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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 137v

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: 0.83.

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. 136r); this page is its left half.

The machine reads it as

  1. Differentia inter duas Hyperbolae ordinatas proximas
  2. + S a + X + 2βX + = s a + X 1
  3. Ergo Z (2a + 2X + 2 PX + - S a + x + 2 + A a + X
  4. . . . . . ..
  5. 1 +.
  6. 9u - a5 Y - 4 X + g a t 4 Ha X + 83X +x +D Cx + +geX n a+fa fexa +XX
  7. .
  8. Unde delelis alius fiet 3a + ba∞ + 3X H 0. Unde feret a Y) - X. Quod
  9. den
  10. est absurdum. Sed unde error
  11. si fecissenus a +x ++ x + ( F1Z + V a +X
  12. habuissemus +X + 2X + B F y + _+ X + Z Sa +X
  13. Unde 2X (Z Sa +XD sive AaXB a + X, vel a X a Z Z X
  14. vel
  15. Z1
  16. ax Hujus ergo datur quadratura.
  17. Sed non possum satis mirgri rem priore methodo ventum fuisse ad impossibile. Nec video
  18. curo fuit ergor calculi non praefixeram binat
  19. vinomii quadrandi facto.
  20. Sa +X
  21. quaestio an idem sit locus differentiarum, ordinatarum ad eandem curvam. disfercutium
  22. ex differentibus licet axibus v.g. an idem sit locus differentiam, inter ordinitas, Hyperbole
  23. sane idem sempu pro gressioni cuuae
  24. et Asymptolon, et ad axem.
  25. homogeneus, undecunque sumatur. Curvae autem locu sit ex quadratus locorum differe
  26. Ergo et idem locus quadratorum ejus perptu locus quadratorm
  27. en
  28. em componitur ex loco quadratorum, differeatiarum, et loco rectanguto, rectamus uli autem additur
  29. quadrata cutem loci qui.
  30. aut subtructio non mutat locum. Ergo idem est semper locus dquadratorum, differentiarum
  31. ipsius curvae. Ergo et idem semper locus ipsarum differentiarum, pois ex emiusta modo scilicet
  32. Hinc sequitur ax esse
  33. quantitates quae calculum ingrediuntur omnes sint verae
  34. Restat tantum demontrandum, quod
  35. ra
  36. ordinatam Hyperbolae cubicae.
  37. idem semper sit curvae locus. quod patet, quia locus est qui curvae, qui ipsi homogeneus qalo
  38. a -rat 4 X sed a k = V a 2a +2 +Y
  39. den g
  40. s
  41. 1Z
  42. 4
  43. in
  44. opoemom
  45. unom B. Curva
  46. ipsa expleabit
  47. duboliamn
  48. B
  49. licribola

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 137v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0274?run=74