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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 324r

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: 0.78.

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The machine reads it as

  1. il
  2. tanvier 1676 Requationes tetragonisticae per calculum
  3. Y)
  4. differentialem
  5. y+ YX. Ergo b+ SCB y+ 3y EX p, b + tc.
  6. 9)X, 6yX + X3H C. et qC x
  7. 3xy
  8. X
  9. orebyr et X⊓ B b- y
  10. sit BF tage portio axis inber tangentem et ordinatam +, B bXZ, et AD
  11. eit
  12. e
  13. b
  14. bx
  15. brE. AY + bx =,
  16. Y b 4 cX + dX + aX arc, fieri sit A
  17. 2ft X? b + cy + dy + eyte uide-
  18. 2XF 1) b + cy + dy 4 e v ea tp cy 42dy + 3ey ox
  19. VLV +OdV +Cy
  20. b + ca + dX + ex B Y. Ergo c+ + d Xt + 2y
  21. et fiet.
  22. + p, 2 b + ec X + d X + aCX et Ergo quando potentia u ipsius ordinatae ration
  23. +
  24. est rationalis modo
  25. c C+ 2dX + 3 ex. er.
  26. usa incognila
  27. cum _ d F=K 1 = = seu dp y - = y. Eruntue DEr X~.
  28. a
  29. erunue De ra habebunt eandem potentiam rationatem quam habent y. verbi grata
  30. si y est radix quadralica, erit: dDE
  31. 2b+2CX+ 2d X t 2eXC
  32. posita b 4 Cx + d X + ex ex , y fore DE B St ob +C+ 2dX+ eX er.
  33. A. SDEH SX dy ut ex alibi a me demonstratis constat, quaeramus ergo
  34. CAudxEe e Cop (ZY
  35. dy. per X. Z 1 . et + X 7i2
  36. c+2dX +3 ex ex
  37. utra Jam seo semper haberi potest, e . Ergo Explicando Co et y, habe dimus theorem.
  38. Sequens Arihhmeticae infinitorum promotae, sane memorabile et mirum
  39. Sinur Erdato brCK+ Dx rexSobetet Exex A Yb + CX+dX + ex eu B ScSy
  40. Brez V + Cx+ dxtexeu
  41. (ilem (DE + S y ( VX. Unde Bheorema Arichmeliae infinitorum:
  42. b+ CX + dX + ex e. A + X V ob R 1 + 20X+ ; d H X VbACX +X Fex
  43. Ergo Ex hoc posterione Reoremate habemus s commodi, ut smper cummar C possimus redicere
  44. ad summum omnium D quae utique simplicior est.
  45. Si sit X2 ( _ b + cY + d3 cc. erit at pphy +2dy et res fobrcy +dy
  46. 21
  47. Ergo vel CZt A vet jam S + dy B Sydx
  48. sit aequatio: Xb+ (Xy + dxy e + fY+g erc ponemu):
  49. 4b + cAy + d+y erc B eo + fy + 23Y ex, = CXy = 2dXy e
  50. Z+XY
  51. et LB eet fy + 393 cy - 2d8 e+ fyt 9Y Quorum in dy summap Sar
  52. b+c7+47 b+ cy+dγ c b+ cyt dyt e
  53. si ad sumum tdus addatur summa ady, habebitur area productae quantitatis, Et S+ + X temper haberi potest
  54. Ex hoc loco. S ec =153F.953 b +cyrdy = Cy- 1dy 5 e+ fyt 9y o 4 C rsy tgy) b4 cy t 27
  55. (2t b + cy+ dy
  56. HC + fV + 93, 2 b+cy+ 2y, ay
  57. b + cy + du 2
  58. jum pB Z. Ego P)
  59. si b+ CX + dX + ex er ⊓ y eut t⊓ e 2Y
  60. C+2dXY3 ex
  61. sive Et quia semper sp) γ fier c+ 2dX + 3 ex er
  62. imo aevenium ab enore
  63. + ex + da tex
  64. CAOEHOe
  65. A 2brcerdirer
  66. brCxrIN rexer
  67. (Ex+ er cr bc a B: bcx
  68. Ses
  69. 2
  70. Ergo
  71. Sesu invonitur.
  72. (XVdu
  73. us in
  74. 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 324r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0643?run=74