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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 6r

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 7v); this page is its right half.

The machine reads it as

  1. umeriquadrati progressionis
  2. seia
  3. 9.
  4. CEmeticat, se quodem ita ut
  5. difcentia eorum sit data
  6. sint fresquadrate XX yu
  7. ex
  8. - yy = yy -XX
  9. e
  10. bo B
  11. Ex aeq. 1. fit ZZ+ XX = 2yy sit X = y - l et Z= y+ m
  12. fiet: (9y) + rym+mm 4 yy - 2yl + U= (29y) seu fiet
  13. yle l+mm : 2 1= m. jat e quam quatton
  14. aequationem 2 jungamus cum aeq. 2. et 4. rtique ex
  15. ag 2 et freto, Et primus jungamus aequationes etq
  16. extaequ. 4 fit l= y -X. (Ergo lG+X = B ex 8 et 2.
  17. en = CB ex seu y4 X = B: l quam componendo
  18. 2)
  19. cum aeg. 8 fit 2Ry (1 + B: L quod (per 7 eq. l + tum,: l- m
  20. Ergo fiet (13 = Vn + lB - m B = (13 + lmm seu
  21. mm + I M= B seu per 19 et 11, mm + 2ymL yy =Btgy
  22. 6)
  23. B. L
  24. seu me = SB+yy - y. seu
  25. seu m = 1 B+. l: 4 + B. 2 + BB: 4 - l - B. l. seu
  26. (17
  27. s U: 4 + BDg +3AB∞Z = l - B: l
  28. n (8)
  29. Superest tantum, ut faciamus in rationalem
  30. 1
  31. seu ut IC: 4 F nm 4 _ HC: 4 + BB: El + 3B:2 sel
  32. sit numerus quadratus su multiplicando per a ad
  33. ut 1 F BB + 6BH sit numerus quadratus.
  34. sit ( 4 BB + 6 BII BB + 2B nl + nn L
  35. fet 1 +6B = EBn + nn 1 seu fiet
  36. 6B - 2 Bn, : nn - 1 = l. Ergo si B ponatur
  37. 2
  38. esse datus debet 6B - 2Bn: nn -i esse quadratus
  39. ponatur B esse quadratus. tantum opus est effici
  40. ut 6= 2k; nn-i sit quadratu. Efficiendum
  41. est ergo ut 6- 2n. nn-1 sit quadratus seu ut
  42. 6nn - 6 = 214 + 2nn, On ∞rM- 214 +8nn - 6
  43. sit quadentus pro n scribatur p+9 fiet:
  44. p 1
  45. 9 12 p9 8p43 294 8p, 16pg184.6
  46. quadratus efficiamus slltem, ut a 24 +80

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0011?run=74