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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 1v

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. 2r); this page is its left half.

The machine reads it as

  1. parna proredente, secunda aeque olatione6
  2. sed reu actu ipso tentemus pro invenienda dimen
  3. ∞(1,
  4. fiet aa dio= 2rX x + at dx et ex aq. . fiet qa ta s. rx tatax surax tantx + a aaep
  5. orxxtagex + aass
  6. j ra Quaeritur saus, Pyy -cc esit y = aX + h. fiet esqu.
  7. oori
  8. r= gg: 2a h= at - bg, : 9
  9. (10)
  10. bg X+hX t aete
  11. r = 1099. seu nog: 2a = 1299 seu n= 2a. 10
  12. a el
  13. et ant = 2 10 agh seu f. a. 1t = f. sB. 9h ergo per 9 fit at = at - b, g. et fit 60
  14. pp = 10 t et h= at: g jam pp = 10tih - 10. cc fit pp = 10a a tt = 10 cC995dd
  15. Similiter qu = gg seu 999: 2a =99 seu 9= 2a. et aqt ragh seu arat = 2agat: 9
  16. pro nominatore,
  17. quae est aequatioe
  18. identica seu per se succedens ex positis per 19 et 14 denique restat
  19. 55= (hh - ee = aatt - ggee, : 90 Ergo fit fy b
  20. (23t (5x + at, ex, 1099XX + 2. 10 ate 1 aa tl - c199
  21. Ergo fit ex 7 fit Z: aa si a
  22. e9xx + 2a + X + L aatt - ee0d
  23. posito esse co = 8 agr yy 2agpty + arC
  24. +et y - 49t
  25. : 9
  26. Eb q. e 21 si pro x ponatur - X, (aderq pu dx - dx) et pro + ponatur - t,
  27. sed ex his b patet ipsam non esse arbitrariam,
  28. sed determinari. Nec quicquam aliud hinc discimas
  29. yu Lcc
  30. yy- ee
  31. says.
  32. quam posse quadrari
  33. in penultinis 1, 2, 3 paginae pracedentis, habemus. Ibi ponumus
  34. 2. 30y+ 31 duct. in 70y+ 71 seu 230. 70yy + 31. 70y + 31. 71
  35. + 2.30.71 y
  36. aeuari coincidere cum 20. 307y+ 20. 31. y +20. 32 et fiet
  37. + a. 31
  38. 70 = 230. et 71 = 20. 32 + a. 31,. 31 ergo fit 31. 2. 30 + 2. 30. 20. 32 + a. 31 = 2031
  39. seu 21. 2. 30 + 2. 30. 20. 32 + 2. 30. a. 31 = 20, 31. 31 et fi 7 23 -20- 23031 - 243031
  40. arxy + +20. 3- 303 = a. 30 + a. 3, 1p0. 30 Y, 21030 31 y + 2 1. 20. 1y , 2 20. 30
  41. 703 l.31 yy +210.31.32y410.3232
  42. Fu∞30 yy + 1131 y + 132
  43. unde faciendo 31 = 9 fit (9 - (dy
  44. nde palto posse nheeus a 10. 30y +210. 36 3L yy + 10. 32. 52
  45. 11432
  46. + 110
  47. tia12
  48. nde parto eliam posse oni 32 =0. Uuo video posito 3 = 0. fieri
  49. 2aa
  50. Ergo sic res procedet trevissime.
  51. aliquam ex his 32 vel 30, vel 20 =0
  52. Sodx Siax LuXE, ) O e sit x ytax eydy
  53. sit ergo:
  54. ( - 23 fydg sitar 2130yy +32 et adx = 2 30ydy et fiet
  55. 20 X +2
  56. O = (2. 30y dy (10. 30y , 2. 10. 30. 329y + 1032. 32
  57. 20. 30yy + 2130
  58. + 11. 30 79 + II. a. 32
  59. + 12. aa
  60. iffertur jam multiplicetur summandum per unum factorem alterutium divisoris
  61. Summae ex quadraturis productorum sponunt C, itaque dantur
  62. sit (C) sux 1XM Sio XX + UX +I2 sit ax= 30yy + 32 et adx 2 2. 30yty
  63. fit (= 2. 30, 30. 40yy + 3240A + a. 41 (10. 30 y + 1. 10. 30. 32yy + 10. 32. 31
  64. 20X+
  65. 11. 30479 + I1. 32a
  66. + 12. a4
  67. 20.30y9. + 20. 32 + a. 21
  68. Habemus. Ayy s, y + ju + y _ et sdu sy . gy + y. prius ex aeq. 4
  69. vel faciendo num. et xomaiquates
  70. ponendo 3240 + a. 41 = 0 = 20. 32+ a. 2). P posterius ex 4q. exdem, ponento 40 =0 = 20. 32+ 44
  71. habem, et 57dy 15a.. yyt.i, ponendo 40 =0. et fygay+.fy. y. y
  72. gyt. fauendo in in uta nempe faciendo ut inag. 4 numd e hom habertit diisorcauem
  73. (e seu sartere csre
  74. 2aco+. at 0
  75. posito esse c0 = rXX +atX: a per 2. set qquia X = ay - a t; g9 per 67)
  76. fiet
  77. d
  78. et fii
  79. du
  80. ex L= i S83sux Sodntriaom iteh
  81. y- ee
  82. ia fB ix Aexxaphan patit
  83. (11.
  84. Sione curvae Conice sit = S, deo Snct. sit aco L r I afit C = 2. 72 50
  85. 900+55
  86. (26)
  87. 8d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0002?run=73