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Leibniz-Handschriften zur Mathematik LH 35, 3 A 22, fol. 11v

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: 0.77.

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The machine reads it as

  1. sit irrationalis quantitas.
  2. X aequ l+ m+ n. ubi l et m et n ponuntur esse irationales
  3. cubice. firt: X aequ l +3 lm X + blmn aequ. 0 quod ubi si linspationalis et ima us est absoluto
  4. sin minus ut generaliter procedamus, sit. Erit l aequ X- mXX + 3m: X - _m
  5. eatl
  6. + l XE. 16 ma
  7. 2
  8. t lam in A IM + Nm dat p l- n in U R IB + Il dut n m3 + n
  9. Genimuliter
  10. n
  11. at 1em per mmt mnim dat l seu l + m per l - in + Mm dat 1- m
  12. l+ m +n per A+ n l per I a = Im dat l - 3 lmra. Ergo firt : (3) L - 27 l2m n
  13. I+m dat l- m 1 m3. 1 - m erc generaliter. l- m mulliplicando per l
  14. lamtn dat quadr p -4l
  15. 22
  16. quad ut B - 27 lmin gy P - 6412, cgcultaliter SI2 =y Imu Ejus
  17. 1
  18. + (12
  19. mulliplicanido per 12 I2 m + I nim erc. in 1 SI2
  20. inu
  21. ZImt S Z erc
  22. +m + n + P mult per V ∞Im +A dabit M 13 -3Imn verum ita runsus qualuor adsunt termini, unus rationali
  23. et lies nationales tam luum + emp + mp lnpemup. plures quam ante cui malo ut occunramus
  24. dividamus in duas quasi Um + ntp, et fiet: l +3Im l. sda +R3 +3AH sed ita rursus quinus
  25. Termini Cubl = 27 cub Ima est autem cubus Imn aequ Vmn +bC 1 12 l
  26. lamen per l y plm fiet t
  27. F +
  28. X aequ lam fint: X aequ. l+ _ 2lm X + m seu X = 1= m aequ. 3 ImX. fiet (3) N = 12 m 3 lequ 27 13 m 3
  29. sit rego tm+n sit X aequ 13+ 3Im BX + 6Imn seu X2 (2 m aequ. X3- (2- m sit aequ. s.
  30. fieo S. 3lm X aequ 6tmn seu et cubando N6 Bm n aequ. s - e 13) 3ImX
  31. n
  32. fier. S’ aequ 6 Im n + 27 X () im + + rts lua X f fiet s- 3lmX aequ 6 lmn
  33. et cubando 0 12m n aequ 53 - B) lmX + 3s UmX s- 3lma) Ima
  34. rusus lem (3) 3ImX, aqu 53- 6 l’ mn + 356 lmn s. bimn.
  35. Ergo 3
  36. deuique S’aequ 6 12 m dn + _ LBlmX + 3. 3lm. Imn X)
  37. Xaego l + m +n. fiet l’aego B -M - 3mum = 3 in X X seu - l’+m En _ +X sfago X+m in 3m
  38. n seu erit saequ 3 m +n mn + X. X- m-n
  39. seu laequ. 3 X. I. ma +Xl. sec fago 3Xmn 1 dxxb Amn 3XV go siet X X sit manaequ. t
  40. siet Saego 3hma + 3hXX = 3Xhh. Ergo shaepo isid aeqo _ m n + . ex 3 mnx+ tomn + X 3
  41. =Lx
  42. seu ( a 27h3 rgo MhE + IalKX - EX = 3 mncmnAXX - LX. XX.hx hamm dudium
  43. aequationum ope translata primum X colcitur h. Sed haec prolixiora quam ut absolvi
  44. mereantur
  45. lun olmap

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 22, fol. 11v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068235:0022?run=74