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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 151r

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.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. homveoncolarm
  2. um differentralium rationalium ordinarae
  3. sit aequalio rationalis Generalis deteantia
  4. O= 10 + 11X + INXy + 123, + 12I X9 + 13X, + 1A2XyF 131Xy + 14 X + 12Xy , 41X7 +15X et
  5. 1G
  6. 1
  7. ee
  8. 14B
  9. iffiulset Hujus aequatio diterentialis
  10. CMax + 11Xdy L M XAx 12 12IXydx + D2IX ay +rge ix +, 122 Xyty +3. 131 Xyex + 13. Xay 2 X ax 4. 13CX yaxr2 172 du 13. y l 1
  11. du x ixgn ite
  12. fye rydy yex yay
  13. xydys yax y dy
  14. gix ydq
  15. 0 = 20 dx F 3INay + 21 adr + Z1 Xy Ax + 3_ Xdy + 2 _ X. lx 1 321 Pydy. + 221X y ex + 9X Xay + 23 X sx ~e xisa 13 3. KB) F23, E1B St 4
  16. dy
  17. conferatur haec aequatio cum data,
  18. y
  19. O2
  20. y dx
  21. Gdy jax xisay yex yay irix Ryius sex s
  22. 1= 20 1 = 31 B = 21: 2 121 = 2112 (9= 32 13= 12. 3 1 - 3112 131= 211. 3 = 33 41 - 23.4 11 ( 2 132 C 12 3 . N. 1
  23. dy
  24. yily
  25. yax
  26. 141 = 231: 4 = 34 15. 24.5
  27. it gencaliter fit aequatio X
  28. m na Ergo
  29. Et genemaliter sit terminus X Y ejus differentialis M. X = + n. X
  30. n
  31. n
  32. terminus in data aequatione, ut sit summabilis debet coefficiens ipsius X divisus per M
  33. nKXd.
  34. aequari coeffirienti A ipsius X y diviso per n, seu n. h X y =n K X. y
  35. Sed ene jam aliam methodum qua pergatur ad transcendentes:
  36. o= 10 + 1X + SR SP s2oRAL+N ) + s2B+ g+ 0
  37. 30+ 31y
  38. 30+ 3IX
  39. defferentrando +11. 304 + 11. 30. 31 X dx + 11. 30. 31 ydy +,, 31 Xy ex
  40. 2. st dy
  41. Y 20. 30
  42. y dx
  43. y1x
  44. + 21. 30 +20.31 V
  45. Imo videtur 10 et et plane posse omitti
  46. dy
  47. m-1 n
  48. + 21. 31 ~
  49. C2
  50. Sed forte
  51. sed quia abest. yu et xX posset forte tale quid adjic
  52. Ae
  53. 30 + 3D 31 X + 31 f habet differentiam 4030. dx +F3 Xdu
  54. Si homoeplosin negligamus fiet sic:
  55. ly
  56. ax
  57. d, 30r71X, gV, k
  58. aque nevi gt hrex Tx ydu
  59. 10 + HX +ny + (30+ 3IXdx + 540+y Ly + s ndX + 81 dy
  60. Asi
  61. (30 1
  62. 60+61y
  63. Chor3X +)2Xy 132
  64. item sic = 10 + UX + inxy + 12X + f( Ct
  65. 50+SIX
  66. unde diferentiaado fiet 1 1. 40 dx + 1. 41 XAX + 1. 41. Xdy +.
  67. 9dx
  68. ydu
  69. + + ing0
  70. F12.40
  71. dgouus
  72. 1. 41 X dy +11. 41 X ydx 482
  73. ydx
  74. 712. 41
  75. 49251) 432 1)
  76. du
  77. 40
  78. + 12 1n
  79. + 326)
  80. homoeo plota
  81. F 30 5) +31.41) +31 151)
  82. Ergo vodetur quaevis aequatio diffeentialis simplex primio tansentialis simplex se in
  83. qua indeterminata non excedit primum gradum reduci posse ad quadhaturas.
  84. Idem de non homoeoptota derum puto. et subo summaelorio vinento 3.33 Yy +5ds
  85. pro altiori padum ascribemus: e0 121XG + 1353 unde differentiando ad
  86. ad cg. 2. adjicietur.
  87. 2. 12. Xydx t 1ux dus ZisX ex
  88. y Ax 3.13) ay
  89. ponamus Si ia servit indicandae
  90. 121. 407 2. B21. to rip 3. 17 40 xax
  91. d
  92. 2. 11. H X ydx + 2.121XAx + 121. 41 Zdy
  93. Xy dy Xy dys
  94. + 121. H.
  95. legi homogenioru nec tamen arb, +3.13. 41
  96. a
  97. +3. 335)
  98. y de
  99. y’ay
  100. 13. 25(51) +33. 6)
  101. +3. 13. 41Xdx
  102. y dy
  103. + 33(51)
  104. 6 = , 11. 40 x 41. H1 nhy L M HI XdX FuI, Y X L u. 11 Xdy +712. H1 X Ex +3. 12I. H. X ydy + 212141 Xy ax + D21 41 Nay + 3. 13. 4, X dx
  105. 33.51
  106. aciter Colligendo in num
  107. +30. 41
  108. 11140 2. 12. 570 2.12.41
  109. 92. 5i
  110. 31. 51
  111. +3.1341
  112. 31. S1 3181 2151 121. 40
  113. 2iu. 4 84
  114. 3. 1940
  115. +3. 33. 51
  116. A 81 = 82 + 11. 40 - 12. 40 B3 = 2. 54 f12. 41 : 111. 41 5b =3.88
  117. 13. 33.81
  118. in
  119. ex
  120. idu
  121. E
  122. 33.51

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 151r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0299?run=74