Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

LBr. 705 · Overbeck, 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: 0.89.

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. 82r); this page is its left half.

The machine reads it as

  1. Locus 8. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 19. 15, 16. 17. 18, 19, 20, 21, 22. 23. 24. 25, 26. 27. 20. 29. 30. ol. 3c. 35. 54. 31. 30. 31. 30. 39. 40. 41. 42. 43. 44.45. 40. 47. 48.49. 30. 31.52. 33. 34.33. 56. 57. 58. 59.60. 61. 62. 63. 64. 65,66. 67. 68. 69, 70.
  2. Residua Progr: Bimalis
  3. Cycli 11.) 1 Z. 4. 8. 5, 10. 9, H. 3, 6. 1.-
  4. Cyeli 7) 1. 2. 4. A A. - - 1. - A. e
  5. Cydi 77) 1. 2. 4. B. 16. 32. 64. 51. 25 50. 23, 4b. 15, 30, 60. 43 9. 18. 36.72.
  6. Cycli 88) 1. 2. 4. 8. 16. 32. 64. 40. 80. 72. 56. 24, 48. 8. etc:
  7. Cyclig9s) 1. 2. 4. 8. 16. 32. 64. 29. 18. 17. 34 68. 37. 74. 49. -
  8. Cyeli 13) 1 2. 4. 8. 3. 6. -1. -2. -4.-8. -3. -6 A.
  9. Cyli 39) 1. 2. 4. 8. 16. -7. -14. H. 22. 5, 10. 20. A.
  10. Cycli(21) 1. 2. 4, 8. 16 11. 2. -
  11. Cychi61) R. Z. 4. 8. 16. 32.-1. 2. -4-8-16-32. a.
  12. Cycli(91) 1. 2. 4. 8. 16. 32. 64. 37. 7457. 23, 46. A.
  13. CyclilII7) 1. 2. 4. 8. 16. 32. 64. H1. 22. 94. 88. 59. A.
  14. Cyclisiq) 1. 2. 4. 8. 16, 32. 64. -15. - 30. -60 roz. 46. 92. 41. 82. 21. 42. 84. 25, 50. 100. 57. - 29 58127. 54, 108. 73. 3. 6. 12 21. 48. ∞. 49, 98. 53. 106. 69. -5. 10 -20. -40. -00 -17. 34 63. 17 14. 28. 56 112. 81. 19. 38. 76. 9. 18. 36. 7Z. 1.
  15. Cydi (9) 1. 2. 4. 8. 16. 32. 55. D9, 11. 22. -5. -10 - 20 +9. 18. 36. 23.-3.-6 -12 -24, 1.
  16. u 43) 1. 2. 4. 6. 16. 32. 64. 128. 256,169,. -5. - 10. -20 - 40. 80. 160 133. 46. 92. 132. 254 58. 100. 200. 57, 114. 128, 13, 126. 109, 48. 93, 186. 29. 58. 116. 232, 121. 242, 41, 282, 21. 49. 198 53. 106. 212 81. 162j19. 38.-76. 152,139. 18 155. 31. 62. 124. 245. 153, 37. 74. 148. 296249. 155, 13.16, 152 26. (. 185, 27. 54. 108.
  17. Malticlod
  18. s Residuu habet a. ibi quoque illius simiplans habet, Rasid. 1
  19. Nam quia integra, sunt eadem, 3pone Egilum Simplantem = c. Multiplantem = gc.
  20. Ergo ubi Multiplans habuit Resid. 1. ibi integrum fuit Zgc. + d.
  21. sed ubi integrum est Z9c + n. ibi etiam Cyolus c. farit Resicuum 1.
  22. Obs. 2. Et quia Cyclus 77. habet duos simplantes 1. _ 7: Non poterit Cyclg 77. facere Refiduum 1.
  23. Obs. 3. Locus ubi primo, recurrit, Residuum 1. metitur omnes locox ubi postea recurrit Refil. 1.
  24. unupro erie faciunt Resid. 1.
  25. Recurrut enim ibi initia Periodorum aequalium sicut ulna metitur omnes longitudi.
  26. nes per ulnam (ceu per aequalem perrodum numeratas)
  27. Obs. 4. Ergo ubi in Simplante recurrit, primum Resid. 1. istelocus metietur omnes locorum numeros
  28. ubi in egilo suo Multiplante recurrit.
  29. Obs. 5. In Primitivo Cyclo unitas recurrit proximo loco ante numerum Cycti seus numerus Cplit
  30. ut Cyclus 7. habet Unitate recunrentem loco serto, e
  31. ubi
  32. Obf. 6. Et quia 77. utriusque Multiplus est per obs. 4. non potenit 77. habere Resid. 1
  33. alio leco quam tali quem et
  34. 11 loco decimo
  35. 6. et 10 metiuntur
  36. Unitale
  37. Horum autem Communis divilduus minimus est 30. Ergo 77. habet Residuum. Loci
  38. REGUL A pro Compositis Numeris
  39. Obs7. Resolvatur cempositus in suos Primitivos Commultiplicantes
  40. Singuli Primitivi illi minuantur Unitate propter obs.
  41. Communis Dividuus Minimus Numerorum ita Minutorum est Locus ubi in
  42. Numero Composito Unitas Residua recurrere debet
  43. Sed fieri tamen potest ut alio loco praecedente ja fuerit Unitas Residi
  44. EGULA pro Qvadratis et Cubis.
  45. Ob. 8. Si Egolus fuerit Quadratus Numerus.
  46. no
  47. Loco X, X - 1.
  48. Residuam Unitatem habebit
  49. ut Cyclus 49. Unitatem reducit loco4
  50. Cubus, autem loco (X, X, X - 1.)
  51. Oblsi Cycus sit triplus Primitivi, Residuum egus 1. est eo loco ubi primitious ipse facit Resid. 1
  52. Obs. 10
  53. Talis sit 3p. e Primitivus p.
  54. a
  55. quamvis per Accidens adem ju fiat loco dimudiore
  56. Part Fit ergo 3p. ex 3.
  57. p - 2.
  58. minuendo Unitate fiut 2.
  59. est p - 2.. (nam p- 1. semper par est, quia primitivus p. ubique impari
  60. P
  61. et utrumue
  62. Horum Communis dividuus Minimus
  63. Quare loco p- 2. recurrit Unitas in triplo primitivi per ipsam Regula uod est propos
  64. Nullus Cyclus facit majorem Periodum ipso Egcli Numero
  65. quam membroni
  66. ut Cyclus 45. non facit majorem Perodum Residuorum
  67. uumeno
  68. Si plara dentur Residua necesse foret aut plures quam 45 numenvr dari ipso
  69. 45 minores quod absurdum, aut idem Residuum in eadem Periodo bis necunrere
  70. i
  71. quod etiam absurdum....
  72. De Cyclis Diversis ad unam seriem. Progressionis, quorum unus Cyclus est alterius Multiplus
  73. 57. 57
  74. 37
  75. 29:5
  76. -2. -4. -8. 16-

Cite

LBr. 705 · Overbeck, fol. 81v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0162?run=74