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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 90r

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: 0.77.

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. 91v); this page is its right half.

The machine reads it as

  1. aa dy + mY aX +andx = 0. sit a constans, X et y indeter
  2. minatae primariae m et n dentur ex X et a. Ajo hauc
  3. aequationem solvi posse, seu inveniri y libere, A
  4. methodo tali: multiplicetur aequatio per h quae ponatur itidem
  5. determinari ex a et X, et fiet (2d) aatidus +hm ydx tahndx -0
  6. et fiat (chmax = aadh secto) sinax = aa log. . E
  7. Et ex 2 fintet nahus + a shndx =0. Hinc quia ex 4 est
  8. 61
  9. ex 5 et 6
  10. mo
  11. sindx: aa = h. pesito logb = 1. fiet
  12. aa b
  13. V
  14. + )R.
  15. Et ita habetur Y libere
  16. 1max.aa
  17. dx.
  18. patet etiam hinc formulam non summabitem
  19. libere, ut est ea quae facit aeq. 1. peddi
  20. summabilem si muetiplicetur per
  21. et
  22. sindx: aa
  23. inde prodire ag formulam contentam in aeque
  24. ele
  25. quia habetmeq ay+ mydx + nogax Attt
  26. it eergo dis
  27. y = 10 Fr. e fiet +du vat
  28. + uttrvx
  29. d P =(1mo )2 dy ydhu tay. sic ergo
  30. y
  31. yy
  32. tkA+ tgax
  33. Hinc sit formula 2o) du + M, 91 + ny yt = 0
  34. 1A
  35. rara
  36. dy my , - dy + mydx + n dx = 0
  37. fiet
  38. LKTaX
  39. t Tdx
  40. eM tx dy
  41. (4t) terr:
  42. 3tro)
  43. multiplicando per h, fiet ((- hdy +kmu dx): 9y) + hudx = osc
  44. Yd
  45. osito
  46. 2t
  47. et va siariti ut.
  48. y
  49. yu
  50. et debet esse hmdx = dh seu (inax = log. h
  51. et
  52. (S+0)
  53. dut (8
  54. et ex aeg. 4 fie 7mo) E: y + stindx =0 seu y = h: Stindxbis
  55. 1
  56. posuto log h esse Sindx sec aq. 5, et ita solvitur aeq. 2
  57. nempe -dy + my dx + nyu dx =0
  58. si sit aequatio du + myde t n qu dx 4 y
  59. Et save
  60. hoc compretendebatur jam in praecedente, nam
  61. 648
  62. ma au + nax =0 posito = =Z, idem
  63. y
  64. yy
  65. est quod Zmdx + dy + nax =c
  66. sequia ut patat ex frac p. 3. nondum habemus
  67. ady +. y ax L. qy dx + . etX =0
  68. Ecibemus autem summabiles aequalionet formulas haadus +hmyax talnax;
  69. et Kaady. + KPYAx + Kqju_ posito h= (smexi aa et R =. .
  70. hi summa exambabus erit summabilis, quae orreranda erit formulae dato e
  71. ibilemnem itidem per datim aequationi datae ( per datum aliquam a
  72. mulli plicatae
  73. es in unumat
  74. sun
  75. Et haec methodus ulique procedit. possunt plures
  76. i potest et formula haltiplic per aliam, ut fiat sumentones
  77. addi saque ib. corte algudo quae adain primm
  78. etm nrau
  79. tervau
  80. etur c
  81. =Nit
  82. faxt.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 90r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0179?run=74