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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 403r

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.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 404v); this page is its right half.

The machine reads it as

  1. crescente X crescil y
  2. Gy dx + 2yXdx = XX dX + agy dys
  3. yy + CD 2 XAXy + Xde
  4. sit ex = - x + () et dy =
  5. Ege medx Lyt nd_ = X (Et etre du
  6. dertu, sis teutus lexitus
  7. dx-ily duelus
  8. aa Xdx Fry dy elaaxay +aydx L 2a a Xdus
  9. (2)ox. fiet 2dy. dx. 29 ddly +6yy ys tay llx + adx dy
  10. 215 dyt ay dxqedy- dx=
  11. =225 y + 4y dx 2 ly. x 3, =, 4 dus - 4 dyax + ex 44 C LA aa dx
  12. y dx ddus
  13. (3
  14. seu (4y ay day) + 12 y du + 2aydy lax (+ 2a dxay tgly - 6. y. dxdi agersa . a tu tu
  15. (= 4 is dyadys =cay dxddys + ry ty tax (+ ay Ax d X) = (4 aa dxalus liysiae r aidtpo
  16. 12l-Esaxtay 4 29 y dex = 0 seu fiet 6d3yda dius t gdus t d
  17. 6dnd (5)
  18. 6ci - yde ddue 1 G dy ddx = eg et in oy. restabit 2ytys dax (+ 2 duaus y dx daxf ax L
  19. =2ydX dayue (F y dx dax = (D dxds = (4) dy dx Y dx
  20. ubi si substituatur ex aeq. 6 valor ipsius y in aeq. 5 prodibit aequatio
  21. ita igitur inveniendo dy pery, adeoque et ddu pr oe dex
  22. equatid
  23. habemus potest in aeg. 5. tolli du et des diu, adeoque ibi
  24. remanebit solum aequatio qualis oporturtt inter du, ddus
  25. Unde sequitur posse pro arbibrio
  26. regulaniter) assumi divelli aequaioes differentio- differen
  27. qualem fingere licet.
  28. tialis modo id fiat cum fructu, ut hoc loco
  29. 1
  30. e
  31. in pte est quoties e quo
  32. Tae Methai ad diferentiali est solum
  33. quantitas determinata est sotu unius gradus, ut hoc loco aa
  34. tantum in ea datur
  35. (1)
  36. si sit y-42
  37. a fint dy- ardo- avdx
  38. n
  39. us cn liceat
  40. Ca)
  41. extractione dfferentiando fet aXda i a x + 29 dy 469 di t a ylix a dydeo
  42. fiet a e ax = 2ydis: dx = aest et a d - 2 2dXy ddy - 2dx 3y dy + 2y dyditu
  43. 2)
  44. -atx ydye seu a + 2aydu + 3du =y du du 2 dydiu El y x du ara ax
  45. seu a= yVy de ay- 213 i daque -69 ax ays + ryd cy dxtax
  46. et ex aeq 3. fiet sg seu fiet seini eoplicando a ( nempe BB
  47. 403
  48. ex
  49. ex a faciendo a in advalor. et ex 2a faciendo a + avabr.) fi et
  50. Eydyax y de dis etc.. Tfa de ydy = - 2dx y lgs - 6dx ti +2 y dus dax
  51. ydy dx = ydy sas a us .. ..
  52. quam aequationem divellendo in duas. habebuntur duoe
  53. aequatines differentio- differentiales, earumque ope tollendo y
  54. habebitur unica aeq. inter du, adus, de ddx. solubilis.
  55. tle. Necesse autem erit ex his investigare quaenam isto casu
  56. sit quantitas constans, ut in
  57. Car cum ex a videndum an non tollem
  58. aliam
  59. duo
  60. ex et dax
  61. verent ne incommoda producat
  62. aliant polee qan op inguloren
  63. o duas
  64. tetotats y,
  65. videndum an non cum dantur aequationes differen
  66. tio- differentio differentiales, licett aequavem divelles
  67. in tres. et pro altioribus in plures Et idem est si plures literas indeterminatas adhibeam
  68. 407
  69. u e e spert aeit aniterie aest teribut

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 403r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0801?run=74