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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 204r

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: 0.78.

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. 205v); this page is its right half.

The machine reads it as

  1. Atrithmeticorum o+I=
  2. 34b 43C+3 1+
  3. Si primus terminus sit 0, secundus 1, ultimus l, erit summa L+1, l
  4. vel posito numerorum
  5. terminorum esse n = 1+ 1, fiet ex theoremate sx: nl = 1: 2 seu (x = nl: 2 = l+ 1, l: 2 (3+ 3
  6. Quadraticorum 2+1 = 3 + 0+ 1r 4 = - 5 + oFirara -
  7. SXX: nH = 13 + A a seu SXX = IH, H, + d st
  8. Cubitorum e+ 18
  9. OH + 4 + 9 + 16 - 30
  10. =3 + 8 1onorib netib 4u a
  11. Ot 1+8 = 9 = L -t ot 1+8+27 = 36 = = = + 1. oideoque sx. nl- 4t4
  12. 8+8 +8 e Autululus Kapinorum Z7, 12 +7+ 27
  13. slous Quod si L sit infinihus evanescent t,
  14. C, et. Itaque sisit series infinita quam
  15. utatum a puncto seu o incipientium et continue prescentium, in ratione primanorum secundanorum, terrianorum, quarta
  16. norum etc, erit caseries ad sertes aequalium ad eamseriem, ut t ad reciproca ad 2, L, F, E cH. (seu sa six, sX SX etC)
  17. seu meo stylost.s Xax SXXdx Sxdx Sx dx EtC = Z, ZXX, X, x x B et generaliter (Xdx = Xet 1
  18. Hinc autem et datur summa subsecundanorum, subtertianorum, etc dux Sdx x, sax Yx (Ax Ex.
  19. Nam sit X = y fiet X = y Datur _. Sydx = L XC+1
  20. Sed sydx + sxdy = xy seu sxdy = xy - sydx
  21. peri - = XeY = Xet, est 1 - D. Ergo sy e du = , X
  22. quae regula comprehendi petest sub priore SXex =
  23. Tabula sesti sar,
  24. Hin stritX. sis
  25. f
  26. six ix Exe ix Ex. EN
  27. Y 2x 3X 2
  28. EX Z u. 36
  29. Y 4X + X a G X 1 414
  30. YEx EX EX 35 B
  31. quae regula Adeoque et
  32. y. yte = e
  33. pe dx = +
  34. Ye+ LB x i Aoet ns petu anti primanes, autisecudan antinteriomos
  35. tantum pro e augando
  36. Tabula mea Recipiocorum. Hi teres Edrisetur minino equalium
  37. A series aequalium mulcato serie pitmranorum, secundanorum, 3tianorum exc. quae ranturque summae, fiet
  38. S1 -X, aX S IXX dx f. ( - X, dx Si X, dx
  39. seriei aepo potenti a serie apstomurum, seu residuorum a pimanis 1.X, quaeeatur summa
  40. X1 -x 1 - 2X LXC 1 - 3X + 3XX + ∞ 1 - ax + 6XX + 4 X + X
  41. Siax, 1 - XX IAXXFX
  42. Sdx, 1- e
  43. Sdx, 1- X 1- 2X X
  44. Su x, 1- X
  45. Et generaliter, 6. 1
  46. L- 3 43 -
  47. 1-3X + 3x = X
  48. 53+2-2
  49. 1.3iaKS. 1X)
  50. 1- 2 +6 - 4 +
  51. (- 4XX+6X- 4 X6 + X
  52. - 3 +6-2 +
  53. gxi aperix
  54. 4 +6, - 4 +.
  55. G. IX, (1 - XC) = en, en , en -2e, en- 3e, ete
  56. Hinc quantitas qua sinita CA, 1, Cn. e+ B en 2C + 1, en. 3e+ etC
  57. Hinc quantitas ista finita , et haberi potest, modo n sit integeri ita
  58. enim mavitesum est exhuuriri tandem multiclicatores. Evenit antem
  59. pulchre, ut quoties l est, ,, etc. evanescant cumeratores expli-
  60. catione facta, it nominatores sint sigurati, seu Arithmetice replicati
  61. 10 13∞, as
  62. Seidx, (X - Xn = en, en e, en 2C, en - 3C, et
  63. entMI entne entnHe, eninHL. extnt1- A
  64. uodrepere donec scilicet in numeratore en -. e est 1, et donec in
  65. numeratore en -. e est o. quia tunc superest n+I
  66. 5, dX, (XX- xer2)n =en en- e, en 2e, en-3C, et
  67. SX x =
  68. Et generaliteo extrati, ontrume entenr Ze, entent-ge, entin +1 - 2e, t
  69. Indx (X ern = en en e, en 2, en - 3C, etc
  70. entratius entrnti-e, entrnti- e, entruti 3e, entrntiae, ecorit metur
  71. donec scilicet in numerature, minimus multiplicator fiat 1, et in menominatore. rn +
  72. Patet etiam numeratorem semper esse eundem, utcunue variet r. Et ut
  73. sastu ntiteee s nnor muctitioinem qumiener dentmnts
  74. 0+ 142. - 2
  75. 3+3t243= et ila porro
  76. oncralivores
  77. foii minde
  78. Semper reduca
  79. potest ad
  80. SX dx (.xe)n
  81. duii quadrati, cubi; Biquadrati
  82. Sndx (1fXe)n
  83. 15 Et1, ZH, 3+
  84. ds pratin, at
  85. 1t1, 2+ 12 4, 21
  86. bene compinuum
  87. ae intra et quae suera primanos
  88. am unam Tabulam, nam indices supra sunt progrissiones
  89. Hart Arithmeticae, intra prodressionis harmonice
  90. subtecandani, primani, sesquip
  91. in cntisiundum
  92. _3, uet L vel Z vor le HC selundrase hon abie
  93. imltatos sero pruimanoum
  94. per autem denominatores ultiplica ooces multi
  95. ne appeat emem utrbra
  96. arpicatorum motitudtntm.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 204r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0409?run=74