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Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 12v

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: 0.86.

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. 13r); this page is its left half.

The machine reads it as

  1. Sed res omnis proponenda est distinctius.
  2. er X+ pX gX X+ SX + =0
  3. sit aequatio, cujus radices quin HE, L, M, N, O quarum quae libet vocatur X.
  4. radicis unius partes irrationales quatuor h+l+ m +n, compendio h = X
  5. H + L + M + N + O = p
  6. H vel L vel M vel N vel O = X
  7. HLMN vel dc = 2
  8. h + l + m + n = X
  9. HL + HM etc seu HL = 9 HLM = Y HLMN = 5 HLMNA. F
  10. HL vel HMvel Adc = Y
  11. ALMNO = TI
  12. hl + hon et = hl = y
  13. HLm vel HLNecc = Z. HLM NoelSC = 2 HLMN-
  14. hilm = 3
  15. Elium = co
  16. hlumco in veniri potest quid sit rationale in qualibet potentia ipsius
  17. ut in X, X, etc.
  18. Inveniri etiam pt quid sit rationale in vel in qualibet potentia
  19. ipsius Y, ut in V V etC. et ita quoque in Z, 2, et
  20. . Sed non aeque vid etur facile definire quid sit ravate in ipsis
  21. qu
  22. ex h, l,mn copositis seu in y, Z
  23. ie invicem et cum X.
  24. Xx = Ah + 2hl
  25. co, et et horum poteneris atque factis in
  26. h, C, in n = sa sb sc B
  27. ergo quod in X est rationale erit et in 2ab
  28. X3= + 3hl + etm
  29. erit ravale in 3ab r abc 3h C+ 6hlur
  30. illud manifestum videtur hi, h, tc. nihil continere ravale
  31. jam htrx eliam nihil continet rationaleSa + sb + SC +Sd inta tbd
  32. dat sa + sab
  33. videndum an in generalo calculo unquam aliquid ravale prodeat ex formula
  34. je
  35. tale, eut forma maequaliter se habente in exemplo, ut Sao vel hat
  36. Nota. Quae farimus pro X, e ex p, qr; eadem facere
  37. possumus pro _Y ex 9, seu HL ex HL. HM (cujus valot invenori potest)
  38. ex HL. HM. HN (cujus valor etm inveniri pb quae et eunt HL. HL. HA MC. Ma. aV
  39. ad tactand habendum y crsque Y,
  40. Y1
  41. e
  42. is
  43. loco
  44. Vecum illud in quaestione est, an
  45. liceat inde transires ad y. seu an possit haberi ontor ipsi,
  46. y et
  47. eigue quadrulorum potcabiar, itat ut coincidant y er Y. vel saltem, ut
  48. quoad rationalitates ut se X et ejus potentiae habeot ad P, q,r, ec. ita se
  49. et et ejus potenliae habeant ad qseu HL. HC: HM, eC.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068231:0024?run=74