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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 119v

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: 0.83.

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. 120r); this page is its left half.

The machine reads it as

  1. (summari
  2. Quaeritur ergo du
  3. n. atdu
  4. sit
  5. nn
  6. =
  7. utan O= du
  8. n. n+dn
  9. Fn. ntdu Ergo du C= an - du
  10. (du (du
  11. n. nt an utan
  12. nida
  13. no = du
  14. +du
  15. Ergo fiet
  16. Ergo ex 28. per 33,
  17. n. ntdu
  18. n+ u)
  19. le + du l2
  20. Hinc si an = 1 tolletur summa quadratarum fractonum naatium, et
  21. habebitur sum Sn. atdu
  22. sed si e dn sit alius amnerus
  23. constans sma snn et sdu ex se invicem pendebunt.
  24. n. ntdn C
  25. jam an
  26. t ogt( . ati du = + est ergo summabilis, t et dabtatio
  27. sun an sas
  28. et, tt L, 1o est (5i soli pares vel socsimpans
  29. HHinc sequitur summam quodratorum i a sinctionibus artthmelici de–
  30. nominatoris invenili posse; modo sumg differentia
  31. non sit unitas Ergo si diff. sit unitas haberi prt
  32. tam prope quam quis volet, ob discrimen a summabili
  33. quantum libet, exiguum. Eadem methaus piraliis potentiis.
  34. u
  35. sent
  36. praeter
  37. 2 = = + L. Hinc si dn =2 erit hoc
  38. =nn =1
  39. generalius
  40. n+ 1
  41. n- 1
  42. summabile m-1
  43. tit + si dn = 2h
  44. nn- ph
  45. n+h n-h
  46. Eit summabilis
  47. M1
  48. Ln-hh
  49. praeter hanc Methodum alia est a quachaturis, vig.
  50. sit (
  51. n posita, du constante sit L = x + HX + X et
  52. n+ h
  53. sumu est et
  54. 2et1
  55. So = . X + Xet 1+ L X 4L
  56. 2C+1
  57. 3e+1
  58. um mnt mntmta tantu ergo si X est 1. summa prodit data progressionis Harmonics
  59. amni muntmude mandu quae procude semper reducibilis ad quadr. Circ. et Hyp. vel psi
  60. omnes, autem series numervi ravatim qui ubi non est inde-
  61. terminata in exponente possent reduci ad harmoni castux
  62. et potentias et erae vnsu ad hamontems. Nontum oes potentiae n
  63. humionilas reducunt. Itaq circa potentiam sumericarm summas adhuc
  64. haereo Sh+sgi= su sit F et 9- L 5
  65. map = Smndp + smpdu + Sapdm Cr si M = 1 p = L dm - - dn, = c
  66. in L = ( -2fdn + ( du +s 2 du + du (an. X
  67. mup= Ann n spn. ntdn sim
  68. du habetur =O
  69. n.ntdu
  70. sdn
  71. Ru. ntan
  72. = d fdn
  73. t ntdu
  74. ntan
  75. n. n+ an
  76. fn, ut du
  77. +dn? san
  78. habentur
  79. un, nedu
  80. quia liceb habere suum. e pab = n b et hac in bris infialita, per quadraturas
  81. summabitir si sit series
  82. nn- bb
  83. nubo infinita habebitium per quadraturas. Ergo et quantulacunque sit b.
  84. an ergo et si sit b=0 videndum foret hic utilis methodus
  85. illa contianitatis.
  86. pro (an hoc incuil: sit LX + + X + X X ere = sydus fiet ydy = + + LX F L X + + X etc
  87. Sinn et X ydy = X + h XX + X + L Xt etc. = sdx =d 0g 1: -X. Et fiet
  88. yy = (2x logsi s lgh i + sx logk = log X, log ix
  89. jam alibi desi
  90. Eadem pethodo
  91. oene graditras
  92. quodem
  93. elum sublatis summutionitus ducetur ad Xy ady + Xdydys, + y dydx = ax :, 1 - X, ubi o sint progross
  94. hadem veltutus et pro i. 8 g. cq erc s po labis
  95. du pabystantes fiet: 291C posita ex constante
  96. ta
  97. mus ingan
  98. am pam tu
  99. +dman p

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 119v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0238?run=74