Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 11, 18B, fol. 106

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: 0.91.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. LMN
  2. autem vesocitabi-
  3. bus cres cunt actiones, quia cres-
  4. centibus velocitatibus es manente progressionis as sumatur alia series progressionis,
  5. Longibu dine tempora decrescunt
  6. per prop Z. Cap de resocitate in
  7. motu aequidistributo e uniformi)
  8. decrescentibus temporibus ma-
  9. nente Longitudine cui impendun-
  10. tur crescunt actiones (peraxioma
  11. hic)
  12. Prop. b. Lemma
  13. Siduae sint progressiones Geome
  14. tricae simus crescentes; termini
  15. eadem aut
  16. unius erunt in muntiplicatatratio
  17. neberminorum respondentium
  18. alterius.
  19. geometricae progrossiones vel
  20. Pint Series A, B, C, D, C, F: 8 L, M,
  21. NBB, Aio esse A ad B in ratione-
  22. eadem vel
  23. mustipficata L. ad M vel contrat
  24. Nam interposando continue serien
  25. priorem omnes aliae quantitates
  26. homogenea vel abillis parroerrore differente se in eum cadent; itaque
  27. & in seriem priorem ABC cadet
  28. LMA
  29. series posterior , e quidem
  30. intervallis seu Logaribhmorum
  31. differentiis aequasibus quia ipsa.
  32. quoqu.
  33. Sed majoribus inbervallis,
  34. tum terminiposterioris sunt in musti
  35. plicata ratione derminorum prio
  36. ratio
  37. ris B quidem cinultipLicata est in
  38. ratione inbervassi maioris adminus
  39. seu intervalli seriei uniusad intervalum eriqu
  40. quod in una quaque serie est con-
  41. contru
  42. stans. termini prioris sunt in ratio,
  43. submuptiplicata terminorum posterioris.
  44. Dic si sint duae Leries simulen
  45. crescentes progressionis Geome-
  46. tricae 1. 4. 26. 64. 83 2. 16. 1218. 102
  47. tunc interpoLabapriore, ub ineam
  48. incidat posterior res ita stabit:
  49. di
  50. 64 128 256
  51. 513 1024.
  52. quoque progressionis Geome
  53. Fricce est. Jam si in serie qeomedricae
  54. t
  55. 10.
  56. 5. 10
  57. Peries comq.. +
  58. t
  59. Logarithm. . . . (0)
  60. Peries prioruum
  61. Logaritrm.... (0
  62. intervatha.
  63. Series
  64. posterior.
  65. Logarithm...
  66. intervaaha.
  67. aut subtau pucerta
  68. igeometrucae
  69. eadem aut
  70. +Lad M in omultiplicata
  71. ratione A ad B (quocasu
  72. erit A ad B in submultiplicata
  73. Lad M
  74. indefinite

Cite

Leibniz-Handschriften zur Mathematik LH 35, 11, 18B, fol. 106. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068192:0106?run=74