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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 37r

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: 0.84.

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The machine reads it as

  1. sitit duae aequationes differentiales simplices ad litoras X, y, V, et sit dx
  2. constans, simplices voco ubi ordinatae non du habent affectiones invicem ductas.
  3. Aequationes ita stabunt 1004 1oydx + 101Vdx + 120c dy 120 a dy + 102a dv = 0
  4. u
  5. Et
  6. latens
  7. 200aX + 210y dx + 201 vdx - 220 ady + 202 a dv = 0
  8. videndum est an liceat obtinere Equidem non licet efficere, ut simul tollantur do et dus
  9. alioqui etiam evanesceret dx. illud tentandum an liceat simul tollere
  10. Y et de sit sed vibeo si v facias verb. gr. BZ, perinde esse ac si una litera
  11. quid ergo si faciamus y = + pv:a, et habebimus
  12. 100a +X + 110ZdX +120a dZ + 110sp: a) vdx + 120p dv = 0
  13. 102 a de
  14. 101. dX
  15. 120 V ap
  16. Et pari jue 20 adx + 210Z dx + 2eo adz + 210 p: a) vax + 220 pdv =0
  17. Lcoradv
  18. 201 vdx
  19. Hinc poterunt V et dx simul
  20. tolli si sit
  21. 110 p ix +101dX + 120adp 12OP H102a
  22. 210pdx + 3o1a dx+ 220 adp 22op, 202a
  23. Huo. Propp dx + 110. 202a pax + 101. 202 aacx (+ 120. 20 10 2
  24. 220 D ap
  25. 0 = - 120. 210... . . . 210. 102.. . . - 201. 102....-220. 120 a pd p D2.
  26. +101,220....
  27. ita res reducta est ad aequationem disserentialem unique - 207. 120...
  28. Hic apparet aute omnia non licere destruere terminum ep, aut aadx, aut aado
  29. indetermi si indeterminatae
  30. nam prae supponeretur quaesitum, si enim esset 10 ad 120, ut 210 ad 220, vel tale quid utique
  31. utiue simul tolli posset y et dus; idemque est in reliquis; sola ergo aequatio praestanda
  32. superesset 110. 202 - 210. 102 + 101. 220 = 2B1. 120- sed hoc sublato non juvamur nempe termino
  33. apdx, non juvamur. sit aequatio P
  34. sit aequatio, 13 pp ex + 4 apdx + 11 a dp + 10 aa dx =0
  35. data resolveni
  36. Assumatur aequatio e pdx t deadx
  37. sed ita in producto non coanescit pax
  38. sit quid si faciamus y = Z+ p. a et = qu:a, prodiibis ex duabus datis initiaeqqu.
  39. 2t pdx +21 adp +20 adX multiplicanda per 31p + 30a,
  40. p Et fiet
  41. 100 a dx + 110 Z dx +120 adz + 11osp: a) Hx + 120( pduvia, = c q- X 120 + β220 p
  42. 101(9. a).
  43. 120l: a) Dax
  44. 102 (a: a) d d9
  45. 102 4du
  46. 200 adx +210ZAX 1 220 adZ + 210(p. a) Wdx + 220 p du
  47. 201 (9: a) Wdx
  48. 220(a: a) Wdp
  49. 202 1a. ) Wdilq
  50. 202 9du
  51. a102 + β. 202 fas
  52. ((ano+KY 1OUxL a. 102iF - -
  53. 620 + B, p. 201 45. 202a
  54. firt, 110. 220 ppdx + 101. 220pqdx (+ 120. 220 pdp) + 102. 220 pdg
  55. Ergo ut tolli possit sumul 1 et de
  56. iist
  57. +101. 202 99dx F110. 2029dx + 102. 2029dq) + 10. 202 9 dp
  58. hot a voirapi notpiron ip i
  59. +
  60. Pdlus-qde
  61. dFa-
  62. paq-gap = sp a x
  63. pags -gupe- F 44
  64. p9
  65. d(9. p)
  66. 210. 120 ppdx - 201. 120 poax - 220. 120 pdp) - 202. 720 pdq
  67. -201. 102 99 dx - 210. 102 p9dx - 202, 102 9d97 = 220. 1029dp
  68. Haec aequatio fiet solubilis, si ponamus p habero rationem ad q co
  69. q
  70. imo B et 2 a multi plus
  71. catae
  72. ter
  73. C
  74. omantutur uvicem
  75. pet a suop
  76. ante ut a ad Y
  77. seu esse q = rp: a et soluta res erit per quadraturam quod miror videtur tame spes esse spucessus
  78. si Y esset = a Coanescerent paq et gdp, adeoque et dx, et p ut 4 rediceentue
  79. omnia ad terminos cognitos. Imo video nec hoc licere ut fiat qLrp: a, natu
  80. ila everescerent hoc loco pdus et qap, quia paus fart = qup inio idem foret esi x non esset onstans
  81. Dfert tamen adhuc se aliquid quod spem facit, aequatio C divellatur in
  82. duas 110. 220 ppolx + 101. 20299 dx) - 210. 120 ppdX) - 201. 10299x) = 30 ac X) c
  83. d(G: p)
  84. seu vy2=
  85. et +1BI. 220 dx = fivc. 220. 10 20V) +102. 220)
  86. 101. 220 + 10. 202- 201120 - M. 12
  87. 102. 220 - 120. 202
  88. Ergo aequ Patus dividamus per P4 Et sane si aeg. dividamus per p videbimus revera non adesse
  89. - 120, 2025
  90. sed nec hoc procederet quia ita bis haberetur q: P
  91. duas arbitrarias sed unam p: 9, et habituros nos (p.9) dx, (1: p) ax, dx, aequet L (q. p
  92. 4 u. 202
  93. = 201. 120
  94. 2g. 102
  95. nihilus adeo lucrati sumus
  96. aqua tio O reducitur ad 4q
  97. tn almide haec lucta bilia quia p et 9 servant inter se lere q.p
  98. q et d ande nuilor licet assumere allerius cu
  99. homo glaeom
  100. scolis sit determinata
  101. domultre ie
  102. ulieissimulae eu
  103. in oeffud

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 37r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0073?run=74