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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 166r

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: 0.79.

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The machine reads it as

  1. primi gradus
  2. sit aequatio differentialis, vig dy: dx = Xxtgy, : aa, d
  3. ctipe: y y ux Cde dx 2x d dy e: n ae seu dy aa = xxdx + yydx
  4. sit Xxdx = aa dco, fiet dyas _na du a ddus ad = gydex + rydydx
  5. et XX ddx + 2 x dxdx = 0 seu Xddx + rdxdx 20
  6. ergo adue aa = gy Axdx aadeo + 2ydy dx
  7. rdnox
  8. quidi si faciamus dus sa
  9. ya de. dx fiet et de constans, fiet ddu avx texa
  10. seu
  11. aadu-adddo a dodi, ved edutr an dvab; vrdxx
  12. y =-aado: vax, fiet actus = (dux) vddo vav: vo = xx dx ta doariou
  13. unde
  14. aa ddr-aa B de do = 2
  15. seu -at vddv (+ at dedv = vuxx axdx (+ a dvdv seu - a ddv: dp = xx dudx
  16. sed si sit du constans fiet y= sitque = ab dv: v ix et dus = aeb vdv a bdvdvax =
  17. in aequ. 1. ponatur
  18. Cp dxde d tda abb dodo (: velxd seu -abvde. ldx - a bdy dvax = vuxX dx racbbdrdu
  19. sit B: d= (tlarara)
  20. 2 +l
  21. Atiter k are gia = do: x
  22. sit g: a = 100a + a f + a gg 2a et, a 0 a M + a nn + a3 p etc
  23. 200.C
  24. y dy: dx = XX+ yy,: aa
  25. et sit f = uOX +1OIV et gg = IROXX + IBIXV + 1020V et h = 13OX + I2IXXyt 112 Xyy+ 103y
  26. m = 210X + 201V et nn = 20XX + ZIXV = 202VV et h3 = 23OX + 221 XCy + 212Xyy + 203y
  27. et ita pono df = d dex c 3 + des f et d(99) = dx A(9) + d +99) et ita pore Bm caeteris
  28. ita ex. 9. fiet, dgq = 2. 120x dx + 111bdx et d(99) = nxdo Z o2vdo. Et ita porro
  29. et
  30. exprimi per aequationem rationalem qualem posuimus
  31. Cdx)
  32. dy: a = (200a + a m, etc) ((a d f + a agg etc) dx + (a 5 + a ggene
  33. Et sane si y anlt
  34. 2ann + etc) ax + (a am + a Anner) du )
  35. (2) (200 + a m + ete
  36. et gy: aa = (2), 100a + a f + et, :, 200 a + _ m + etc)
  37. 3 (200 a0 + aet m + et) C(a +5 + ex) ax + (a f + etc) dx)
  38. et ex a aady = xxix + gydu, fiet
  39. (Ca dm + et C) dx + (ae Amterc) du)
  40. a 2(100 a + a f tet)
  41. = (2) (200 a + a M + et) XxdX taql 2) (N + a f + et) dv
  42. facollimum est
  43. Ha Hinc apparebit an tali arte tolli possit a, id enim omnium quae fieri explicando possunt,
  44. in
  45. facillimum est. 200 a 20 videamus an omnia reddi possint homogenea ipsi
  46. dateri
  47. Caeteris destunctis ia erit. sunt autem homogenea hunc a a a dx hododer px + Ap +)
  48. Fggdx +p gdo a f.dum + fann aV) aa a. a 2. 10g9+0
  49. 2
  50. fn. f. n mg. a mgg.
  51. +a a a
  52. 200. 200a
  53. aaaa
  54. isi facicur onm, n, seque=0. Et h et seg9. g. 0. al sit sole
  55. ge
  56. proditi raaa
  57. non devet. D et praeterea 2a a 100(4G+ 0gdV) qod estinferiu ipso xxa
  58. si non debet assami ultia Xxde eritat m, , P etc =0. ergo debet maneo
  59. adeoque tolli debet 200 a 3200dggd + dggdv) + aa. 1b0 . a
  60. et
  61. Si nolumus assurgi ultra gradum indeterminatorum qui in XX dx
  62. trde xedx
  63. ta e2Bdv
  64. ffdo, quod
  65. oportet aute omnia n
  66. +a’a a 2otf ax + a a 20 sdv tad 2oodggdx +a a2200 dggdo r d taa. ff
  67. esse aequales nihilo. Deinde
  68. a e
  69. IC200. 200bb d
  70. aaaut d
  71. e
  72. tr, et sequentes
  73. +aa a a 2100 f dv
  74. retineo assurgi ad g’av
  75. sed video si ddeui
  76. si gonito
  77. = 200. 200. 262 d Z
  78. non p
  79. sin b
  80. mmxax nec
  81. quod si faciamuse
  82. 12. sed literae solum ad sunt
  83. et prioribus 6 tollenia
  84. yn a 100aa + afd
  85. simul reperientur m
  86. sed tunc non aderunt sifficientes literae, quia fit debent esse
  87. fractio in valore exax destinetur
  88. 3dZ, ergo tres sunt gradytollendi et in qovis gradu duae prima aequ. 2
  89. et fiet xdx = a 26Z160 + b8, (971 80 +C)
  90. qua i f et dd
  91. sed restat restanit ergo
  92. asserigitur ad gradum FY
  93. sunt in universum ae
  94. ra +FdR + OvaSLGBA2
  95. 1oa m t100
  96. 2804: 7218V +C,
  97. 9019 (326vel) ar +3dv) et liat 200 aat aam +un-(orrioro
  98. 2+ b +5V ft etq orpittamus quod si retine
  99. iri ultra C et q et m
  100. Ergo faciamus. X
  101. licebit
  102. A.
  103. eD
  104. u Bete
  105. restabunt ergo gq et f, fiet q sit- 2tb
  106. e
  107. ene
  108. 1 C, 5,9 b, et in
  109. detur
  110. 200a4
  111. en
  112. una adi
  113. Aegdz + 20045 4g9 dv
  114. amtun
  115. 200a + fdv +200
  116. 10 a 4mav. 100454 indZ + 100 a d AN
  117. ama
  118. 1do a tm a p 100100 e 0
  119. 5
  120. aa
  121. in secundo 4, in 3tio ae
  122. l200
  123. laque recuo
  124. esperata ideamus:
  125. t upra. Ex aadus xax lgus axsiet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 166r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0331?run=74