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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 76v

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: 0.81.

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. 75r); this page is its left half.

The machine reads it as

  1. B 5y+ 9dy + , 10 2ut y + +..
  2. 10F. 10 -ad z. 5 = a Z. 9 fit 12 = 5 47 - l9 Z - 9
  3. a
  4. 1Z - Bt S (5 s et W = a b3 5tg
  5. Ergo fgradus a f9+ gaus, ab sstig summabile est
  6. 1g dato rationis ad 5, se sit q s f - l cg. a, fiet
  7. (9+ c3y + gdys, a ben summalit
  8. Cby + ab dus eut summille = Z d (27) - te bey
  9. sat g habeant inter se rationem onstantem
  10. ul f9 + gdys summabile
  11. V) = cHfix Cb x + V ay
  12. A2 B2 y + B dy est summalile sit ues hine avi
  13. = 17B2. 5
  14. dole dy + b dsay
  15. = b + 1 2u, .g = V: h
  16. 8y + 8 ly
  17. Ay +8
  18. +. Idy
  19. Se 1y + Siu
  20. Gy + qdy +
  21. de y + 9dy
  22. didus + Valus
  23. av b dus + b daque
  24. 5y + g dy +hacys
  25. videtur id semper comparatione illa
  26. obticeri ut obtineatur aequatio differentialis
  27. in qua obti absit terminus absolutus seu homogenens
  28. Ex gr. Nempe ex aequatio f y Hdy +9-
  29. reducitur ad v + h du =0, quae est solubilis. Et
  30. aequalio y + fay + ddus +g 20 reducitur ad tatem
  31. V + ldo + m ddv =0 sed talis non ideo est solubilis
  32. idemque est in altioribus.
  33. An licebit sic procedere
  34. ay + flys + gddy = 0 (quia res eo reducitur) multi
  35. plicetur per ly +mdy fiet
  36. alisse Estag+ l9 ylbus hijtus + gndy ddus =
  37. tamydus
  38. quae comparim potest compositae ex his
  39. vadn yy tun ydue
  40. +adpy du + ap yddus tap dydus
  41. adqu adgaydus + aglyddus
  42. se
  43. P = du g: a
  44. im - 4 ag. 9 p = 1g. a l = dn = ap. 9 d et sp - du dy +. g tln
  45. restat duf. + aaq = an + gddn
  46. sed ita tollendo q vetriemus _ ad d.’n
  47. dyt aue alysagus eben + l iby + in =0
  48. Aay + Bdy
  49. aq = gan + a dq
  50. sis aadu + dius + amy =0 ~ ns amy + amfdy + mg ddus = 0
  51. fit al = ng et aa + adl + alli9 = 0
  52. a d du
  53. ml dys
  54. medus ytm + ndus + d dys + ldlu + adu + P =0
  55. a
  56. mpu Alx ay + al ddu + Anp ~ agy + 4fdy + 4g dus + agh -
  57. my + l du tan
  58. aam y tamdus ubi circa termnum ultimum non est difficultas
  59. taadn = o-
  60. fec mpraam = ag (98q ncam + ag 17 + b 4 2sq =0 es.
  61. = 49: 0
  62. tadl dus
  63. p ren + radm - raque = 0
  64. sit m = β9 + V+, erique n = adm = β d9 + quB + yat
  65. et t aqualuo s 9d (4 t + agaq + als 9- at 120
  66. pe + rpHt + redq + rq uB + 1)) it 3
  67. tiat gp + aβB + adu - af + rp C + ra B = 0 1 ut evanescat 9 1
  68. it habebuntur , et )
  69. et ag + rβ =0, ut evanescat dq
  70. et fiet aVt + rppt + W at = 0 unde habetur t
  71. porro valore m et dm s quem assumsimus substituto in
  72. aeq. C fiet aequatio in qua sola superert incognita 4, quae
  73. non ib qrae non ibit ultra, 9 et dq, et ita si nihil
  74. in calculo turbamenti est, habelitur 4 adeoque quaesitum
  75. et fBZ + fat -hdz = haec aequatio multiplicata per Y abjiciatur priori, fob,
  76. sed sic video deveniri ad βB, dB,
  77. q. N redit ad hoc
  78. dZ b. y + b cdys
  79. vac
  80. ag: B et p = a Bt ady - a57 : (9- 8 et
  81. sit aβ+ a d9 - af +rd (3 =3
  82. et quia YB = ag hinc tollendor
  83. ccenditur ad βC B, d
  84. Hoc
  85. sucedere
  86. Ex pau praeceedente su mantus aequationes:
  87. fZ+ fpX + sBaz +G afa at - 07
  88. (Z + f do - gdz -0 fv - h dZ = 0 fiet vet si v. - βZ + at;
  89. ac
  90. rat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 76v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0152?run=74