Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 56 · Bernoulli, Jac., fol. 37v

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.

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. 38r); this page is its left half.

The machine reads it as

  1. in aequ. d
  2. graduum ad inferiores possint reduci ulteriorum differentiarum reduci
  3. possint ad differentias citeriores. An vero quod sane si hoc ponlicet,
  4. novae circumspiciendae sunt construendi artes. Cum dico nii ess non
  5. eHse desperandum, intelligo, quar quamdia non adest Demonstratio impossibilitatis
  6. esse desperandum, id int elligo dum nullum adest argumentum inpossibilitatis
  7. dz. Z= X dx solutum haberi suppono, quoniam reductum est ead logurithmos.
  8. suffecerit dZ. Z Uti dZ: Z = X dx summatu aequatio est quae solvitur
  9. per quadraturas, ita fieri potest ut aliqua arte ddz: Z= X dadx etiam solvatur per
  10. nec reforre
  11. som seers quadraturis quadraturarum inaequo
  12. 23 itx AaA cB
  13. aZax ad Fa du tubus ta,. Z2 cxdx
  14. -fdxda Zu + dedy dx) d Z ddx =( Z didu) F Xp Zdx
  15. Cax- yy +pe gu ax 1 el fiat g.- dZ: x Se
  16. padraturas
  17. dxx dadydix -2Xx dx3 =0 s addx: dxd si esset
  18. dZ dZ (: Z2 dxdx) dx, + Xx A- +.p
  19. si du opdis
  20. lapeod
  21. Aliter
  22. V dxlaazue + dZu ddx. Ergo exaequ. C fiat -axditz tdz ddx Zxxcx
  23. dxdx
  24. am _d
  25. Axdx aa ddy = gyddx F2ydydx + XX ddX + 2X dx dx
  26. Xx ddx + 2xdxdx ponatur =0, fieret Xddx + 2dxdx = 0 seu dix: dx = - 2 dx: X
  27. = - dZ: dx = sZXXdx
  28. seu loglx = log. XX. unde aa ddy = gy ddx +2ydydx seu aa dely: yy = ddx + 25. 2dy dp. y7
  29. si px = o fitet accddus = 2 ylydx 4 2Xdxdx aa yddus aadus e : dx = E gy L XX
  30. (smo 2a nali , 2Xd Z1 xx a 2xda + rgilus 2 ado eA = av. gy dx = ado ryag: 2 Favgu
  31. tq firit dz = 11 212 xdX + 3. 1∞+ 4. 14X et et
  32. Het gadus ado- 2ydys)= av seu aadusa aabus
  33. qn diZ f1. 2. 12 dxdx + BR2. 2. 3. 13X dx (+ 3. 4. 14 XXdx ax 4 4. 5. 15 X dxdx + 5. 6. 16 X dudx etc
  34. proaequ. Da2. Z - X datix
  35. oaaox
  36. () Z = 1 11X + 1XX + 13X +19 et
  37. + 11X3 dxdx + 12XY Axdxrec
  38. Erit 12 et 13, ut 4 = 0, sed 1 = - 11. 6). sed 16, 17, 18 = 0, at 19 = - B 15: (8. b)
  39. et ex Ad Z+Z p dxaxfins
  40. et 20, 21, 22, = 0 et 23 = = 19: (12) 13) sit 1 = p. fiat 5 15 = - 4. 5 t
  41. et 19 = 4. 5. 8.9
  42. 48
  43. et 23=-
  44. 4. 5i 8. 9; 12. 13
  45. X = 45i 8. 9: 1215
  46. 4. 5; (5. 9, 12. B;16
  47. seriem tuam pro aequatione ay: dx = gy+XX,: aa vri qua ex primis valorem
  48. ipsius y, stideris duxisse ex aequ. - ddZ: Z = XX dxdx ponendo y = - dZ 2 Z dx, inveniendo
  49. pe per seriem, et ejus: ope y. quod si ipsa prima aequatione uti maluisses
  50. + 15X + 1626 etc. (int
  51. L 10 10a a + 2. 10. MaX + 2. 10. 12 aXX + 2. 10. 13aX + 2. 10. 14a X + 2. 10. 15a X + 2. 10. 16a X erc
  52. 12 XX + 13X
  53. +11. I1 XX + 2. 11. 12X + 2. 11. 13 ,4 + 2. 11. 14 X + 2. 11. 15X
  54. + XX
  55. 4. 197
  56. +12. 12X + 2. 12. 13X + 2. 12. 14X
  57. +13. 13 x6
  58. - 5. 15X - 6. 16X
  59. 2. 17 X
  60. = 2. 12X 4 3. 13XX
  61. si istet 10 = 0) firul et U 12 =0, sed 13 = Z, d 14 =0 et 15 =0 et 16 =0 sad 17 = a 9.
  62. ec
  63. Raisus :. 18 =0
  64. 3. 137
  65. 19 =0 20 =0, sed 21 =
  66. obtinuisses aequationem y- _ x + - X
  67. 3.3.3.7.11
  68. si autem non
  69. et linea regularis re regule
  70. non posset haberi perfecta aestimatio
  71. ctis compar comparari possunt casus inventi, et reque observati,
  72. ducenda
  73. i ex ille
  74. Si utae menstrua excerpen Germanica
  75. c sumahebat, apud ine fonta idic pensionar, de Wic liballus exiguus est ad usum ubi communiuli aestimatione
  76. in pirica aestimato
  77. in praxi n.D
  78. siur qua possibibitate cascram aequalium aequali, et hinc ostendit ia pro reditus ad vitam sufficientes
  79. oltus Beegire scripsis est, ut aequitas rei in vulgus appareret.
  80. ti scrptis casu reperi in schedis simili me aliquanto artificio usum in solvenda
  81. factum potavis solvi
  82. emperus exemplicausa
  83. ydu capdx = XFg: a, fiat dy: dx = Z: a et Z= ∞ +y et dq= ex tdy unde Az= dx + dx C a) seu
  84. cujusmodi d sit Xty, da utcunque data ex dy: dx dico problema solvi pus
  85. AZ. 9 14 (Z. a)
  86. per quadratu
  87. seu E per X. positis quadraturis, seu transcendentali
  88. a et sooi potest di dus Xty: a
  89. betur X per t velhodo ulta tase semper Inventiquidem dim semper
  90. liac quoque y per
  91. oblitus sum notare,
  92. semper posse separari inceteminatim jam dudum quidem ne invenisse
  93. dissu equationibus iit rictibus differentialin ac
  94. ad inferidres Sed non ideo posrem non posse redigi ad quidra-
  95. heteregenedtates quadratorias qualis est Podax b quoniam
  96. semper posse separari incognitus pro
  97. niuscunque gradus defenivendo adhac
  98. xp ax + xdax summar
  99. iest et dat meraliter et dat Coatu Cddu)Xd
  100. latio problemabum
  101. differen vel saltem
  102. On fratium tuum ita loqu
  103. exemplo
  104. ed vides ex hocippdeam non
  105. e in separatione incognit. in determinata rum
  106. daze . d2 = XX axax; eam quod est adeo simplex
  107. o cangii cave ranto mmus in magis compisitae optatam quidem und
  108. Pimatio
  109. idet minusc
  110. turas quia sole
  111. et Vialtum cous

Cite

LBr. 56 · Bernoulli, Jac., fol. 37v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 153). https://leibnizlegible.com/page/DE-611-HS-958800:0074?run=153