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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 84r

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: 0.76.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. NIB H
  2. b yXX + byx + CcRy = exX + f x + g. seu
  3. seu y = exx + fX + g,: XX + bx + cC. Hjus figurae sic
  4. expressae datur utique quadratura rationalis sel jam
  5. secundum Cydx. Datur ergo et (xdy, quadratura non-
  6. efit quaerendo valorem, ipsius X, fiet:
  7. e
  8. rationalis
  9. XX + by - f : g-e X + =(3 b2-5: y - C = = (2) by. F:, 9- C= Ccy+9
  10. seu X + bg - f3: 2,9 C = YL by f -2ccyr9 y e: 2y-20
  11. datur ergo (1. S,ay Y1y9+ my +n: 29- 2C)
  12. jam sit ed G Cx + a D: X+B = Syy+ Cy1f.
  13. st
  14. datur (xdu per quadraturas rationales, ope reduction
  15. praecedentis, quaeramus Cydx. sit exta = m Xtb
  16. ex 1 fiet: m m:n = yy+ ey+f,: y+ 299+9
  17. seu xtun yy +enegonnus e=bFfnn
  18. = um
  19. a
  20. sg un
  21. 29 mmy
  22. gy + hh. R y = 13: K seu y + hh: K 9 + G hH: 4HX = h + VK,: 4XC
  23. seu per compend
  24. seu v =hh + B+ BK: 2K se y. t2gmoc enn+ Y
  25. ∞)
  26. seu y = + 29mm-enn + 14g9m = qcomman+ etn eGarf.: 2mn - Emm
  27. D
  28. o
  29. 4g
  30. f.
  31. Ancbidetia tia cdari ad +
  32. Hinc videtur via dari ad dimensionem
  33. ec
  34. d so
  35. Curvarum Ellipseos et Hysbolae et
  36. superficiei, eoni scaleni. quae duo ad huc in Cunicis restant.
  37. Nempe sit y= 2gmm-enuce: Enn-Erum +ZD habebitur X, (vax rationali
  38. habetur
  39. quadrarura, quia habetur ea, ydx, E eequev Ergo summari debet V = 13gom et c: . 2n
  40. aprae plerasque formas
  41. aplectitur
  42. ractenus desiteratas pro ut abitrarias a, b, C, e, f, 9 interpretamur.
  43. B.Hujus carvae momentum ex condirectrice est
  44. areae
  45. fb∞ DR +C:X_
  46. summa omnium x ab +Ct d. Ejusdem areae momentum ex condinectrice
  47. ut
  48. abetur pe
  49. ecetet
  50. (XXdus est autem ex 1, yyx = x +b ,c, et sit X Al XX 1 + b+7. robgus = rl: py Eblysus _C,: 9
  51. X = n - b Ergo m = Cn- cb sit cb = a fiet m= n. seo hoc non licet, quia etanescit
  52. goum fsnn
  53. un. mi
  54. e
  55. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 84r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0167?run=73