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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 129v

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: 0.83.

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The machine reads it as

  1. 0 = 10 + 11y, differentrando det o- d10 + y d11 + 11 dy seu ddy =- d10 y du, quod conferendo
  2. dutae differentiali dum dya = 20dx + 21ydX fiet dnc: 11 = 21 dx et dio = - 11. 20 dx
  3. 0 = 10 + 11y + 129y differentietur fit d10 +y d 11 + vyd12 + 11 dy + 2. 129dy. + 9y 42
  4. Do
  5. quod si jam 2 sit constans fiet d10 + y d11 + 11 dus + 2. 12y dy = 0. Esto jam
  6. data differentialis 102∞ 20 dx + 21 (B dx + 22 d + 23 dv. faciamus
  7. V = y + 31 fit de = dy + d31. Ergo ex aequatione data fiet.
  8. 0 =
  9. 20 dx + 21. 3dx + 21ydx + 22 dy + 23ydy =0 ~ d10 + y du + 1 dy +2. 129 dy
  10. a 20 dx
  11. + 22 d3) +7 la + gedus
  12. +29y13 239431 2331d9
  13. 2
  14. i d31
  15. coincidentiando sit 23 = 2. 12
  16. 21 dx da seu 1 = f21 dX
  17. 11 = 22 +31 Ergo 31 = 11 = 22
  18. 11= 22 +23,.3] d1 = 21+ 23.8
  19. Ex hac ullima fit 11 + = 21 dx + 23. 31 sed hoc = 22 +23. 31. Ergo fiet
  20. Coinciventando primum primum fit 2.12 = 23.
  21. 25
  22. (21 dx = 22, quae est limitatio. sed ita 31 calculum non intrat
  23. V = 32y, et do = 32 dy + y d32 ex Et ex data C
  24. fiet 20dx + 21.32 ydX + 22. 32dy 47,32. 32 ydy +23yy d32
  25. + 22 Y d32
  26. + 2397 d32
  27. faciamus
  28. st 12 = 23. 32 + B
  29. et 12 erit constans
  30. sed ita non est similis formula
  31. 25 2. 12 = 23. 32.32 = 2, 23.32 + β
  32. 20dx + 21 V dx F 23 dv + 24 vdo
  33. fint ae = 3yee di4 + yd13 + 13dy
  34. 22. 14. 14dX + 22. 2. 13. 14yax + 22. 1313yy dx
  35. d
  36. sed ita 32 adeoque
  37. Juo et 11 frat constars, contia quam oporbt
  38. L22Vex
  39. 20 dx + 21 V dx +22 vV de + 30 d v + 31 v do = 0 =0 fiat V =
  40. sit da la differenlialis
  41. 20dX + 21. 13ydX
  42. 21, 14dX
  43. 30d14 +30y d13
  44. 3I. 14d14 +31. 14y d13
  45. + 30. 13dy
  46. + 3l. 14. 13dy
  47. + 31. 131
  48. +31. 139y d13
  49. + 2. 12 ydy=
  50. 12 = =. 31. 13. Ergo d12 = Z3Bd13 + L 13d31 = 22. 13. 13 + 31. 13d13. sed ila
  51. +1. 13y d4
  52. recidetur in quaesitum. Ergo multiplicetur per liucem una aequalio per 2. 12
  53. + yd1
  54. a0
  55. + 11 dus
  56. + yy d12
  57. alter a per 31. 3 et fiit 31. 13 d12 =
  58. 2. 22. 13. 13 12 + 2. 31. 13d13,12
  59. 2.30. 82.1 + 2. 31. 12. 14.6
  60. d. 1 = 31. 13. 2 d30 n 13 + 31. 13 2.90. d1. 13431. 13. 2 30 12 d1z
  61. e
  62. adeoque
  63. 12 = 2. 22. 13 2. d13
  64. 31. 1
  65. 20 + 31. 14
  66. 2. 30+31. 14 d12 + 2. 12 d
  67. 2. 12. 2. 22. 13. 14 dx + 2. 12. 30 (13 4+2. 19. 31. 14. d13 + 2. 12. 31. 13d14
  68. d11 = 283 2
  69. A1
  70. et frat
  71. 30 +31. 1, 12
  72. de2 = 4. 22. 13, 14 dx + 2. 30 d13+ 2. 311 4 d13 + 2. 31. 13d14 -
  73. 2
  74. 2
  75. 20 + 31.
  76. 2
  77. ad
  78. 13
  79. d
  80. 30731. 14
  81. 1
  82. si ene affectiones a 14
  83. Et
  84. oErgo in aeq. 4 ponamus 13=
  85. fit 3112 = 2. 22. 12 dx seu dn. 12=
  86. un
  87. invicem
  88. haberi ad 14, nec opus aat adhiberi a)
  89. non ducum
  90. imo polesfieri 13 =1
  91. ipsiu 31 L aequando fit L1 = 4. 12 14 f 4. 31 a14) = 2d30 ( 2. 31 d ).. et duos ipsius d12: 12 vatores aequando, fiet
  92. idenim in pelestata est fint 3c du
  93. 2. 30d12+2. 12d30 + 2. 31 12d. 4 72. 1 4112 (d A =
  94. t2.
  95. Bdi quos duos valore
  96. Ruisus 31 du = 4. 22. 12. 14 dx
  97. .22. 30 d + 2. 22. 14 dx = 2, 22. 51. 14 dx = 31 d30.
  98. OF. 31. 14
  99. R sumamus pagina versa, nam veceor ne
  100. quis sit calculi error
  101. Et ita 14 habetur ordinarie
  102. 13y + 14
  103. Hoc coincicentiandam
  104. hydy
  105. 4 psi C
  106. 20
  107. + 3
  108. 2. 22 134
  109. 31 12d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 129v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0258?run=74