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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 85r

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: 0.82.

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. 86v); this page is its right half.

The machine reads it as

  1. pry.4
  2. 10C1 + 1 edy + 12 eddue + 13 = 0 fiat 10 ey + 1 edys + 12e ddus F13 =6
  3. debet. esse 10∞ = d(ne -nde - dne)
  4. e = 20, 51 - 41.30 = d20, 51 - 40. 30 + d (20. 51 - 41. 30) + (d 50. 30 - d30, 51)
  5. 0
  6. 12. d20. 51 + 12 d (20. 51 - 41.20) + 12 (d50. 30-d30. 51) 20 - 71. 20.51 + 11. 30. 4)
  7. 2051- 41.30
  8. 12
  9. 40.20
  10. a Exdd 26. 51
  11. d12 d2051
  12. 30
  13. G0.51) + plo 3o .7 d
  14. - 30.50 = d30.51
  15. C
  16. 0
  17. Decta aequatio sit 10y + 1 dy + 12 ddys F 13 =0 multiplicetur per e, et dividatur in binas, fit
  18. 12dc
  19. + 10Cy + ne dy + 12C ddy + 13C (2) 00fy+00gdy +ooh ddy
  20. Assumatur aequatio quaerenda 20y + 21 dus + 230 = 30y + 31 dy. quae differentiata dabit:
  21. 12) d3oy + 30dy
  22. + d3idy =31 ddy
  23. -00f y = 00g dy = 00h ddus
  24. + dec dy + 21 ddy = d230
  25. a, d2) + 20 dy
  26. a
  27. Identiticentur Aequs Z et 4, primum sinistrum sinistro, deinde dextrum dextro.
  28. in deptris per is fit f = 10C - d20a, 1: 00. in sinistris per cyfit f = d30a, : 00. Ergo C = d30 a + d20a, :10
  29. per ddy 1 = 12C - 21 a, : 00
  30. perctdus, h = 31 a : 00 c Ergo e = 21a + 31a, : 12
  31. per dy g = 20 1tC - 20a per
  32. dea
  33. per dy 9 =ne-20a, :00
  34. : 11
  35. perdy, g = 30a + Ergo C= 130a d3i a
  36. d31a)
  37. valorem cum tertio, et secundum etiam cont cum tertio, habemus ex et 3 pumo et tertio Sta +50 114
  38. e
  39. Ita contrahuntur literae, et f. sit
  40. Eex prime et tertio d50 = 50 + d51 Et ex secundo et tertio 5 = 50 + d51
  41. 10
  42. sit d fit d50 = s ex 1et 2. Enjo 51 = 12d50 et d51 = d() d50 + 1dd50 Ergo fiet
  43. 10
  44. ita saltem aequationem datum reduximus ad faciliorem, ubi abest abisolutus; et quae proinde fingendo
  45. d50 = 50 + d( 12) d50 + =
  46. 0
  47. 101
  48. 11
  49. 11
  50. 10-1
  51. ui eio =: V b. reducitur ad differentialem primi gradus
  52. sed idem obtinuissemus sinetot literis comparudo 1029 + 11 edus + 12e ddu + 13C a = 0 cum
  53. differentia ipsius 20y +21 dy + 230 =0, quod est d2oy + 20 du
  54. +230 =0
  55. duidy + 21 ddus
  56. fit C = 10 d20 = L. 21 - , 20 +, d21 fit 7 = 1 d20. Ergofit, d2o = 1 20 + + d (1 0)l2o r: 2 dd20
  57. seu 20 + d() 420 + n dd20, 4 =0 ut ante ita 50 1a 20 et 21, ut ante 50 et 51 et frustia
  58. multiplntur literae a, d 2o y + 20dus
  59. 10
  60. fe 30 ~ 104y8
  61. deidus + 21 dilus
  62. udp y + a pdus
  63. (multipliantur literae
  64. 11 alxus +2. 12 apdus + 12p ddy + 13 =0
  65. fit 21aa = 12 pC et d21 aa = 12 p de + 12 edp + dir ep = 11 ep + 12 e dp - 20aa, adloy
  66. fit 21 aa = 12pC et dEtaa = B pde + 12 edp F der ep
  67. fit 20 aa = uep H12edp) = 12 pde (= 12 edp) - di2 ep. Et d 2o aa = 1 p deft i eap, + d ex - 12 pd de. 12 dp les pd
  68. Si dit + dd 12 possent aequari 10, primum in alliuma aeg. tolleretur ex
  69. dupdest dne ap. + de12 ex
  70. 10 ep ( n eap, + 120 d dp
  71. ceinde per de et ddx, tolleretur reliquum p. et iavenretur restatet aplap
  72. sit aequatio 3C + 315D + 32ed d + 33 =0 debet 30 e = d31 e + 31 de f3 rC + B2de +Zrdde
  73. fint 1B = py et fiet Xe py
  74. Anthu potius v- 47 3ledpys 43epdy
  75. 3eapG F.32edp dy + 2e pddy +33C.
  76. sodco et ddl bat. l dcono + d ddco
  77. d. b
  78. so
  79. -0 et debet esse 300 - (31 edp dus ep
  80. Bcende Creaptrane
  81. 232 deap
  82. sud hoc quaesotis dificullate aequalia
  83. 1050 + 11 d50 + 12 dd50 = 0 sit 5D = b fit 10 + udeo + 12 deo du + 12ddco
  84. I 40=
  85. 12dedus + 12dedue ∞
  86. ndire dy. + diredys
  87. rursus
  88. +32 Cdd p
  89. 32 p ddc
  90. 2.g dp de
  91. 2B2edp
  92. pde
  93. 2832pC
  94. dancep

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 85r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0167?run=74