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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 26r

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: 0.80.

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The machine reads it as

  1. exemplum sumamus. in venire tres numeros, quila da ut
  2. ductum quoramlibet summa et differentia sit quadintus Numeri Xg1
  3. X 10 + nC 1 nC +9e 19C41 eu
  4. C1
  5. y= 2012 Cs n 5 +23 C 124 e +25 e Mt
  6. 7 = 50 +31C f32C+53C +3+ +35 cM
  7. (2)
  8. (4)
  9. X + y quad quadrato v X + y= M, x - y = n X + Z = p x+ q x- Z = 4
  10. 7)
  11. X y+ q(2) r y-
  12. 9)
  13. 2
  14. 6)
  15. = 55
  16. Ex et 2, Z2X = mm + un Ex let 2 = mm- nn Ex e 2X; = pp - qq
  17. Set6
  18. (11)
  19. 12
  20. rr + 5S Ex5.t 62Z = rr - ss
  21. (
  22. (o
  23. Ex 7 et 80 fit nin + una = pp + 4q. fiat m p+ foi a ex 3, p+pt1F +n- paq
  24. 5)
  25. (13
  26. 116
  27. 1ex ay. 14))
  28. seu p seu mn - pp = 49 - nn sit M+ p = t q+n fiet m- p = . 44 q n: t
  29. 8
  30. 4)
  31. rursue ex g et 12, sit pp - rr = 49-55 sit p+r = v g+S et, ex aeq. 17
  32. fiet P- r = q 5: v. Ergo ex aeg. 16 et 19 fit m == g-n: t + p.
  33. 19)
  34. et p qu s: D + Y. Ergo ex 20 sit m = q - n: t + 9- 5: v + r.
  35. Jam ex aequs. d et 11. superest aequ. nm= nntrrtss ubi tantum opus,
  36. 13
  37. est explicari m, fit. 99: t - 2gn: l + n: t + g. v - 295. v + 5: v.
  38. F 2gY: t - 2nr: t + 2gr: v = 2sr: v (+ WI) Teuarr si
  39. G 44: tv - nq: Lv, - 95: tv + e ng: tr
  40. = nn(rDiss
  41. porro ex 15 et 16 fil 2m = + gin + q-h: t.
  42. pursus ex
  43. (27)
  44. 25 et 22 fit Y q- n: t + p 2t qin + : 4n: t. Ergo g- 5. v + r 4 4 9. n: t = it gin
  45. g. 5. vir
  46. (28)
  47. partus ex +8 et iu rursus ex 18 es 21 fit v. qis r = 9 5: v +r seu
  48. fit (r = sit 2Y C29 b. 9+ - 45: v
  49. 30
  50. In polius post 19, fiei ex 15 et cb, 2m = t qtn + q n: t
  51. yr
  52. et 2p. = t qin = q- n: t et ex 1g, 19 2p = a v. 9+5 + 9-5: v
  53. +
  54. et 2r 23lv. 9+5 - q- 5: v et ex 31 fit + gin - q. n: t = v. gus + q. 5: v
  55. Unde habetur g. nam fit tg + tn = g: t + n: t = v9 + v5 + q. v - s: v uunde fit
  56. (25
  57. Q tn +n: t = v5 + S: v (. v + 1: v, - + + 1:t
  58. q
  59. Coe
  60. (90)
  61. jam compendii causa t + I: F sit (3, v + 1: V sit D _ t - 1: t Fit at v - 1: V sit e
  62. 3
  63. 7)
  64. 39
  65. et ex q. et β+ A = t, et B+ n = v fit et ex 36. fiit en - nBC:, b - 5 = q
  66. (41)
  67. (+2)
  68. rursus per compend β: D. X sit r et n: B- A sit o et ex ag. 47 sit Hn - v = q
  69. +
  70. 45)
  71. qui valor ipsius g substituatur, in aeq. 30 et 33. jam ex 30, 37, 39 tit 2M = β9 + An
  72. et ex 33, 38, 40, sit 2Y (2 n9 + 85. Ergo in 47. et 48 pro q substituentae vulorem
  73. 0
  74. ex aq. 46. fiet 2m = BNN - β~ S+d et 1 EY = (n Nn - n 15 + 65
  75. jam in aeq 23, qum nn trrass pro m et r substituantur valgres, fiet
  76. )
  77. vel copendio e B1+ At _ sit et + sit ip
  78. 54
  79. Ergo 2m Gn = βa5 et 2Y = v5 + (nN n
  80. Ergo denique
  81. in aeq. 23, qnim = 4 un + 4rr + +ss substituendo hos duos valores q m, Y ex 46, 53, 14
  82. fiet gn + β~5 - 283V n5 = 4nn + 455 + W5 + eAn + 2Ip ni nS
  83. (5,
  84. ponamus BN 4 F et habetur solata aey. 35. pervalorem ravalem ipsius 5. jum 56 ita solvetur: sit
  85. rC explicemus 1 = - nov +b = n: B- A. Ergo =-(n n: 6- X + B, ergo ex 56 si B n: 6- 1 = 4+ (. B. d
  86. a6-a n A: B= X sen β5 = 4B- 2 + ei + d8. X. 2D et B.
  87. iquae revoranda ad t et i verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 26r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0051?run=74