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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 97r

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: 0.86.

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The machine reads it as

  1. atae Aequs, 100 + 111 y = 12 dy F 121Z + 122 dz =0
  2. 200 + 211y+212dy + 2217+ 222 d 2d
  3. 400 + 4IIy + 412dy +4214 + 422d7 =0. uti
  4. Hubita aequ habetur aej. B) adeoque et Aqu. 4.
  5. + =11aZ= 0
  6. ubi pono 321, et 312 20, sic enim qe omponeriu tentemus ipsasi et
  7. fortasse videnmus in simplicioribus Multiplicemus dats pe f et g, atque inde componamus,
  8. itaque fingamus haberii ipsa (3 et 4ratus
  9. quaeslaum primam 3, +300f +315y +312f dy + 3 etf 1 + 3. 2fdZ 100, t u( H12dy +1217 +122 4Z
  10. odem modo rarsus multiplicemus dales per 4 400g. + A1gy + Hgdy FarI9f quigd2 2 + E y + 2 a tus 221 BZ + 222n VZ
  11. i _ 422g = nin trun 42g = iim t2itn Ergo (um tian) l = (121p + 229) 9
  12. O
  13. h,l; et quarllas per pia 5
  14. 42l = 12 p + 2249
  15. Et (122m + 222n) L = (122p +5229) g fit umtrum = 4
  16. Eodemmodo 422 b = 122 p + 2229
  17. Superest 311f + 4119 = 111m + 2uIn
  18. 122p + 22c
  19. 312ftang = am + 2Nn
  20. 12em +22In
  21. 121p + 2219
  22. h = Mprrq. Nul,; 31 = 12p t 2ng. trilis 3
  23. 312h +412l = u2p +220
  24. f= ium + ZIIn = 4119,: 31 = 12m +212n = 41293: 372
  25. 3uIh + 4ul = 111 P 4 2110
  26. Tandem 300f +4009= 100m + 200n
  27. Et 300h +40ol = 100p + 2004
  28. fit f = 100 m +20on-4009, f. 300 l = 100p + 200q 4vol, . 300
  29. prioribus fit III. 300 M + 211. 300n- aug 300. 41g = 100. 31m + 200. 311n = 400. 349
  30. W’alor postremus ipsus f aequetur dugbus
  31. 112. 300m + Z11 300n = 412, 3009 = 100. 312m +200. 312n - 400. 3129
  32. = 100. 3up + 200. 319 - 4u0 3Il
  33. Et 112. 30op + 212. 3004 = 412. 300 l = 100. 31 2 + 200. 312 9 - 4u0. 312l
  34. Er eotem moddo ex fit 1. 300p + 211. 3009 411. 30
  35. Hatemus ergo aequationes 10, nempe 50, 2, 3, 7, et 0, D, 8, 6,4, E
  36. M, au, si Gto 4, n 4n an 31. 312
  37. supersunt 300, 400
  38. item Diorae ex m, 2, P, 4
  39. literas 41, 412, etC.
  40. 4u = u1 m + 2uIn = 3u f, : 9 = uIp + 219 - 3 uhr, l sit 3u = nulm + 2U Im Hegg 2u94u i, f -ti
  41. sed malium f, diferri, quaeriqus adeo aer tris isins L valores et h
  42. pro
  43. e412 = 112m + 212n - 3125, : 9 = H2 + 212g - 31h, : l fit 312 = 112lm + 212ln - 112 9p - 21299, :, f. - h,
  44. 400 = 100m + 200n = 300f, : g = 100p + 2009 - 300h,: l, et 300 = 100 m + 20479 3:, f. - h
  45. Hac methodo videntur omnes aequationes disferentiales simplices
  46. primi gradus quotcunque incognitarum solvi posse, et quidem per
  47. interventionem merarum ordinariarum aequationum
  48. si sit aequatio duarum incognitarum praeter unam varientem samtam pro cognita
  49. ita ut liceat tassumere novam aequationem videamus quomudo inptitui possit
  50. assumtio v. g. 100 + jHy + 112 dy + 1 dy + 121Z + 122 dz =0 hoc catures
  51. lacillima est, nam fiet 12 dus 2. hoc casu facilis est divulsio fit enim
  52. 200tmyt 1r dy = 0 et , + 1212+ 122d2 = 0 et 300 + 200 = 100
  53. ubi alterutrum 200 vel 300 est arbihrarium prorsus.
  54. sed si sit 100 + Icy+ 12 dy + 1+ Z, .. ydy
  55. Eliaf videtur brevior via esse haec, ope a94. dataum 1, et 2, tollantur quaerantur
  56. valores ipsarum aus et dz, per meras cognitas, hi substituantur in aeq. 3, et +
  57. lum quae vantur valor ipsius y, et valer ipsius Z, et uterque sed uterque
  58. fial identicus, ita ut y et Z evanescant ita qualuor juo quia utrisue
  59. valoris communis divisor, tres aequationes destrnctibiae sa tit facient quaesisu
  60. quod unrum, et incogntae non vescendunt ad differentias. Hoc pulcheriinum
  61. Et locum habet ubicunque pes aequationes differentiales pluriliterae sunt
  62. i plicari hoc potest ad collationes ordinarias in differentialibus
  63. selverdae
  64. investigundis, ubi res credit ad auxiliares sunt rnerae differentiales
  65. simplices, sed ex sed mistae incognilis ex mullipleate oit
  66. Ex. gu. sint aa sit aequ. diffialis du: Ax = kx 149:aa, assumatur
  67. 10 + uy 4 129y+139+ 14 20 ubi quae aequalio differentretur, et tollendo dus: dx
  68. ope priorbus uartur, nova aequatio (3) e, itaque multipricetur data per
  69. tomNg. 2. per formulam arbihariam, ut comparam possit aequasioni,
  70. aequationes comparalitiae continebunt simplices aequ. ubi tantur sunt
  71. y
  72. 10, 1 18, 14, ara tus discaertat, talentur oiffeata

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 97r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0193?run=74