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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 22r

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: 0.74.

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. 21v); this page is its right half.

The machine reads it as

  1. t. vel p
  2. si ordinata et abscissa simul sunt rationales producta semper est rationalis
  3. N
  4. + - x
  5. Ergo p p Xt yx = y
  6. y+p
  7. Ergo +y- p+p, 1y. y =P 1 3
  8. + - X
  9. C
  10. Ergo pt B yX. Ergo tpagt ty - XY
  11. Ergo +p Xy. e1
  12. Hinc patet rectangulum sub du abus
  13. productis aequari verdangulo sub ordmata e
  14. abscissa.
  15. 2aX - X H y. Unde sta. Xxtr N, sive tB 3
  16. LX
  17. Data qua figura, invenire lssum ordinatam
  18. continetur tota ars numero numeris rationalibus
  19. effidendi problemata quibus insunt potestates.
  20. item fax - fX H FXP, sive p, ax -x
  21. sam p t ⊓ yX. Ergo t p VX
  22. Ergo y
  23. a x H WX sie
  24. Ergo L
  25. P5XI
  26. ax - X 2
  27. ex Y V 1a X. X ax. X vY
  28. a -X
  29. Ergo V Y 2a - X a ∞X
  30. 2a = 2AX = aX + Z
  31. v
  32. 1aX - X af- et yt
  33. a = X
  34. ∞X B Pt. Ergo 3 H X
  35. ut d
  36. FH F (F:
  37. Mimmam item, et si figura est in se recurrens maximam; an maximam infra datam
  38. X - LyX + X= Y - y + a o
  39. X F
  40. V’- a
  41. Ne y1xy) axy +Xb
  42. + lx + am r
  43. X + n Bo
  44. +nX + nlX num
  45. y3- a
  46. bX-g
  47. +-y
  48. vaxvaxy
  49. x XYt Xy + Xy- a3f X
  50. -∞+Xy+X
  51. a
  52. +Xe Al. ebm..
  53. t yk - Xy -X
  54. tyr- Xy-X + X y+ X - a
  55. aap
  56. N +M X ant X + nom B 0. conferatur haec aequatio cum data X + Y X~H X. y
  57. + l +am
  58. c. 1een + n 70.
  59. fiet V e n + l. sie rep
  60. et n 4 3 ul + 12 Cl + bm
  61. +a
  62. Ergo m B - n - 3 p l - 1 - a, - n 3 - 3n Y - l
  63. D. sive a n3 + 3p l + 1n
  64. conferaturcum X + PXFm Pone 0. et tantim opus erit oubstucere
  65. sive X + PX 1mpjo. ludica.
  66. + m..
  67. Pone erx. et Ap+ ap 3ten et nc emp. Ex priore eut Cr) rml et
  68. ex posteriore Ca
  69. 1
  70. 3n
  71. sive l ne, vel c, imp lp+ m Ergo mP + Emp p
  72. n
  73. nx
  74. 12
  75. smo
  76. 3X sive imp et m
  77. sine 7p H P M pne a ⊓ + P+ V, Ret Y suot si P. L pou en Sn, fet hmpom 1d +
  78. 1
  79. rationalem ad abscissam. Hoc problemate

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 22r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0043?run=74