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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 175r

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: 0.84.

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The machine reads it as

  1. Nihil produt novi
  2. Dimensio curvae Conicae consistit in sequenti quadratura.
  3. dylys. 1 tydu de a +(b. axX, :, aa + (C: a) xx sit s addatur utrobique B, et
  4. fiet d dydus tdxd = aa +bXX + Ba_ HL(BC: a a) XX
  5. ax dX
  6. aa + (c: a) XX
  7. et fiet dydy - b: c) dxdx (3) (aa : c), c - b
  8. sit +
  9. c =0
  10. ac
  11. aa + (C: a) XX
  12. seu β = - ab : c
  13. aa + Ba = aa - aab: c - ab
  14. comprobatio dydy- bi estndx = aa (+ B X∞ _- aba (= (ab: c)c: acipX)
  15. dxdx
  16. ac + (C: a) XX
  17. dx dx
  18. seu dx dx : dydy - (b: c) dxdx = aa + (C.4) XX, :, (aa : c), b - c
  19. dy- dx, c: a, XX, quanbitas consta
  20. seu dxdx. (5 Idy - deaa
  21. +
  22. Ay-di (C. a) Xx. sit l a
  23. +
  24. aa: C, b =c
  25. Hbic
  26. et differentiando fiet C (dy + dx Hb. c) 2d X ddx + dx dx (d dys + ddx +b c) L Fddus - ddx) aa
  27. aa:C; b-c
  28. dy + dxVbic (a4 : C), b - c
  29. qu. dy +dx Sb:c
  30. quae res reducta est ad quadraturas rationales, quia daus:dax dantur ratio
  31. 163
  32. naliter ex ipsis dy: dx nempe fit t 2(dy + dx sbi c) dxddx + dx dx (adyst dex )- b - c =
  33. C. qu (dy + dx 1bC) (d dy - da X Hb: c) seu ddy : dex = (2 (dy + ax 1b: C) dx + dxdx 1b. c 3b-C) +C quiqus rebe)
  34. eut na
  35. uus
  36. d nve
  37. B (d(dy: dx): Cdy:dx; 1) - duidx videndum autem on ita
  38. per dynx
  39. naent
  40. a Ax.d perdetoda
  41. nat mi aum
  42. evocar
  43. et jam (ddx: du
  44. et videtur cnon qudem fortasse generaso ratione, sed tamen artifiio et aectura rei suppedulato
  45. uadla
  46. per
  47. neralis, omnesque
  48. N e niri taudon possit logaus- logilx
  49. ad rationales. nam aqt in quae edg formula
  50. ra ergo
  51. x gabeturit
  52. rationalt aequalis nihilo in qua reperiantur
  53. potentiae, hunc differentiando ri erit aequatio, in qua du
  54. t
  55. dx,
  56. potertici
  57. di
  58. et ad
  59. c consgia qualis
  60. assumatur jam formula disscex nu X, a, dy multi dx, dus qualis
  61. p
  62. e constanti differentiasi primi gradus et hanc differentiando, ut Aco evanescat,
  63. dlad
  64. habebitur aequatiolim qua dyni dax, dayu, dx, dy, X, a, itaque ose
  65. quae sit talis ut in ipsa X si ponamas jam talem assumitatem
  66. ut ejus ope in aeq. 3. ut ex aequ. 1 et 2, possint haberi valores
  67. et a. etsideo ascendat utcunque ad potentias.
  68. :dx
  69. rationates ipsarum.
  70. Aequationem, differentiando habebitur aequ (2) in qua ad (dyide) datur
  71. ratio naliter
  72. assumatur xia per dy. du et dx. deo
  73. rationaliter per xia, Assumatur alia aequation, in qua xia habentur
  74. et per da
  75. per d rationatiter per du. da et per dy. , et Lidco, atque
  76. dy: Axde
  77. et hanc differentiando habebitur (4to) dxia rationaliter per dy. deo
  78. et ddus: deo et fdxia ): Tady: deo) rationaliter per dy: deo Ex aequ.
  79. 2 tollatur x aeer vatorem rationalem invensum postum in aequ. 3.
  80. in qua a d(dy: dx): dx habetur rationaliter per
  81. .ope hujus tollatur x: a ex aequ. 1 et ex aeg. 2.
  82. et habebitur aq. (4) ex aequ. 1. ubei dus. d, deo. Haec aequatio differentietur
  83. u
  84. et habebitur aequatio
  85. ded dy. de. id est ibi
  86. in aeq. 5
  87. Rursus in
  88. exaeg. 2 tollatur x: a, et habebitur aeq(6.) in qua _a ddgs. dx): dx
  89. et habebitur rationaliter day: ddx per dy, dx
  90. p per dy: deo, et dx. deo et dyx: et ddx
  91. sed hoc aequatro quadratoria reduci potest ad eam quae careat,
  92. per x: a
  93. et quia assumsimus hy-dx, xx a
  94. H Et sit habetur x(day: ddx) ex
  95. XX + 2dyA 2XBx ax 2Xduderio poset hunc tolli. sublata hinc du per aeq.)
  96. ipsis dax: day. Nam dydx habetur =0
  97. constantem fit (duus - ddx) XX + 2dy X du
  98. et ddue per equ E. habebitur
  99. anX, et sed si d dx assurgat ad quadratum
  100. ddx
  101. Quod totum varon inde dantur quadraturae. Verum quia ex equ. habenus quadcaloru
  102. tax: dx
  103. e dix
  104. .l poilpere
  105. dxV: ddx =(daus: ddx) X X + XX,:, 2xdy + 2Xdx et pro ddy: ddx
  106. dax. x substituendo varo dabitus 1. 2 et pro dy valorem ex Equ. 1. (sed rifignorem
  107. c, et x: a, sed non rationaliter
  108. tenta pgnoa
  109. aventa sgno 51

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 175r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0349?run=74