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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 435r

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. 434v); this page is its right half.

The machine reads it as

  1. fingamus aequationem inter A et B generalem, quae
  2. sit e s. ∞ ex n + _, A+ a5B + 4 A
  3. Oa nA + 2+ B + 012 A1 22B, 8n2t AB + H
  4. 2 A + 3B + 4 AB + SA + 6B = 0 multiplicanda per 7A + 8B+ gC
  5. et 2B + 3C2 + 4 BC +sB +6C = D maltiplicanda per 10 A + nB + 12
  6. nam non licet solum assumere A et B servantes homsgeneitatem
  7. quasi caetera essent numeri quia alioqui daretur ratio
  8. inter A et B. porro componantur duae aequationes
  9. productae intersc invicem, et fet nova comparanda
  10. sparand
  11. 3 Nempe termini in
  12. est ers com
  13. habemus autem arbitrarias 2. 3. 4. 5. 6. 7. 8. 9. 10. H1. 12. solimodoqe
  14. unde spes solutionis. Ren reapse tentemus vitetur decollare
  15. 3
  16. 5
  17. 2. 7. A + 3. 8 B 4 2. 8 A B + 37AB +
  18. 2, 1 3 0 10
  19. 1 4 10
  20. Tres literae A + 4D habent
  21. pro qu tas literae A, B, C thabent in primo gudi for in gradum
  22. nullo formulam 1. in secundo 3; in tertio 6 in quarto 10 etc
  23. inde videtur calculo praeviteri posse, quid praestari queat per
  24. comparares. Duarum iiterarum equatio sit gradus cujus cunque pro
  25. Summa omnium terminorum copletorum pro duabus literis, si uujus gradus
  26. est + se duo si assurgit ad 1. gradum e inde a nullo est 3, si ad
  27. Hinc si potentia sit e
  28. Edum, est 6, si ad 3tiuu 10, ex.
  29. fiet numerus terminorum pe p+ 1. p+2: 2. Haec multi.
  30. plicunda per aliam formulam trium literarum ubi prodeunt
  31. it ergo
  32. pyramidales ut a+1.. _+2. 4+3: 1.2. 3
  33. numeus arr arbitrariarum +1. +2CE + bis quququ
  34. (1. 213
  35. productum autem pro numerat arbitrariam. prodit autem
  36. formula assurgens ad p+g. trium literarum, cujus proinde
  37. P+9+I. p 4+ 2. p+9+3
  38. numerus terminorum erit pyramidalis
  39. padum
  40. 1.2.
  41. data jum aequatio assurgit ad leium 3. (nempe ACC + BCC - 2B3)
  42. haec multulicanda per formula lium literum gradus
  43. cujus arbitrariae sunt numero
  44. + q- 3
  45. P+92. p+4-1 pIq sunt ergo
  46. in universum crbitrariae i p F1. pA2 + bis 4+1. 412. 4+Z + P + q. 2. p Aqu. prus
  47. +
  48. 1.2. 3
  49. 1- 2. 3
  50. quae summa simul major esse debet quam p F4+1. p +4+2. pF 413 + 1 436
  51. et videntur primum lantres procedat Pa sumendo 2 etul. 2. 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 435r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0865?run=74