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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 85r

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: 0.84.

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. 86v); this page is its right half.

The machine reads it as

  1. dats
  2. quaesita 8 =0 E = 30 + 31 y + 32y + 331 + 34y + 35 y +36y etc =0
  3. d8 = d30 + yd31 + y d32 + y d33 + y= d34 etc. e B6 + 1. 31 + 2. 32y +3. 33y + 434y etc. dy
  4. seu ede seu dE+ dody = 0 seu dy = - d9: 49. jungantur aeq9. 1 et 8 fiet
  5. Od + D d920 Quae debet esse identica saltem virtualis, cum ipsa aeq. 4. jam
  6. aeq 4 est indivisibilis, ex hypothesi, nam talem assumere licet, ergo non si aequs. 4 et 9
  7. non sunt formaliter coidenticae, oportet aeq. 4 posse diti esse divisorem aequationis 9
  8. Explicetur aeg. 9. pet
  9. 20 d 30 + 20 d31 y + 20 d32 y. + 20 d35 17 + 20d34y . ...
  10. + 21. d30 y + d1 d3iy +a1 d32 y + 21 d33 )
  11. + de d30y + 32 d31 y + 2 d 32y ...
  12. +83 d3017 23 d31 y
  13. ...
  14. +14 d30...
  15. FD. 1.51 F 63.G + f0. 3. 339 + 10. 4349 + 10. 5.351)...
  16. +7. 1. 31y + 81. 2. 325 4+1. 3.339 + H. 4. 34y...
  17. Fg2. 1. 31 y + P2. 232 9 + Y1. 3. 33y....
  18. F13 1. 31 y+ 13,2. 32y....
  19. +14. 1. 3, y.. . .
  20. dividatur haec aequatio 10 per
  21. aeq. f id est 5. ita ut astendat
  22. sitiavet a 3o+ 3IGy. vel 30+ 31y133G
  23. vel 30 + 31y + 3279+33y
  24. et ita porro
  25. Sed quia divisio instituenda est per , e praestabit ita scribere
  26. aequationem 10.
  27. 3ed301434212 d20yix
  28. ) vicquia est super
  29. lineam unam
  30. quicquid eA superlineas tres
  31. valet si sit 30+ 319+32y
  32. quicquid super tres quatua
  33. valet si 8 sit 30+31yt3ry
  34. et ita porro
  35. sud
  36. 1e a319+V a3y +~d31y+ 23 d3, y
  37. 1
  38. 90d32 y + 2d32 y
  39. valet si Gpoheth
  40. l
  41. H1. 232y F +22. 32G + (7. 2.32
  42. itaque ordine rem traetemus unum gradum aequationis
  43. quaesitae 4 vel 5, post alium adhibendo, ut appareat
  44. quid in eo fieri possit reductibnead et atm
  45. rationales
  46. ad quaenam aequationes differentiales datae
  47. possint reduci ad 30+31y., deinde videbimus etiam
  48. quae rationales differentrales datae, possint reduci ad 30+317+ 32y,
  49. et ita pergemus donec sese offerant aliquod treoremata
  50. vel saltem Tabulas condemus in oblatis usui faturas.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 85r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0169?run=74