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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 93v

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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One image of two folio pages side by side, registered by the library under both labels (also fol. 94r); this page is its left half.

The machine reads it as

  1. siom dx +, dua t att n dx + 13 an
  2. 10m + un + 12 diffeentiando 10dm + mdio + 11dn + n du. + d12
  3. Esto aegus. 20dm + 21 mdx + 23 dn + 24 n dx + 25 dx = 8
  4. e3 (tom + Hn) dx F sit g = rom + un
  5. Solvi potest (ex rgyax + dy. sit y - tom + un
  6. qux + P y dx + + dy
  7. solvi potest fdx + gydx +hdy = 0 sit y = 10m + un, et fiil aequatiosruble e et fiet
  8. Squalio solubilis fax +g.0m ax + ∞ un dx + iolam + utan = 0. haec comporretur dalae O
  9. fiet 10 = 20:h et 1 = 23: h et f = 25
  10. 120 -2odh = l20- 20dh. et g = 2h = hdro = 20d 4 24h - hd 23 +23 dh
  11. +Em dio n du1
  12. 21 = g. 10 + hd1o C seu g = 21 - hd10; 10
  13. 24 = g. 11 + hdu seu g - 24 - hdu: 1
  14. du
  15. et grodx + h lo = 21 b
  16. Unde si calculus probus sequeretur rem succedere, seu haberi summabilitatem aequationis cqualis
  17. dio = hdro 2odh hd10 = h
  18. tch 20:h
  19. in quibus m et n nunquam habeat
  20. Resumamus Dectasit aequatio differentialis trium literarum, m, n) solbi potest ( dx + qydx + hdy =0 sit y- +60n
  21. erit dy = 4in d40 + d
  22. affectionem replicalam, ut 20 dm + 21 m dx +33 dx=0 dato
  23. dn
  24. 31 n dx
  25. 31, 1ondbo +fix = 3.
  26. g = 21dx - hd40, 31 dx - h d60
  27. 40 dx
  28. om ax g6onx
  29. 60dx
  30. 40h = 20 60h = 30
  31. h d4o = sid (20: h) = ( hd20 - 20 dh = hd 2o 20dh, et g = 2 1hdX -hd 20 + 20dh uh dx - hd2o + 20 d h
  32. c
  33. b
  34. a 60 du
  35. Exprodibit
  36. q4n fiet f = 23
  37. sed pari jure h dbo = hd(3o. h) = hd - 3odh et g = 31hdx = hdzo +3odh seu g = 31hdx hd3o+ 30dh, quos duos
  38. t, (20: h) dx
  39. e
  40. d: h) dx
  41. 20dx
  42. 30dF sed ita evanescit h
  43. BCha∞ +20. 31 hdx - B20h d30 ( 2030 dh =0:
  44. quod non mirum. putem tamen succuri posse per arbitrias fiat 2odp + 2 pdx + E3 dx et fiat
  45. 30. 2
  46. 1. 30)
  47. 319dx
  48. 30hd20
  49. o= c0m et dp = sodm + m d5o g = yon et aq = 7odn + n d70. Ergo in 1eq. C pro m et n, pe fudo p et 9, est
  50. dq
  51. explicando pper Som, et 4 per 70n, fint exaeg. C. 20. sodm + 20 mdgo + 30. 7odn + 30mdzo F 23 d
  52. =O
  53. on x no 50 et 30 substituantur
  54. 40h = 20. 50 60h = 30. 70 9= 20d50 + 2150dx - hdgo Y 21 3
  55. valores ∞ = goh 20dso = 20, 20godh p 20h d40 - 4oh dro - 40dh + hdg6 - 4 teda) goh d2o: 20) et 30 d 7 0 - bodla thd6o eh as
  56. Ergo ex ducbus mabbilbus ipsus gnfiet aodAM 4. esu d 40 ) h duo + 21 L ex C m. 14) = ut A n 190). h ago + 31 ( hac
  57. 10
  58. 66
  59. Licebitne in data aequatiane O poro m ponere p+9 et pro B ponere +p f9
  60. essi lergo ne sit quidem nam quaesita evanescunt
  61. piastar
  62. o= 4oh20dm +40h 3odn + 40 h rimdx + 4ot. 31 ndx =F 40t. 23 dx
  63. h = 20. 40gdx :, 40. 21 _d X - 20d 40 - 20. 69 glx:, 40. 31 dx - 20460
  64. 0= 20. goh dm + 2obohan + 2olmdto + 2ohndbo F 20fdx
  65. + 20940m dX + 20gbonax
  66. 40. 40.31 dx - 40. 20 d60 600. 21 dx - 60. 20d40 60= 684. 30, 20 unde
  67. 40. 30 = 20.60 seu 30: 20 =60:40
  68. a 60 = 20. 40d30 +20.30d40 = 40. 30d20, : 20. 20 20460 = 40 d30 +30d40-40. 30 d20
  69. et fit 40. 40. 31dx = 40. 40 d30 - 40. 30d40. + 40. 40. 30 d29 = 4 V 40. 40. 30. 21 dx 40. 30d40
  70. Unde omnibus divises per 40, fit 40 sc3idx
  71. 20
  72. ille
  73. corax
  74. sed tollendo utrobus - +0. 3od40, connescit 40
  75. et fa 21 dx = d30 L30d 30 = 30riap

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 93v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0186?run=74