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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 374r

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: 0.82.

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The machine reads it as

  1. += y = dx: dy = aa +Xy,:, ax-xy -ay seu y aady + xydy + xydx + ay dx - axtp -0
  2. Si XC 10 + nyFny + B9 + 14y + 15y+ 16 y
  3. X~ 20+219 + 2yF239 tury +29+2696
  4. dx = 1 Ut 2. 12y +3. 1394 4.149 4+ 5. 15y 4 6.16 5 4, 717y
  5. ax (1. 2 + 2. 22y +3. 237 +9. 2419 + 3. 25yt +6. 261 +7. 27 y xap
  6. dex 121 25, 1 3+. 147 ddx = 1. 2. 12 + 2. 3. 13 3.4. 1y + 4. 5. 15e etc. et denique
  7. ddx = 1. Et dax = 1. 2. 22 + 2. 3. 237 +3,4. 245 + 4, 5. 25 is etc = 2 dxdx
  8. + Xydy = X 10y + 111 + 12 1 +13y+ 14 y +15Y
  9. +4y dx - = a, X 111 212 3.13 414 sit5 6.16
  10. =aX dx =a, 1.21 2.22 3.23 4.24 5.25 6.26 7.27)
  11. +X9dx = 2
  12. 1.21 2.32 323 4.24 5. 25 6. 26
  13. +aady- aa
  14. axdytus
  15. xd cenri
  16. (10
  17. Quaeratur sam differentialis ipsius1
  18. =0 fiet:
  19. O Xdlys + ijdxdus L ndi dyt yd xtx taijuprajib, atu
  20. vel saltem ex valoribus 1q. 10. a dyde
  21. differentutos O=
  22. o= d xyilus
  23. Xotis = Wo any y + 16V dxydy = 1 My +BEy a +5141 b2s
  24. ydadus 11 in 2 +B 41t 15 616 dayix = a, 1.1 4. 12 913 (16)14 25. 15 3616 62)
  25. atrs a dxau = a, 1u X12 3B3 4. 14 515 626 f. 17) -adxap = - a 12. t 23 23 24. 24 4815 56266Y. it
  26. Tayddx = a, 17(2 2313 3714 4,515, 5. b.16. 6.7. 175
  27. adyex 7 Ra 412 913 1614 25.1 36. 16 49 17 a xyix = 1, 1. 4 4. 2 923 1624 Cet. 15 36. 26)
  28. b
  29. Ex aequationibus 10 et 12 excerpartur aequationes destructitiae o, . quarum ope tolli
  30. poterunt quatuor tres literae, 22, 23,24. Ut autem incipio autem abtus, quia sic non
  31. ings inpeditur 10 in quo est varietas. Nam post O vel S in infinitum omnia euut
  32. eoc tondo C a Ut autem calculus sit generalis, facciemus pro numeris veris
  33. 2
  34. 14, 1.2 n 2. 313.4
  35. Coepficientibus 2, Z, A, substi tueraga., ) n+ 1( nt 2 nnan unem nn+3n+2. Et fier
  36. D Eitnan = a n+ 12Z + nEL= D42I + 2II113 -n+ + nF 123 L0
  37. id jam video 3 et 4 nihil prodesse cum nihil aliuo sint quam ipsae C et 3
  38. 8 2u2 duplicatae.
  39. si distructius scribatur
  40. itaque redeamus ad ae9. 11. quae erit talis
  41. =a d xax
  42. Xdus + ydxdy + ay ddx + adxdus = axia antx + X Ydix Xapayr y axdu 2 0
  43. a
  44. Mattiplicetuur aequ. 1. per , quia et ista dis fiet ex aqu. 1.
  45. ac aagydus tadg adu t xydgydus + pydus adque +xydrydque + xydxady + aydx ydus taydxadus
  46. atque yy aedy
  47. lccet
  48. -axdx ydus axdyadus L0 jam pro gaxdu
  49. cde
  50. posum,s quidem aqua quia autem haec aequatio differentio. differentiatis
  51. non hac aequationes nisc jam lalentes in differentiali; ideo cogitaevi posse
  52. novas obtrueri si differentaetur esqu. 1. ut differentiando tollatur X
  53. Nim ex aequ. 1. est X =
  54. nady+aydx: adx y ay ydx unde
  55. dx a dx dx = 2 aydydxdx - 2ay dx dx + y dydx f 2ist dus de + yydx dy
  56. un
  57. Caydux ddx= ayddxydy = aydax ydx) - ax addx aadus = addx aydx
  58. sed ibi assangitur ad terminos uubi se valores ipsius X
  59. valoris coefficientes, hi enim lalent in dxh. Quod si aequ. 1 multipliceuus pert
  60. = y ddx aady (+ yddx aydx
  61. et productum differentiemus vel ex ag. 11 tale productum fabticemus. pote rit mjus
  62. ope giuu hanc ipsam differentiationem fatricemus; et deinde hanc qulingamus
  63. cum t. 1s videtur tolli posse dxh sed relect ne in novim aliquod tale nos induamus
  64. X = 204 21y + 22y + 23 1s +24y eu
  65. da sit ipsius x defficiens vocetur a 10 ipsius X vocetur 2OG et X vocelur 3C
  66. X X = 10 + 1y + c2 ist et
  67. d Naneus designans pr gradum vocetur seu exponentem
  68. coefficient iatiu
  69. dx = fn 11 nV
  70. ipsi Numerus gradus seu exponens e sit e
  71. sic ax = 3X AX = n31 2-1
  72. dX =2Xdx = n. 21
  73. X = 10. 10 + 2. 10 1y + 2. 10. (2 est + 2. 10. 13 1 + 210.4 y aet
  74. 11.
  75. dx = u u + au L. 12y+2. 13. I.B3y= + etc Ergo dx = ( sed hine vndeo non posse dx exprimiper
  76. Ax = e H a M
  77. 2d X dx = X = 2X dlx +2aX
  78. 2. 2. 2. 12. 12..
  79. respondentibus terminis
  80. etsi eare e
  81. veri coeffirientes ubique bariant
  82. ingrediente se, nume
  83. 11. 13 Ct
  84. ut in yEs
  85. in hii st, haebel 11. 13 habet 1.3, et 12. 1.
  86. habet 27. Et i institei derivatio in summa,
  87. sius ax
  88. itaque video non posse hac methodo magni aliquod ngi

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 374r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0743?run=74