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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 81r

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: 0.88.

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. 82v); this page is its right half.

The machine reads it as

  1. 1
  2. cec
  3. pr qu 2grad . 9 abe + 2. 9a abid, qu -.
  4. si 914 g grab x 43 abc est nota dyadica
  5. porro hine habemustecum
  6. 37) = 9D = pD - 2pCD vel (0D) - OD, : p = d - 20D
  7. (06) = 06 + p6 - 2p06 vel (06) -96,. p = 6- 205
  8. (04) = 08 + p - 2pO vet (04)- O=, p - 4 - 208
  9. Et ita porro. Ope jam harum aequationum generalem
  10. exhribeo determinationem columnae cujusque methodo una
  11. eademque, ut nunc apparebit. Es Columna aequaevis
  12. post d, vocetur 5, et Ob vocetur D. Fiat
  13. 6 = 92 ab +93 abc +94 abcd + g5 abede + 96 abedef + 97 abedefgh + ete
  14. D = 102 ab + 103 abc + 104 abid + 105 abcde +106 abedes + 10) abcdesque t etc
  15. C unde erit
  16. (D) - , : p = 102 a + 103 a b + 104 abc + 10s abcd + etc.
  17. sed ex praemissis aequationibus est
  18. (D) - 6, : p = 8 - 20; seu ((1) - 6, p) + 20 - 5 = 0
  19. quam aequationem per asumtas series explicando, feet
  20. +102 a + 103 ab +104 abc +105 abcd + 106 abede tete
  21. +2.102 +2103 +2. 104 +. 105 +ete (=0
  22. - 92 - 93 - 94 - 95.
  23. - etc S
  24. sequentes
  25. quae aequatio ut fiat idenfica seu ut evarescant, habebimus pro invemendis a
  26. aequationes pro ssuntitiis 102, 103, 104, etc. sequentes:
  27. 102 =0 103 = 1. 92 104 = 193 - 232 105 = 19t - 2. 93+ 4. 92
  28. 106 = 1. 95 - 2.97 + 497 - 8.92, et ita porro. Sed quia aduc
  29. alia adf duplex est ordo assumtitiarum, seu praeter 102, 103, 104 etc,
  30. assumtae etiam sunt 92, 93, 94, etc. ideo adhuc una opus est
  31. equatione, quam habebimus, si actu ipso valorem ipsius assuntum
  32. multiplicemus per valorem ipsius jam inventum, ut prodeat.
  33. nimirum
  34. Ot seu , ita iterum habebimus ipsas 102, 103, 104 +C, per ipsas 92, 9, 94 et. Constat esse
  35. = Cd F, 3abe -4 abed + 8 abede - 16 abedef t etc. Eum ergo
  36. aorem ultiplicando per patorem ipsius 8, seu per gu abt guabe
  37. +94 abcd + etc. prodibit productum rges en eciem,
  38. cujus singuli termini aequandi sunt singulis terminis valoris ipsius Od
  39. vel ipsius , seu nempe formula 102 ab + 103 abc =+ 104 abcd + et c.
  40. Hoc productum prolixum in speciem, mirifice contrahitur per
  41. pre singularia numerorum compendia,
  42. ounibusque, t ordinatis prodit elegans admodum
  43. abula hujusmodi quantunlibet continud ilis
  44. 102 = - O,l.B2
  45. 103 = + 1. 3.2 + 1. 113
  46. 104 = - 2.6. 42 - 14. 9 - 014
  47. 105 = + 4. 10.92 +210. 13 + 1. 5 44 +1.1. 95
  48. 107 = + 16. 2. 92 + 8. 3. +43594 +22. 95 + 1. 7. 6 +1. 197
  49. 108 = - 32. 28.)2 = 165613 - 8. 7094 -456.95 - 2 28. 1f - 1. 8.97 -0. 1. 98
  50. 109 = +697612 + 32813 +16 2614 +826.95 +4.8496 + 23697 + 1. 9_ + 1. 1.9)
  51. Quos valores assumtitiarum 102, 10, 104, et c. prioribus
  52. earundem valoribus aequando, tandem pro coefficientibus columnae d
  53. quaesitis 92, 93, 94, 95 etc. prodit Tabula sequens, non minus elegans
  54. O - 11 91
  55. 0 - 11. 93 + 192
  56. C= 1195 44. 14 + 4. 1. 43
  57. O= 1197 teB, 6 +43.95 +8. 117
  58. O- 149 +. 418 +4697 + 8. 4 1 146. 1. 15
  59. B - 1 191 15G2 1 4. 10. 19 18. 10.B +15 97 + 32.96
  60. ita quivis columnae propositae e coefficiens impar generali methodo
  61. habetur per coefficientibs ejusdem columnae praecedenti competenti
  62. numero in geometricos binarios, et in combinatorios ordine ductis.
  63. prodire bis, exempli grabia 95 = -4. 9 - 4 93 sis prodit, mempe
  64. tum ex ex valoribus duobus ipsius
  65. 105, itemque ex valoribus duobus ipsius 106. Nam valores
  66. duo ipsius 105 sunt 105 = 1. 94 - 2.93 + 4. 92 et 105 = 4. 1092 +2. 10. 93+ 15 99 + r195
  67. unde pror. 92 substituendo - 93 prodit e dictus valor ipsius 95. sed
  68. imatii i u tate m es it e o
  69. idem prodit si aequemus valores ipsius 106, nam habuimus
  70. is aerciorbusis pro caleuli quam compobat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 81r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0161?run=74