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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 164r

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.

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The machine reads it as

  1. dit aequatio data 100 + 10y + 101 dy + 120 yy + 111 ydy = 0
  2. appet Aissumatur v todo +Y _ =0 ipsa v existente mgy +ny, fiet aequatio nova
  3. Y+ ny + + myu
  4. per y fit r = 100t.)
  5. +Gany x quay +qun yy + 29 dy
  6. 100L+ 110 Ly + 101Fdy + 120tyy + I1 F ydy
  7. er ydus sit g = lIt: 2m et per dy fit g = 1oct: n, quos duos valores aquando fit
  8. IIIn = 2. 10c M seu n~M n = 2. 101 M: I. Ob y fit n + gdn = 1ot seu explicando
  9. a per n, sit E + nn + 101E dn = 110Fn, adeoque F = nn:, I1On = 101 dn. Eodemmodo
  10. ob yy fit m + gdm = 120F, seu 2mm + uIF dm = 2. 1otm, seu F = 2mm:, 2: 120 11Id m
  11. ut siet
  12. N
  13. -
  14. 1IOn = 101dn
  15. 3BIM
  16. 2 mm
  17. 2. 120M = III am
  18. IO βm = 101 d Bm = 101 βdm
  19. 2+0 jam 2. 101: I1 compendio vocatur B, cognita
  20. e2 Mm.
  21. siet n = BM, et fiet
  22. ubi feliciter evanescit mm, et fit
  23. 2. 120m - 11I am
  24. + 2. 110 β3 m = 2. 101 _Bam 1 = 0 adeoque tandem
  25. Lm
  26. _. 1220BB + 101 d β - 110 βB
  27. 11I (3β = 2. 101 (3
  28. sit sit jam data aequatio aax XXdx + yydX = aadue fiet 100 = xxdx et 10 = 0 et 101 = - aa
  29. B
  30. = 2. 101 aBm
  31. = 2. 120 βBm +. 111 (3β mS
  32. Z N
  33. infinitu
  34. fiet
  35. dD: 1I
  36. quia 181 = = et 1II = 0 fit (3=
  37. Adx idaased dur: m Aadx. aa seu X logm = 4X: aa
  38. et (20, = dX et 1II = 0 s. fept lur p27
  39. u et
  40. oacvura hyp.
  41. scit et fi vel B
  42. B= 0. sed non B ergo 1
  43. seu M = b(+X. aa 7 t + = 2 btBX :aa : 2 b(4X 1a = e B F2X: a4F
  44. seq ita dmim quarq
  45. et do
  46. M. 2M
  47. Ergo g 1
  48. Ergo dm: 2m = sed ita fit dm: n evanescit
  49. iaque ut habeatur supplement cm ex 44. data frat. eit
  50. X = yZ et dx = ydZ
  51. sit 7 = hv + W fiet Xxdx BB +hh vodx + 2hWvax + 20W dxaat rdzaa vah
  52. = aa ) hdo - aa Vdh F aahvdV + aaW don
  53. nga D an
  54. fial ut WoWdx +aa dv= 0 fiet 10= aadv
  55. et ciet
  56. sit v = B A ny min ny m t M + ny tly,:y, et ex b+ qdv + r fiet
  57. Edsiet 100(+ 110y + 10rdy + 120lyy
  58. fiet Ce q= 2ot. m = 11ot =m: dn
  59. et fit C∞0- 120F dm 10 tm nm, seu L = mm p. 1O n- 12od p
  60. tqnus ( gnydue andus e
  61. 1
  62. O
  63. B. X X dxa + hh V dx dx + Ergu fit x de Xx Vda thh vdx Zhaad V - a a Vdh
  64. ex
  65. quaesitum siesset f-x = aa B. W seu cxagescet a sed nit inde
  66. es habebitur
  67. Ai m+ nyu + qudus
  68. per d
  69. 2
  70. : V et yy = 2Z(. vV et dy: vaz + 7do ergo fit Cxxdx WB + ZZ ax aa vaz taaziv
  71. - y =
  72. +4
  73. C
  74. fit = u ob Ao lut + = - 9m : 11. Ergo ob fit H M + gdm = 1109M:1
  75. +ryusqnydu
  76. =gm: 120 per y fit + = g4m: 100. fit dm: m = - 100: 120 Set habetur et _ C: 9 = =m: 121
  77. M ob y fit m + gdm = pomgitzo, et fit g = - 120m :, nom + lodm. Ergo pomanel narbitraria
  78. fit t
  79. ino potuset esse n20 Fresumamus pagina vers

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 164r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0327?run=74