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Leibniz-Handschriften zur Mathematik LH 35, 7, 12, fol. 2r

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: 0.76.

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. 1v); this page is its right half.

The machine reads it as

  1. posfe li5
  2. L10 95 38
  3. quiguos, L15 1o na
  4. sexies 1 (2 296 3006
  5. uo ne
  6. y = 1y
  7. y =, y - 1 y
  8. 1 = 1 3 f + 1 V
  9. y+ = + si - 6 d + 7 V
  10. = 1 f - 10 f) + 2593 - 15 5 +1y0
  11. 1Y6 - 15 y 4 95y - 90 5 + 31Y - , y
  12. Iliss
  13. 1+2. 3 = 7, 1+2.7= 15 Bc
  14. ubi nunerorum ratio ex Tabula manifesta est, nam 1+ 2. 1 = 3
  15. Et 3+3. 1 = 6 7+ 3. 6 =25 15+ 3. 25 = 90, &tC Et 6+4. 1 = 10. =5+ 4 10 = 95 90 + 4. 95 - 350
  16. Ande perfacile est potentiarum communium in integris summas mire, nam sy- Y et dyt-
  17. (B quia fy= a 5ist 19 esc. Hini faet:
  18. et fg 5y - 5 5 = 5 4 5y - f 2y + 2s
  19. Sy - s Cf 2y 1 5 et fy
  20. . fi - : y
  21. (y = 2= y - 2 f 4+ L
  22. 5y = 5 3 - 8 5 + 7 1 - y
  23. Etc
  24. esc
  25. dy = 1dy
  26. dys = 121 dy - 1. dy
  27. dy3 = 13 9 dy - 32y y + idy
  28. dyt = 1. 4 sy - 63 y y + 7 y dy
  29. dic et C
  30. sunt autem y idem quod naturales divisi per 1
  31. 1-- triangulares..
  32. 4.
  33. posito y esse pro-
  34. gressionis Aride
  35. triangulabiaous lies ... . .. . . 1. 2.34 Arhme sica naturalis
  36. 3 () pyramidales
  37. Si contra velimus proucarum expressionem ex potentiis puris
  38. potentiaumque
  39. tentiobimus Methodum similem:
  40. et p = f 9+2 = 1y2 + 1 y
  41. + 3
  42. = y
  43. +3 d3+ 3.3. y
  44. et S V. G - . y + a 3.
  45. et y = y. 9t1 = 1y +17)
  46. = 1 y + 3 y + 2 y
  47. = . y + 6y +10 y + 6 y
  48. +1_ y3+ 4.1d,+ 4. 6 y
  49. et y - f 9a5 F 13, 4 d s 17, 5. 5 3 . 1. 35 1o B 21)
  50. itaque omnibus collectis
  51. F i
  52. (4) = +
  53. isitusro
  54. 5 10y+ 35y3+50
  55. - 196 3y + 8s Ptus tary + 10y
  56. X. 23 45
  57. 6a 2 6 24 120
  58. 1 3 y 50 274
  59. (V) - y. X = v
  60. V) v aC2 H
  61. CyD. (X) (y) quodva
  62. nin
  63. pon
  64. a
  65. ∞ 35 3t5
  66. 10 ex
  67. p
  68. u d.
  69. Tabula Numerorum
  70. 10 35, 50
  71. Nempe
  72. 3- 41. 2 + 1
  73. 10 = 1.4 +6 35= 6. 4+1 50 = 1. 4 + 6
  74. Ubi jam si fiatit aequationes: l. verb. y - 1 = 0 y - 39+2 =0 y - 6y 4 1 y - 6 =0 y-10 + 35y - 501 +1420
  75. se e
  76. (14) (∞) XrI
  77. 1 vel 2 vel 3 vel 4
  78. 15 85 225 274 120
  79. 1 ran
  80. 1y + 10 y +559450y +24 y
  81. 1y+ 15y + 85 y +225 y + res m
  82. Numeri exigui in Tabula
  83. significant quomodo
  84. tiplicando per ipsos
  85. dertoque majore
  86. uto ad
  87. fextum
  88. duppositi
  89. pleducantur
  90. l sivi udan affiruntici, sed hunc ambir aeguderes
  91. E Erunt radices progressionis arithmeticae: iodem muneri al sint algation
  92. y5 e
  93. qu et. omnium ternionum
  94. 5225 sunt somma binionum ab harmonicis;
  95. siit naturalis 1, 2, 3, horum Ergo; + = in 1. 2 = 3 R arsus sint naturales 1, 2,3, horum recipioci L + L + L in 1. 2. 3 = 2.3 + 1. 3 +1. 2 = 11
  96. eo
  97. in
  98. At1X3, 11,50, 224 ex. sunt summae unt
  99. 10, 85 summae ternionum ab Harminicis es. Nempe sint raturales 1, 218
  100. Ergo 1+ = = 3 et = + 2 +3 = 1 et L + + 3 + = 50 et + = + + 2 + + = 274 Nempe posita
  101. sint n. Nibile eller ali modo
  102. qua aquatio itonlia est ner qu l ut s) int sequar lin
  103. nu aetquatio itculica est, nec quiculeum vine distins naci invonimus Avel is

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 12, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068083:0003?run=73