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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 92r

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: 0.85.

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The machine reads it as

  1. si Ex Hypothesi, quod in parabola sint arcae proportio
  2. nales rectangulis circumscriptis, et situs centra gravitatis
  3. idem semper invenil regulam clari grar schotentus hoc culdo
  4. Nempe ponit d ecs ete arem ABC2 dari, et centrum ejus E
  5. Hinc dabitur et area A(B) (C) A, et centrum ejus, calculo instituto.
  6. Taudem posito coincivere B et (B) habetur quaesitum absoluse
  7. idem valeb. et
  8. ehsten. lit. 1, ad lib. 2. Cartesii
  9. ea
  10. qu pro aliis curvis simplicium aquationum stiinariarum
  11. Transeamus ad curvas in quivus area non sint propor
  12. tionales rectangulis circumscriplis, sed habeant se alia ra
  13. relatione sit s sydx: s(y) dx = Xy + ab,: X) (y) + ab
  14. sumatur medium sydx: Cs(y )dx = Xy + ab, :, (X) (y)) + ab
  15. et rurgus S_Y) ex: 5(V) dx = ((XV (yy + ab,:, (X) (V) + ab
  16. fit S(CyBdx = S(y) dx, CX) (y) + ab, :, (X) (y) + ab
  17. =sydx, (XD ((7) + ab,: xy + ab
  18. felcus sed ita res furtur prima aequatio
  19. Ex tali aequalionetient constanter β Sydri = xy + ab, et gerimaliter
  20. y ((B- 1) yax = Xdy. adeo
  21. d β- l, ax : x = dus: y Hoc ergo etiam reducitur ad aequationes
  22. As (ydx: A) Sasex = X(1) + ab,: B ynt ab
  23. et β ydx = Xdy + ydx, seu
  24. lofint sed
  25. dubitari potest an tale quid possibile, et quidem absolute quod libet curlibet
  26. simplices
  27. ddd
  28. Sed socus erit si
  29. conferendo res probabilior sperabilior, quod libet uni conferendo
  30. quam
  31. sit ergo unum LB ARes sila sumenda est ut etsi (X et (y) evanestant
  32. tamen bealfiat aequatio, quod huc contingit. Assumumus st sydx = AB.CA
  33. Assuunamus (yNax = A 3B3CA. fietu
  34. syax + s(yDdx, :, sydx = X (y)) + ab,:, exDy + ab. Tollamus
  35. 1(7) ax = A _2B 2C A.
  36. ydxe nempe 41 + SCyX: sydx = X (Y) + ab 1., x) yt ab, et fiet
  37. (y) dx: X 4y)) + ab + 1
  38. GXγy + ab
  39. (ydx = 5(7) dx .
  40. Ergo
  41. y dx
  42. 3)ax
  43. X (Y) + ab + 1 =
  44. (X)y + ab
  45. X. () 4 (xy + nabu
  46. )+ ab
  47. nam fiet sy
  48. X) y +ab
  49. + l
  50. X (Y) + ab +1
  51. (Ny +a6
  52. Xesry + ab
  53. d
  54. Ergo habemus legem
  55. reductam ad
  56. differentiales
  57. ((XD y Fab
  58. Rdx = constanti, ubi considerandae X.
  59. ut constantes,
  60. suidx: ac
  61. (X 9+ ab Hoc ricissim utie ad proprietatem duammmareara
  62. f(y + ab +1=
  63. exhat ducendam, si scilicat ad lansxpposito SCX, e g- Y
  64. et fipt f et prodit curvae aequatio
  65. Majo Itaque in ec est aliqua difficultas polius, si prima aquatione
  66. ionis, nam unam
  67. a
  68. sunc hoc statim ex primo polebat
  69. aponamus
  70. ex hiic pres lo constantem et ulters
  71. aovia
  72. tab
  73. vaitur elatio
  74. antrale reduncibilis
  75. gax
  76. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 92r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0183?run=74