Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 146

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: 0.81.

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The machine reads it as

  1. DE L LH L Y L B 1 S
  2. Prop. 9. X = - LX3 -M M X X - ( M N - p+ ∞O.
  3. Per transpositionem est ~+= LX3 ∞ p+ = M M X N - n3 _, ideo-
  4. que situeritx+ ∞ l~3, hoc CA, X ∞I, CrIEMM N X ∞ = n3 X p+
  5. ex per conseguens m m X X ∞ -n3 l. L p+, _ X x ∞
  6. e D V
  7. In
  8. mm
  9. P4 = In3
  10. mn3ee
  11. .Ouod serso laequalis est V P+ = In3
  12. mm hoc ett
  13. Si fuerie LImm ∞p + = ln3; radix aequationis propolita aequalis
  14. erie unicuique terminorum aequalium lec V er =In. id eoque l
  15. in m
  16. in hoc casu in aequatione propolica loco pa substituatur ejus
  17. valor, nempe lIm m-L ln3, apparebie iplam dividi posse per
  18. X, aeque nullam aliam radicem reram admittere praecer.
  19. Si vero x fuerie majus quam lx, hoc est, x major quaim l,
  20. erit _ p majus quam m m ~ X =Ln3 x; d contra, (i tuerie l ma-
  21. jor quama. eric etiam mmx x n. x majus quam pa. Tam (1X-
  22. quatio propolita estrealis, erit xrealis, e vel xguolis. vel ma-
  23. jor, vel minor quam n. L.Ctoisitur, quodx major quam l sIc vel
  24. aequalis rel major quamn; quare cum _ p + tunc imajus sic quam
  25. MM Xx. L n3 x, erit quoque p majus quammmn x L n3 X; id.
  26. p4
  27. eoque mmn. Fn5 majus quam x. Ouare in hoc CalU CriE X major
  28. quamt, et minor quam mmn fn. Ouodsix, cum major est
  29. quam l. minor tuerit quamn, eric _ pa majus quam mm X X.
  30. _3x, ideoque multo iajuS qua M M X X + nB X X, e conle-
  31. quentes
  32. P+
  33. PX
  34. mm. f nn ajor quaM N.
  35. Ouare in hoc casu n erit major quam l, e minor quam
  36. mm. Fnn. Ouddsrero_ cumminor elt quam l, vel aequalis
  37. Euerit vel major quam n, erit mm XX -L n 3x majus quam p+,
  38. ideoque mmXx-LBnXx ajus quaim p+, _ X x majus quam
  39. nm. F nn de x major quam V mm. L nn. Frso in hoc casu erit X
  40. minor

Cite

Ps. 2, fol. 146. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0170?run=74