 231 331. 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 81v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0160?run=74