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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 371v

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: 0.83.

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. 372r); this page is its left half.

The machine reads it as

  1. An ergo aliter tentemus verssumendo primam aequo pagiuae scedentis:
  2. aa du +x ydy + xydx + aydx = axdx quaeratur X per V, et sit
  3. XC 10+ Wy + 1y+ 1393+14 y4 15y+ 16y ex et X = 10 + 210119 2ronus et fre
  4. Xydy = 10Y + 11y + 12 y3 + 13 y + 14 15 +15 y
  5. aydx =a, 1.1, +2.12 +3.13 +414 +5.15 4616
  6. xdxte pion ru asuiva et. eu ert
  7. Eiri
  8. Bxip -i 12. 10u1 25 0 3( 2 . 1
  9. aa = - aa
  10. 20.
  11. si fiat Zydu taydx-axdx +yxdx radys-
  12. opt; s qe qua differet d valore
  13. ipsius X nisi quod 10-0, videamus an
  14. aliqud hinc duci possit
  15. Nempe si eq aequ. 4. suferas + 10y
  16. =a, 1, 2. 10. 11 2. 2. 18. 12 y P3. 2. 10. 13)14. 2. 10. 1415 ey
  17. XY
  18. . 2. 101ry +2. 2 1c. 12( 4 3. 2. 10. 13 1 Cx
  19. seu 410) =a, 2. 10 aX + L. 2.10 ydx.
  20. residuu inaeq. n 4 non differet ab aeq. resullante
  21. ex explicatione aequationis 5
  22. sed saccurit alium scilicel 5g. 1. et 2 habent eandem diferentiu differentialem; per
  23. quam invenietur, a quatio communis utrique et valor etiam ipsius X Mer y ubri
  24. fiet
  25. quatio ota
  26. et X 20 +21y 4 22 + 23 y et.
  27. primariarm albesariar
  28. , 2 21 4, 22y + 3. 233 +9. 24y tC ixdx data Ny dyt agdx axdx tyx -aquo
  29. 104 11y. + 12 y etc
  30. dp cndy + 2L vd 5 13y a dy estc
  31. + Xyay = ( X 10y + 11y + 12 y + 13y714y+15 y etc
  32. etc
  33. fdx
  34. L.HI. 2.12. 3.13 4. 14, 5.1 6.16
  35. = aXdx = -a, 1. 21 +2.1 43. 23 1914. 45.25 6. 26 7. 27
  36. + aydx =a,
  37. etc
  38. dlax = 1. 2 diy + 2.3ydy 13. 4ydis et
  39. quatuor
  40. + aa = taa
  41. + yixdu-
  42. 121 222 323 4. 24 5.25 6. 26 ex
  43. + y dxx 0
  44. a dx dya.
  45. Fagdax =a,
  46. =ar 1
  47. Unde talis oritur aequatio
  48. 10 tuy tres r3y ay +15y 116Y etc
  49. 3.13. 4.13 3.18 si 6.19
  50. 121 23.13 3.4.14 4515 5.6.16 6.7. 17 etc
  51. 1n hE
  52. Hinc jam per aequationes compa
  53. +22 2323, 3.414 4525 5(. 2b 6.7. 27 7. 828 eH.
  54. 1.21, 22 3.23 414 5.25 6. 26 7. 27 eu
  55. ratitias O destructitias
  56. sunt tolli
  57. O. D, 3 et G invemeri possu
  58. tres literae 22, 13, 24 bm
  59. et habetur relatio inter
  60. Notui autem
  61. 11, 12, 13
  62. 10 et 21 ingredi calculum,
  63. ut scilicet servatur generalitos
  64. 12 2 2315 3414 4515 5616 67 27 ete
  65. Txdxdy = h
  66. ut vero hic calculus sit communis omnib ribus literis impediatis (demta
  67. prima 10) sit 2= n siet 3- n+1 4 = n + 2 1 = n - 1, 1, 2 = nn -n 23 = n + R 3.4. n13, +2
  68. cmttishi term
  69. +ylx = 2
  70. Et ita putcherrime et brevissime habetur regula generalis fimita pro terminoru e
  71. potuissernus etiam aequationem multialicate
  72. per vel per ay vel per simile aliquid, pro arbitur, unde rursus novae aequationes. Et videndu
  73. an sic obtneri possitet tales aequationes ut composititae quasi ntio aequatio esset ordinarium
  74. Quin et certo casu poterunt
  75. aet
  76. progressione, non alioqui facile epuenda
  77. Javenori quadraburae speciates, ~ o. Esto aequatio axdus + aa axdus + baxdy
  78. explicata, ut si semper simul exearent a1 + b21
  79. ax dy + baxdus + caedus + Cy dx B.5 a dx = ft Ergo in casu quo es -5 = 0. sit
  80. iterum Ax + Iax + ca = 0 quod quidem ex ipsa corva patet eu differentiali: sed securius habet.
  81. ex seriebus. Et ita invenitur tam y quam X. sit a Saa + XX a et + est dx: fdX
  82. E 2Xax = Cy Ax - fdx + Saa + xx dy = 0 Ergo quo casu ey - f -
  83. tiet y Fa 2Xdx: taa + XX = dus sed an licet hinc inferre? esse aatX = y + b
  84. eo iesa quo ey - f 20
  85. videndum quo modo ex seriebus talia jastificentur, a quatenus
  86. x = 1. 2. atus r2. 31. 19 iy 13 424y dy = (p 6) 2. (X ax
  87. Fairdys
  88. quae ratur differentio differentialis aequationis B1 fiet: xdus Fi dedtus + a gadx = a d pdx A Xte ay
  89. + yxdx = 2)
  90. + Xdu =
  91. et

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 371v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0738?run=74