Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 705 · Overbeck, fol. 41r

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: 0.84.

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. 40v); this page is its right half.

The machine reads it as

  1. Coefficientes D
  2. 24-
  3. 3.
  4. 25 = 4
  5. +2
  6. =0
  7. 26 = +5 - 5.4. 3. 45. 4. 32. 1. = -4
  8. 3.
  9. 3. 2. 3. 4. 5
  10. 23--
  11. N= A 3
  12. X.
  13. X axb
  14. + (2. x. 1. X. 2.
  15. 2. 1
  16. Sumtis 81. 8E. 83. etc: pro 8XF capit
  17. , (2.
  18. yxFi = l = (A - B+ C - D +E- F fet
  19. GX12 = + (a - B +Y- StC. P ret
  20. cex regula generali pro
  21. X12 capi
  22. (en. x gr3 un 2s
  23. 2.99
  24. y
  25. Crp xFi- g) +B7. c. 1 1 2 37. eq
  26. u H Xr)FyR
  27. 1B-2C
  28. oriu
  29. 2yXHI = 5V- 7 +3- 7+ A- ) tete
  30. ex regula generati pro 29X capietio
  31. 1.2. 1,27
  32. p
  33. o
  34. 2
  35. ete
  36. reti)
  37. E
  38. (4) (X
  39. Pro ote.
  40. Coefficientes1
  41. + 10
  42. 21
  43. Quarta a ultima Mernoous est per Numeros Combinatorios
  44. =X , n X-
  45. 5. 1.2. 3 7 etc.
  46. S in hoc Calculo fabeat Coefficientes 41. 42. 43. 44. etc
  47. capitque pro AXti hanc Expressionem
  48. + X a 1 X - 10 = X n 1 X - 12
  49. 2. 11.
  50. 1. 2. etci)s
  51. 6 - X. a 11 X - 14. = L 1, 1 X - 22 = X ,. X -
  52. 1. 2. 1 11. 23
  53. 1. 2. 4
  54. etc:
  55. Id est Generaliter si y, sit prior Character Numeri ficti ad quem
  56. libet Planetam dimplicem (y in 0 fac. 1. in D. fac. 2. in 5 fac. 4. ln
  57. 2y+
  58. 2y-1.
  59. X 1 a X - 3y +2 = X 4 a X - 4y +
  60. 1. 2. 3y -1 1. 2. 4 4y -1
  61. Pro Productis Planetarum
  62. fi
  63. a =A(X 9+3) B - B (- 1913) JL. C (u-9 1) p 2mo OD servat totam Aog Expressionem Generalem Otis, ubique
  64. sumens signum +. Sumat Coefficientes 31. 32. 33. 34. etc:
  65. pro 3X fiet Expressio Generalis (non pro 3XF)
  66. +X u aX - 6 + X 1 , X - 10 = X 1 4 X - 14) e posito 3 - y
  67. 7
  68. 2. 4 1y
  69. 2. a 4
  70. 1. 2. 4 a 11.
  71. Cn 4X -2Y + X a n X - 3y∞( + X , 1 X -qy-2 + X , nX 5y -3
  72. 1. 2. 4 294
  73. 1. 2. 4 113y+2
  74. SD habet hos Coefficientes:
  75. 1.2. a n 4y+3. 1. 2. aa sy+ eta
  76. 33 = 1. 56 = -6. 57 = +22. 58 = - 64. 59 = + 162 510 = -372
  77. 1, 63 B = +192) 5i2 - - 1584 5i3 = +3004 514 = 5448
  78. Capio pro 57 7. 6. + 1.
  79. . 2.
  80. Prosus 9. 8. 7. 6. +9. 8.
  81. 1.2. 3. 4. 1. 2.
  82. Pro 51 sumo 10. 9. 8. 7.6+10.9. 8. = 372. Pro f 1. 10.9. 8. 7. 6. + 10. 9. 8. 11.
  83. 1. 2. 3. 45. 1.2. 3
  84. Pro siZ cape 12. 11. 10. 9. 8.7.6. + 12. 1. 10. 9. 8
  85. 7. 2. 3. 4. 5. 6. 7. 1. 2. 3. 4.5
  86. 1. 2. 1
  87. = 162
  88. 1. 2. 3. 4. 5.6. 1.2. 3.4 =792
  89. =1584. Pro 513. 1. 12. 1. 109. 8.76. + 17 2. 11 10. 9. 8
  90. Pro 5i4. 19. 13. 12. 11. 10. 9. 8,7.6. 1 1413. 1.149.10. 8. 76 414. =5448.
  91. 1. 2. 3. 4. 5. 6. 7. 8.9. 1. 2. 3. 4. 5. 6. 7.9.
  92. 1. 2. 3. 4.5.
  93. 1. 2.7
  94. 1. 2. 3. 4. 56. 78 1. 2. 3. 4 5 +
  95. quod facit 300
  96. 13 Ibi incipiunt
  97. diversi saltus nam praesumi debuit Progressio Denominatorum
  98. 1. 2. 4 4 5. Purro 1.2. 17. Porro 1. 2. ia 9. sed pro hoc est 1. 2 nd
  99. Qua vero ratione hic sattus fiat vix loco quinquagesimo vel amplius
  100. deprehendetur quousque Tabulam elaborandi otium nondum datur
  101. OD habet Coefficientes
  102. 6b =1. 67 = -6. 68 = +20. 69 = - 48. 610 =90 611 = - 132. 612 = 415261
  103. Capio pro 68. 7.6. - 1. Pro 69 8.7. 6. - 8.
  104. .2
  105. =
  106. 1. 2.3. =48. Tro 610 9. 8.7. 6 -98.
  107. 1. 2. 3. 4- 1. 2.=
  108. et sic parro totam seriem ad S0 sumendo eandem, sed alternatis signis
  109. +_ cum ad CD in serie esset perpetuum +
  110. Ergo sient ibi erat 512 = 1 m. 10.9. 0 +12. 1. 109. 8. Ata jam 513 fac idem a se
  111. 1. 2. 3. 4. 5 1. 2. 3. 4.5
  112. ipso subtraitum. Ergo ibifu
  113. Progressus horum Calculorum post elaboratos jam Coefficientes non
  114. est difficilis sed ob sum mam Inductionum Prolixitatem Regula Ge
  115. neralis pro Lege omnium sattuum non nisi in magno otio
  116. obtinebitur.
  117. Ubique interim binae Columnae vicinae ita
  118. se gerunt, ut eandem Expressionem generalem admittant
  119. Colum
  120. impare autem omnia membra per + connectunt. Pares Columnae
  121. alternative per +et - Ergo in solis Columnis Paribus Nulli
  122. tates interjeitae expectari porsunt quando scilicet menbua
  123. Nonis fulii Anno 1715
  124. acetentia
  125. Servus subpectisiuus
  126. Columna D capit pro Z XHI. Generalem Expressionem:
  127. = p. p. 1. X 3
  128. X -
  129. 1. 2. 11 1 15
  130. . Caocick
  131. pro yX+I. capietur
  132. fit + (X . a Xx- yt
  133. Alia quae circa hanc materiam
  134. persequi. Ne autem responsio Hucusque Scripturam abje
  135. dudum debita ulterius quam
  136. par erat detineretur haec praesen,
  137. tia tantum praemittenda filerunt.
  138. tentari possunt non intermittam Positiva exacte fiunt aequalia Privativis.

Cite

LBr. 705 · Overbeck, fol. 41r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0081?run=74