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Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 18v

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: 0.85.

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. 19r); this page is its left half.

The machine reads it as

  1. Cum hoc sit maximi momenti, erroris vitandi causa de integro assumer
  2. operae pretium erit.
  3. Esto GBE. Hyperbola. Cujus centraa A. vertex B. Radius ut
  4. ita dicam AC. vel CB. a. AD cD vel CH
  5. vel CF p y. AD, a - y.
  6. vel AH
  7. AF 4 a+y.
  8. DE, a
  9. -y
  10. CF ( AFp
  11. EF HL, a
  12. + L + + + = et c. spatio in infinitum
  13. 11 - y + y - y + yt - y etc.
  14. eique summa omnium HL ad CF. applicatarum erit.
  15. -
  16. aty
  17. Eg D Ergo posita a , 1. eut DEp 1 + y + y +, y +7 etc.
  18. et summa omnium DE, erit applicatarum ad AC, erit:
  19. Posita producto, ACBEm,
  20. Sed HL p a 1
  21. 1+y 1
  22. =
  23. E + 3 + = - = etc. spatio CFGLB
  24. 5. 0
  25. auferatur spatum CFGLB a spatio ACBEM. restabit:
  26. et a
  27. 25
  28. fret.
  29. (9 L ( +) + = (+ 2) + ( ) + ( ) er
  30. sive 2 2 2 ex 1 Z etc.. qua demon-
  31. 2
  32. stration quod satii mirabile est, et ostendit summam ipsius seriei
  33. 2. = erc esse infinitam, et pronide et aream spatii.
  34. A 1. 2
  35. AC BGM. quandoquide finita a CBGF, ei ademta, ider
  36. 2 +2, +2 + 2. quod aequatur spatio GFCAM BLG
  37. Hujus duplo = 4 + + 4 + =. erc. auferatur area
  38. et opposito Hypetom, circuli, cujus dicmeter CF., nempe radius CF. quae est.
  39. 4 - 2 + = - 4 + = etc. fier inde differentia haec.
  40. 8 + = + 8 et c. et si addatur area Circuli ejusdem
  41. si Aadi si diumeter sit 1. Eircumfrentia est: 2- 2 + 4
  42. Ergo si diameter 2. seu si radius 1. etit cicumfernta 8 - 8 r 8 - 8
  43. ergo semicricumferentia, et - += etc. quae ducta in radiam
  44. 1. dat circulum, ergo circulus et == + 4 er. Ergo quadrans
  45. circuli 1 - + erc
  46. Anferatur Quadrans circuli
  47. a spatio c FGB. restabit resen restabit: fier:
  48. + = -
  49. relinquit.) seu nihil notatile adimit. Hoc argu mento concluditur, Re
  50. infinitum non esse totum; nec nisi fictionem, alioqui enim
  51. foret pars aequalis toti. Si ad spatium 1. L. er
  52. addas 1 = 2 + = - 4 + - ex. fier.
  53. potiqus illi spatio pote
  54. fiet: _ 8 + 8 + 8 et.
  55. c
  56. 35
  57. sumta bilicet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 18v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068022:0036?run=73