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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 224v

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: 0.73.

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. 223r); this page is its left half.

The machine reads it as

  1. = 200 r 7 H
  2. (9) + ot e Dd) seumalio. C
  3. - +20B+ B (2) summabilis
  4. y - 2yβ+ B ego
  5. pungantur 1. et 2. ac primum addendo, fier:
  6. + W β+, 32yDest
  7. y27 3+ 2 5 + β4 = 4y
  8. sue 4B 2( (5) 5
  9. y ex ap. y
  10. Jungi possunt subtrahendo, et fiet.
  11. ta se+Berve .
  12. santureu
  13. =- e (. (D):
  14. Cujus serici datur urisus summa.
  15. jungantur, Addendo, tei: (OV (C ) + By ()) 2B est
  16. singantur subtraherdo fiet: B +y + (3 + C3
  17. Hujus ergo seriei + = + etc. habetur summin,
  18. Idem hujus: + +5 + o resi 1o i qua
  19. quae est series popramidalium, nimirum, omnes numeri cubi radicibus minuti
  20. sunt senarii et divisi per 6. dant numeros pestamidatee
  21. 4- 1 9- 1 16-1
  22. duae
  23. 15-,. et. A 4
  24. ont A 3 b g 6i b1
  25. recuml fractionum
  26. potestates exponentium
  27. parium simul sumtae
  28. aequantur tribus quartis.
  29. 16 L - = + - 1 + 1
  30. S
  31. erit. diffecntia:
  32. 2 1
  33. Si invicem addantur
  34. Si invicem addantur:
  35. a. ponendo y esse numerum imparem
  36. .5, seu
  37. s eostaug. in
  38. Aastars fiet: 1
  39. a et a, fiet: at. qua rubita
  40. e yt inte d+ B +y q er
  41. =+ y ex. Addendo ergo
  42. summ fice 20 =ay Y 5 + Y ex
  43. quid si sir: S ra
  44. aerrayayr HX, fiet:
  45. ia- m 25a. + 2avi. 4 5a MM.
  46. qu H 29e, 2292
  47. SyM-41 1r y 1 5
  48. 4 +2, 29, 2, + 1 4 - 1 maltiplicetur pereus 72 L. 323
  49. igiat17, 220- 2, 1x p 83+ ad dipit 2
  50. i nalir qu B du
  51. 2943, -1 V standam d
  52. vertice aliquo, rabit.
  53. 4 Equadruplum summae, habetuo ex
  54. ductu hoc differentiorum, cuu 4y aliunde
  55. vi
  56. etur aliquod duci ad summam seriei
  57. 3 is su 9s ham
  58. Multiplicentur ista per 3 7. H 15. 19
  59. esto y nuneus impar, erit 1 termines seriei quadratricis
  60. hez: 2y+ 1 - 2y
  61. 3 + 1 3-L + i ex l1s 30nc
  62. 40 +4y 1 2y + 27 cujus dinidium 1
  63. Unde auferendo ad restabit.
  64. qy- 1
  65. (172 ay3 +.
  66. 1694 4oyv. 2 16yt 4 - 2
  67. vel ita: 29. 2
  68. Cay. 212
  69. in6 erc. l. 1 t ipt vi botaste cujus dimi idium: Qyr. q, addantur adatio ad Aa
  70. Ergo 5 1 s +7 +
  71. Z + f + L + 2 +
  72. ex 4 + + 15 + 4 i + 2) B4, ut cdu serimus
  73. Sed 1 - = + L-
  74. 1 3 3
  75. fiet 2 f 40 + F a3) sive cuus duplum
  76. erit , uet Hyi. contra
  77. Contra si cddantu slsi ultrum ab altro cnfratur,
  78. cous quodgtum. y -9
  79. 1 35 + iont is is
  80. v N 5+b
  81. D a O. restabit.
  82. ayCayd +ad
  83. Cuju seriei habetur summa Addantur
  84. F et 4, fier: y+
  85. y3 - y N y1 257
  86. contra si altra ab altra anferatur, fiet: y - 1
  87. es . 9 i 2 2
  88. n E F2 2o
  89. in3 3 8+ 3+
  90. summafigurau quae datae seriet
  91. qe

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 224v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0444?run=74