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LBr. 560 · L'Hospital, fol. 5r

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: 0.81.

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. 19v); this page is its right half.

The machine reads it as

  1. du. Marchio Hospitatius mese mihi misit problema
  2. sequens: lineam invenire, cujus aequatio differentialis
  3. sit aax dx + 29 dy + aaydx = raaxdus. Hanc lineam ait habere
  4. proprietates consideratu dignas et a se frustra fuisse quaesitam
  5. suppositis licet Quadraturis spatiorum. Ego sic rem tentabo:
  6. Quoniam revera duo hic sunt gradis constantis a, nempe a, et a
  7. ponamus quantitatem affectam gradu aa, esse constantem,
  8. adeoque et reliqua erit constans nempe- aa xdx aagdx +raaxdus= nux yrydus
  9. sit constanti ad et fiet: _ 2aa Xddy +3xadxdy -aa x dax- audx- aayddx aadlyaf
  10. et et yddys + 3yydu 20 seu yddus 2 3a jam ut differentiando, adhuc semel
  11. compendioe 27
  12. (2 29dy: 2Xdy - xdx- ydx, unde differentiando
  13. (ix)
  14. adi BC3au produs do e jam do= 2X Hyr cdrdy xdt R ydlx dy dr
  15. 03ydy (Oy
  16. tollatur a, ex ae
  17. s
  18. dy p
  19. seu Oty +Oydiu - gt Dyu =0 sed inde sequibur d0 =0, quod jam patet ex aq. 4 Ergo
  20. .
  21. et f frustra adhibetur aequ. 7 ejusque differentiatio
  22. ideamus ergo an aliam viam inire commode liceat, redeamus
  23. ad aequ. 1. et eam dividendo per aay, fiet X dx t 2 vdu
  24. 29 dy = 2Xay = F Ax - dx. cius differentia qua cujus differentrationem divellendo
  25. induas, fit: Gudy + 2 yds 0 seu ydays r 2ty 20
  26. B (est aequas differenti diffest
  27. 2X ddus + 2dyyer a 2 dy dy = E dax - x yta + du F dys - dax =0
  28. da
  29. jam x sit O = 2x dy -xar - ydx et aa fiet = 29 dy: 0
  30. ticlis quae videtu
  31. ncissibilis)
  32. adeoque fieb
  33. differulcando aequ. 2. fiet 20y ddys + 605 aus - 2y dyd0 = 0.
  34. n
  35. Est autem
  36. loco aeq. 2 potuisse
  37. scrbi copendio 2gy du = C. Ergo fiet dD =0 deoque quod aequivalet aequalioni 5
  38. d0 = 2dd x. 2x dby +2dedy- xddx dx.y ddx dydx
  39. 1
  40. agtdF si
  41. Y= 0 seu yddus +2 cus = 0 seu redibilaers a
  42. si follamus ) pro ea ponendo d yitus fiet ex aeg. 8, 2yy detys ty 169d029- 2yd 10
  43. unde fiet yd0 - dy =0
  44. ope aeq. 4 collanus y fier 0 = Exdy - xax + 2dy dx: ddys. et ex
  45. aeq. 9. fiet d0 = 2 X ddy + 2dxdys - Xddx- dx + 2dy ddy: day- dyax, et ex g
  46. sy. p. fit - 40+ +60 du + 4 du d0ctus: ddqo seu ROddy + 2 dy d0 = 0 demque
  47. et redit rursus aeq. 4
  48. (13)0p 0 ddy 4 2dyd0 =0 quae coincidit cum aeg. 16.
  49. nisi unam habermus aequaoem differentio differem
  50. quae ita stabit,
  51. ex. 13, 14, 16. 0- (2Xdy day -xdx dly (+ 2dus dx) + ( Xdus adys + (elx dus. X da x ay. 2 dx dui is ax)
  52. O et d non
  53. itaque explicando,
  54. tialem in qua absit y
  55. Nec proinde quicquam
  56. ad haec aequalio non est tractabilis
  57. 2aa X ddyt raadxdus. aa xdax- aa tx- aayddu aady 2) dest by d
  58. et quia jaa = 2dy qi 2xdys Ax -y dx tis (Ex 2 et 3, (49 de Xd r ay dg lby 2 hyptt, - 2G ayd - 29 tgulital. 2s dg dluy lx
  59. e
  60. du dox: crprumf
  61. Medeetmus rergo ad
  62. diferentrando aequ. 1. Pet
  63. sort Xx D bX dx + cX dy + Cxy dx L f Xy L fX dxdy + gy ax +hy du +m D dxdus t nXy Ex prydus + quy axdis
  64. yx dyddx nascitur exXdus
  65. = (2xdus 2y acys) + 2xdys 69 tu - Xdx 29 ddys -xdxbydus- ydx 2.s tys- y tus
  66. Hac arte conflan pt ae quatro formula, in
  67. et hanc s aequade
  68. et sit constaasfit 0 = ydus adu nascitur exe g dy nam d. Lytis dat e ydus ddy + : d
  69. propositos summare poteum
  70. cx
  71. aquatio ea differentu abit aequalia nihulo. sed video si hoc liceret, ets non tore aequatea nitulo, qua
  72. ram fit d, yxdus ex dat yX dys dax + yx dx day + X dxdu + y dg
  73. e
  74. cujus differculia contineat omnes termines d,
  75. ien
  76. qua continea
  77. stantem hpbebutur
  78. opropositem, dentos quibusdom quae
  79. A p
  80. omnes
  81. videamus n licelet termino
  82. 2Xs dx dy SXop dg -0 fint ydys da x 16dus -y dxdlus
  83. quae si habentur daretur curva quaesita
  84. per
  85. ponr aquales nihilo
  86. + 2 X ydys dcx +1X dyd-

Cite

LBr. 560 · L'Hospital, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-855907:0009?run=74