Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 138

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: 0.75.

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

The machine reads it as

  1. 138
  2. FL ORZMONDT DE BEAUNE
  3. relinguetur = y - = py y F = Pp. F r - 2
  4. 4y 2 ∞ 0. Ouare l E0-
  5. cum mulciplicemus per 4yy, inveniemus y6 = 2 py 4 F p2
  6. 44 ∞0. Ouod demonstrare oportebat.
  7. F 473.
  8. Tam vero (I ponamus x + X = P x = - qX f r ∞0; Suppo-
  9. nendo secunduI HaNCGCOMIELIAI ~ 2 = y X + = yy + = p.
  10. ∞O; etit X = yy - = P∞ 2. ] yx. Vnde quadratum
  11. Prioris partis xquale erir quadrato posterioris, hoc est, v+ L yy x2
  12. F + y + - p X - f = pyy - = pp ∞ Y y X - - 9V - 24
  13. 4yy AC PeF
  14. Conseguens, ∞+ - i yt. 1 p∞ : = Byy- = pp - qX- 24
  15. +y200.
  16. F qua SiFOllatur prima X + X L p X 2 - q X - f r ∞ O, remanebiE
  17. p+ - =PYy + = PP - r. 99
  18. ciplicetur per 4yy, InrenietuT p6 L 2 py + + p2
  19. Ouod erat demonstrandum.
  20. 4+ 97 99∞0.
  21. Non secus demonstrabuntur omnes reliqui casus secundum
  22. utramlibecharum suppolicionum: nimirum, x = - y v. L = yy.
  23. 2P. 7, ~ 0, AUE, ve f y X = yy. = p. =, ∞0, obterrando
  24. tantum signa. e, quemadmodum haec Geometria docet.
  25. Cujus operationis ope in genere aequationes omnes, in quibus
  26. radix incognita qor haber dimentiones, ad Formam, in hac Oeo-
  27. metria propolicam, reduci posunE: nimirum, L y. 2 p g4
  28. P
  29. Vy.99∞0. ligna- e quxe praecipit, observando,
  30. Sicut demonstrarimus. Ouohe, uc, Si dirisionis beneficio e qua-
  31. tionem propolicam ad cam Formam reduCere POTTIIIUS, ita VE
  32. post diritionem radix ejus y plures quam duas dimentiones non
  33. admictat, ipsa per Geomerriam communem, juxta prxescripea
  34. pasina 6 ec 7. hujus Ceometria inveniri postit. Oud inrenta,
  35. mediantibus aequationibus x - y X - L y2. = P. 2 ∞0, ec x L
  36. yx. L =yy. =P. 2 000, Coblerrando signa -) e, ponenda
  37. locis, ubi lunt omisa) invenietur quoque radix x; cujus locoin
  38. altera requatione proradice uppolueramus y. AC rero LL aequatio
  39. (UPFA
  40. 1
  41. a
  42. 1d
  43. ben
  44. 12
  45. Geom.
  46. teeaa
  47. Oped
  48. Supra
  49. Cd
  50. aeG
  51. iibe
  52. elt. d
  53. Be
  54. e+
  55. C
  56. Pracect
  57. niminu
  58. diiitea
  59. dimention
  60. ille eal
  61. d
  62. ltpu
  63. mediau
  64. quentes)
  65. explenime
  66. quod hobet
  67. Omua, 910
  68. E0 quaialu
  69. guamenu
  70. Vat

Cite

[Ps. 1], fol. 138. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0160?run=74