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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 129r

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: 0.73.

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. 130v); this page is its right half.

The machine reads it as

  1. Calculus diffecentratum per aequationes gerarales
  2. ottxes
  3. 0+01 X +012 X +03 X +01 4 X F etc
  4. +021 y + v22y +823 y +024 y ete
  5. L2
  6. + su X + 1IEX L13XT3IIAX, etC xy.
  7. + ay +8122y +f123y + 1r4 yt etc. xy
  8. Ruxirx+BBx et Xy
  9. =f2217+ f22gy +2237 +f224 etc. Xry
  10. + Y3 CCX +(3 12X + 6313X2+ B314X etc
  11. +B 219 2B 21 163 239 53 (7 etc Xy
  12. eu
  13. seu 0 +3IX + 31y + 32X+ 32y+ 33X + 33y.
  14. fiit Ngg. 30 dx + 30 dy +36 dy + 3edy + 32 ex +32 dys + 33dx + 1) dus
  15. Na 0+ 1o1t fo2 + f11Xy +6 12 Xy + fuxie su
  16. Compendio Aequatio ad curvam generalem
  17. Quadratricem sic exprimetur
  18. 30X1V+
  19. Naque d xor ax + dfor dus
  20. d pii, ex Xy + dx + fripdus
  21. 00 + o1 + 02 + 11 + 12 + 21 + 22 et C. aeq. N.
  22. f12 dy A1 G
  23. sit dx Xis (2) Nax +firsudus
  24. 522 dy.. Br2 (2) dx +raydus
  25. 231 dx X Y31B)X x +f316) Xyd
  26. 332 dy .. 1326) ~y x +326) X dx
  27. +02353
  28. ubi 00 signi sicat constantem e+ significat etX oX 1013X etc. at 02 significat Orty+oyid
  29. Ot significat o1IX + O12X +013X +0Vt Xe et i fochy tol
  30. pesignisient 0cy 10225 erc.
  31. 9 significat 111X + 112X + 113X ete in xy e2 siguit. 221 y +1227 +1257 etein xy
  32. et ita pono. In qualibet enim coefficiente trium noturum prima nota significat timensiones
  33. ipsius Xy. secunda significat utrum in multiplicatore potentiae abxy, contineatur.
  34. Xau y, si nota est D. coefficiens tunc continet _ X. sin 2 tunc continet
  35. y. tertia nota cotinet dimensionem ipsius X vel y. Et ita 214 significat xex
  36. e
  37. tarm
  38. erior est diam
  39. Herentialis erit: (dX d 11 +21 + 31 + 3p etc + dus d 12 + 22 + 32 +42
  40. + () Ey 1 (1) 1) + () f1 X y 1(1)
  41. n
  42. s 9
  43. + () 11 X y +Xy. t dx CyyY i+ + B (2) Xy 21 +2 + 3) XG 3I52 etc
  44. Nihaequ
  45. a
  46. vel possumus autem pro dx ponere a, et pro du, ponere Z
  47. et compendii causa scribere dx A+ B ae La D Ma + N, + PZ. vq. H. N.
  48. fiet: Z aequ. C a L + M a
  49. substituatur in aequatione data
  50. N + P.
  51. Ait + yaerX LorX + BX +oUX Aliter y COK LOLK FOIX +05X
  52. umerEx AX
  53. +
  54. Y. uxtEX +X EX
  55. 1
  56. Alitero vihil aequ 3, 00X + OIX + O2X +03X eu seu aequ Y o. y + y ry ere
  57. y, 10X + 11X+ 12 X 4 3X etc
  58. V, 20X +2IX + 22X +23X et
  59. et
  60. I
  61. Lc
  62. Nihil aequ. _ y do dx + (). B. d y do a + 9)0
  63. y de dx + d9, 1 dy seu y di a )1
  64. 5 d2 dx t ) 2 7 dy y de a
  65. W IE
  66. y d3 dx + 6) 3 3ydy y d3a ())3 774
  67. e
  68. fiet Z aequ L a. ht jum aequatio
  69. sit jum equalio: ZV DZ + Z + () L u. 4. 0. posito (e) ogo Cat X 4(6) X 16) a erC
  70. et (et v b) ox 6) 1 ∞ +() 2X etC
  71. et quidem si sit (t 2 abt Z aequo 0. fiet (0) + ( L
  72. O. T. HI. III. sunt mudis it aequalio 18 (0) Z + (1) Z aequ. Nih. tiet: M (0) Z + 2 a (1)
  73. seu O. + 2, + II. 29+ 21I. 3. y + IV. 1. 7 (9) _ dory dix y dle, es
  74. debent coincidere O0 () 1 a Fot) et O. item N 1. 1. (0) + a do (1) et 0
  75. item I1I. 3. (0) + a d2 (1) et 2
  76. item LI. 2. (6) + _ a di (1) et 1
  77. un unm eoseot perereuus ao tarenr srrate
  78. Saegu
  79. Ergo
  80. AZ

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 129r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0257?run=74