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Leibniz-Handschriften zur Mathematik LH 35, 3 A 34, fol. 1v

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.

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. 2r); this page is its left half.

The machine reads it as

  1. caelerum si multiplicatio instituatur alio modo alia veretur productorum repraesentatio,
  2. nempe: Z
  3. (1) Z
  4. F, Z X p Z2 - ZcZ - 21
  5. 2g-c
  6. V.2
  7. 22227-3 1
  8. a
  9. L
  10. Z 3C
  11. et hor rursus multiplicando per Z- 4 fiet.
  12. 75 - 4 y4
  13. 3∞ n + 128
  14. 82
  15. 1on. +4.
  16. +6 .. -24 Z
  17. 3..12..
  18. 3
  19. -7a
  20. 6
  21. Multa in hac dispositione nmoranda, sed quae omnia ex hoc
  22. capite pendent, quod nimorum orminus cujus libet
  23. Liget ad huc unum calculare, credo vero
  24. uneaae multiplicatus
  25. etsi res forte mereatu. Caeterum inspiriend
  26. vec
  27. appa et hoc calculandi modo non in simmus
  28. fantum, sed e per pantes, idem quod ante provenisse
  29. Caeterum summae iniles fiunt aequationes:
  30. et denique: 1Z
  31. 122 43Z~ + 22
  32. - 1074 + 3577 - 507 + 247.
  33. pono semper numeri cuyslibet armitu
  34. inter se juncti uut aequales nihilo, multiplicetur haec formula, per Z - 5, fiet:
  35. seu
  36. = 10Z5 + 3F Z 5023 + 24 72
  37. 4. +40. - 140. te.. - 96Z
  38. 14Z + 757 1902 1224 Z 496Z
  39. ubi rattu plina te mumas srsusserpec aequaratlo.
  40. seu
  41. = 1075 +35Z4 - 50Z
  42. = 5 n 440.. = 175.. +250 4- 120
  43. 152 +85Z7 21573 +2452 1208
  44. Ubi notandum Inductione apparere, quod sempercrescant cognitae terminorum, usque ad
  45. penulti mumi, qui est omnium maxiinusi at ultimus rursus decrescit. Termitni secundi
  46. sunt numeri triangulares 0. 1. 3. 6. 15. Termini ultimi, 1. 2. 6. 24. 120. sunt producti
  47. nuterorum continui deinceps at unitate, rempe in (1,3 2. (2, d6. (1,2,3, 24, (1, 2, 2, 4, 5,) 120
  48. sed reliquorum dfficilior determinatio, v.g. tertrorum : 2. 11. 35. 85 etc putet tamen eos esse
  49. quodammodo sumntos ex pycamidalibus, 1. 4. 10. 20. 35. 56. 84. quanti sunt 6. 50. 125. esc
  50. qui quomodo ex Triangulo Triangularibus, denventur non da fanile judicatu; t et opus
  51. si est prolixis inductimnibus ad ista indaganda. Si
  52. s in qualibet termino in serem pscorum cognitarum seu numerorum inquiramus, ut: omisto ultimu
  53. lormule
  54. ut, 1. 1.3. 16. 1 1. 1dr 3550.
  55. 1.6
  56. 5 25
  57. 1. 15. 85, 225. 274
  58. 11. 70 140 49
  59. 46 70 -91
  60. sed his nunc quidem nissis redeumus ad nostras formulas generales:
  61. Esto primula quaelibet:
  62. by + caV a d dae V2 + ea V2 + fat 2
  63. gy +hay2
  64. +Ka y2 aloyE YZ
  65. 5023 A3. B.
  66. quaeratur ejs differentia a. formula quae hoc solo ab ista differat, quod pro y ponatur y4β: ut autem res
  67. 2bdi 2 ilcaeque v21 + 5das y +4 e a512) +8 5a gV
  68. +7.
  69. in numeris habeatur et vitetur gerror calculi scribemus:
  70. r SYn
  71. 195 gE Antra 5. 121 4, pa 5 y2 41g la u3 4 5 mae 5. yi
  72. 92
  73. et hoc
  74. per, 2, 2 3, vel bat
  75. 1 + 4 multiseita
  76. vel 143, vel 1 +4
  77. eic. multiphenti
  78. dant reriquos, sunt autem:
  79. 1. vel KB
  80. ners
  81. net
  82. sequentem, non ergo considrandi nisi qui lineas
  83. incipiunt, hi enim per
  84. 122
  85. vel
  86. t
  87. _
  88. 87474
  89. 214+

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 34, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068247:0002?run=74