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Leibniz-Handschriften zur Mathematik LH 35, 3 A 26, fol. 10r

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: 0.87.

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. 9v); this page is its right half.

The machine reads it as

  1. 6
  2. 12
  3. 24 2
  4. 4872 9
  5. In sola dispositione p 12
  6. 2
  7. 15
  8. 2 17
  9. 19
  10. 16 14 6
  11. 25
  12. 30
  13. 36 55 5
  14. 49 91 105 77
  15. 64 10 196 182 112 4
  16. Si 204 336 278 294 150
  17. 10 385540 214672 45c
  18. 2 21
  19. 1
  20. 34
  21. 1.2. 3 3.4.5
  22. 3.45 V 1. 2
  23. 1.2. 3 1.. 6
  24. 4. 5. 1.7
  25. 5.6.7
  26. Hinc reciproci figurntirum
  27. seu fractiones eorum
  28. summari possunt,
  29. nam generalite
  30. ex. c. si reciprocimu
  31. triangulo triangum
  32. aliquonsque sumtorum?.
  33. summa motisti pers
  34. aequatut differentiae
  35. duorum pyramidalium E.
  36. extremorum; seu
  37. disse rentiae suocum
  38. extremorum aliquo
  39. Cmmodo multiplscalorum
  40. ut focle delem
  41. potest
  42. ut si sit ex Tabula imparium replicatorum
  43. series H cujus summa est +E 6. ea multi
  44. plicata per 16, nempe quartam polentiam
  45. ipsius 2, dabit K. serdem post hanc
  46. quartam, quae facit 96. Unde putet
  47. has summas, esse terminos progiessionis
  48. Geometricae duptae multiplicatos per ternarium
  49. Et ita semper. sumna habem
  50. potest quilies prima totumna sonisiorsi
  51. est ex quantitatit, aequalibus; vartons
  52. in aliis non procedit, quia q primus
  53. terminus prioris serici, fit etiam primus
  54. terminus senei posterious
  55. Haecnethodus utilis est noque solum ad
  56. ea
  57. summas ordinum seutrausversatium,
  58. sed et ad summas extumnarium seu
  59. perpenidicalarium linearum in veniendas
  60. quod si series non possit revocari
  61. eua nesconte
  62. e differentras aequales tandem tamen revocabitur
  63. ad trancendentes valdes patum a se differentes
  64. sive valde parras; et hac supponendo pro veris, potest
  65. quaeri summa.
  66. In Harmonica progressione et ejus
  67. differentus illud memorabile, quod ordines
  68. 1. 2. 8
  69. coincidunt columnis. Nam 1. L 1. 2. 3. 1. 15,9
  70. coincrdunt cum:
  71. Hinc utalit Quia summari possunt reliqui
  72. ordines poteit reciprocorum triangularium
  73. poterit methodus haec
  74. pyramidatium
  75. erc:
  76. ad summandum vidinem primum ipsorum Har
  77. pro
  78. tionis
  79. s
  80. monicorum, saltem per appropingrationem
  81. adhiberi, si si scilicet differentiae rout
  82. muentur donec fiant salis parrae, ut
  83. negligi possint. bamque idem fieri possit
  84. constanti ratione accuratius semper atque
  85. acturatius haberi poterit progressio appro-
  86. piuquationum pro progressione Harmonica
  87. Moo (73 16 1c
  88. edem et in aliis
  89. Nota obiter: 2 + 4 11 +
  90. E. + 49 36H 5
  91. 4.9
  92. 9. i6t 9us H 194 H 18
  93. 10
  94. 1
  95. 28
  96. 16.25 16. 25 1400 40
  97. 2536t 25. 36I 900r170
  98. 5(36. 49 16 ag 1 6 H 136
  99. 49. 64 49. 5451361 196
  100. 62
  101. 75
  102. 81
  103. Naturalium
  104. Reciproci
  105. 2. 9
  106. .10
  107. 2.9
  108. 9. 16
  109. 5 12
  110. 1. 6. 18. 2
  111. n 10 13
  112. 1.6, 18, 20. 35. 67 8 144 mint poressio 28 32
  113. 16
  114. 5. 12. 2. 15 28 35
  115. 94
  116. 47
  117. 29(11
  118. 7 10 13 B 7 1
  119. 64
  120. 2bosst
  121. 8
  122. 3136
  123. 19

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 26, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068239:0019?run=74