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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 197v

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. 196r); this page is its left half.

The machine reads it as

  1. Itaque nihil hinc discimus, sed redeundum est ad aequationem n
  2. ndv + Cvan = ndy. si jam B sit rationalis quoad y. considerari
  3. pt quousque sit assurgendum, ponamus ergo n adsurgere ad gradum e, et V ad gradum
  4. erit de gradus f- et ndo erit inoe, cujus gradu est n, ejusdem etiam esse y in n
  5. quia si y altissimi gradus ibi multiplicetur per constantem, eam auterri intelligi potest.
  6. sit eogo e gradus ipsius y in n. ergo necesse est ut do sit ejusdem gradus cum dius
  7. seu ut V sit ejusdem gradus cum y Ergo si v integra non pt esse altior quar
  8. 10 10y + 11 et fiet +. 10 ny t 10 ycan + 11 cdn =n du et explicando n, oport et
  9. pudo 10l
  10. aequationem prodire identicam quoad y. s sit Ny + e n = 209 +. 21y 1 22 sit dn
  11. = 20. 2y dy + 21 dy et fiet 410. 20 y + 1021 y + 10. 22
  12. + 10. C, 2027 + 10. C. 21y
  13. + 11. C. 20 2y + 11. C. 21
  14. -20 y - 21 y - 22
  15. et et 11 = 21. 14 2C - . 21 - Bc. 2 et fiet 1 22 Mt E + 211- 10 - toc 11. 20
  16. quae ut sit identica fit 10 = 1:, 1+ rea
  17. et 11 = 21 - 10. 21 - 10C. 21 7 : 210C
  18. 2.20C +4. 20cC se 22.2+0 + 21 1 1010c 12C = 22 +22. EC
  19. et 2. 20c. 2d ( 2iet 21 BeC- 1 MCc. 21 = (22. 2. 20C+ 22 4. 20. cc
  20. et fit tandem 21= 4. 20. 22 CC seu 21 = f2. 20. 22 itaque summatio institui
  21. non pt. nisi sit gg 20gy + 219+ 22 quadratus; sec reducibilis Eodem
  22. modo credo reperretur 209 + 21G + 22y + 23 debere esse cubum.
  23. Ita eum levera
  24. potentiae sunt simplices res reduci po ad terminos simplices. nec multo calculo
  25. ipse opus ad hoec quaerenda.
  26. si sit Z
  27. = f.m. dy: y
  28. co-1- ea
  29. con
  30. Rat y =Y et dy = Ca. v av.
  31. efficiendum ut co- 1 = eco sit quantitas affermativa
  32. imo non licet ce = 1 - eco = h C0 = hal: A- C 2+ Ergo non licet
  33. ergo Z-... c0
  34. yra, vib
  35. du
  36. per y2 b fit
  37. i idem per yta fit b
  38. caetla huc reducerentur
  39. nterdum fit, ut duplex cirnitionalis sit summabilis
  40. yta ytb yta, y. b
  41. ta
  42. quaentique tactavil noster, reseius quoo
  43. ta satu
  44. -HX sar et 1 sa- x - dx. sac Xx et
  45. Saa tarar-aa = J: 2aa + a Vax aa adx: 2 Fax - ax
  46. d San- a Pax- aa = - 1: 2 Taa -a fax- aa a d X : 2 la x- ax
  47. 1
  48. +b - a
  49. ita ta =1 Res omnis ergo reducibilis ad e . vel
  50. ita
  51. ad L...... vel ad e, Y S..
  52. 2aa a fuxoa = avar aa +2 sax

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 197v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0396?run=74