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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 279r

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

The machine reads it as

  1. Quadratrix.
  2. AB sit X A sit diameter et N semmar
  3. et sit AFH semicircum ferentia; AB sit
  4. AG sit AEB sit _Z AG sit
  5. omnium
  6. a Arcus AF habebitur si habeatur summat da
  7. se omnium LF. sit triangulum characteristicum LWF
  8. erit LWF sim. FGE. seu LF; LW: WF:: FE: FG: GE.
  9. seu
  10. LF = B. 1H:, FG. seu da = Zh ax: stx - xx. et a = Lt ax: hX . Ax
  11. e debet esse Z: h: a: H seu Z: h: c h sax: SAx -XX : H
  12. BC sit v. patet fore EB: EG:: BC: GF. seu Lh - Z: Lh- X . v: sLX - XX
  13. seu ih-s ax: stx. Xx: Lh - X :: v. dhx p seu faciendo ThX - XX = y
  14. et X fint Lh - L sax: y: Lh -x.: v: y. E v - C 269 i histx:u : 2h-x
  15. (10
  16. - = h . X v: y = L sit sa X. y
  17. Ergo Ax v. y - a F h x F ydo f vius 2G: til ax: y
  18. Et in casu maxiaues calitudinis ponento de =0
  19. (12)
  20. fiet dx vy + Th. X v dy = hhy dx
  21. cesye ce
  22. ex aey. 11
  23. Eo casu quo X = =it fit v - 4 sit ex 4G.
  24. de =avy f
  25. endum Eodem cusu etiam est X = Z ergo et Z-h. Et eo casu
  26. quo Z = : h = x ex aG. 7 sit = h fdx tunc a senth sax. 1taura siA =
  27. = EH quod et jamcum verum esse constat.
  28. da: dx:: = h: y
  29. C27
  30. seu ZN = ha
  31. (a
  32. Z. h: a: Y. L. h - Z: Lh - x :. v: y
  33. (3) v
  34. ih - Z) = Lh - X
  35. -dZy + dyck- Z = = dx v + dv = k - X
  36. dZ H = h da
  37. jam quia gy = lx - xx. fit y, 2y dy = hdx - 2X dx seu dius = dx h - 2X
  38. Ergo in 8g. E substituendo dy. fit - dq + dx + h - X. Lh- Z = - dx V + dv = -X
  39. Rursus ex aq. 4 et 1. possumus invinire valorem ipsius dx. nam fiet
  40. dx = day: h ex 1 et ex 4 fit dx = dZHy. Ergo ex 8 et 10
  41. Leth
  42. fit:. fd Z (t dZVF. LM - x. ih - Z = - a Z , yV +. d v hh L h - X
  43. seu du: du = _ _ Z hh y + H. L x. L- y + TYyV,: hh. L h - X - - t: Y
  44. an Lin= v. + H. d h. 2. . ita + agu. h. i

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 279r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0557?run=74