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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 174r

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. 175v); this page is its right half.

The machine reads it as

  1. Habetur solutio generalis formulae
  2. C_ byy +RCy +d quadrata ev aequanda
  3. pro scopo meo solutio in determinatae, anqua saltem ipsae
  4. iadeterminatae y, et V, sint extra vincula radicalia non
  5. curando de coefficientibus. Nam Et quidem si b vel e
  6. sint quadrati, res etiam numerice praestari potest. Sed
  7. centraliter fiat V = y1b + X et fiet (byy+ cy+ d= byyt 2xy1b
  8. seu y = Xx - d,: , c = 2X 1b. Sed rg +XX + 2Xb y 20
  9. D
  10. Sca Surgamus jam ad altiora. sit formula, cubica aequanda
  11. quadrati sit surgumus jum ad altiora sit formuta subrea
  12. b1 + Cy + dY + e = vr
  13. sed video magis, uniformiter nos processuros, si semper
  14. ima tollamus. sit Ergo sit b + c + dgy = vv et
  15. fiat v = 1b + Xy Ergo ex 1 et2 fit, b + cy + agus = b + 2xy 1b 4 Xx yy
  16. seu c+ 3y2XYb + Xxy seu y = C - 2X 1b,: Xx- d qui valor
  17. tantum est prioris reciprocus
  18. furgamus jum ad altiora: sit formula subica aequanda quadrato
  19. nempe b + cy + d ys+ C Y = ov sit v = ( sb+ c: 216y + xy
  20. et fiet b + cy + dsG +Cy = b + cy + Bx gy + cirbX 5 + XX 1t
  21. seu destructis destruendis XX YY + c. st Y b + X
  22. et fui b + cy = dyy + e = b+ Cy+ xtv yy + ab XGG n d
  23. Et destructis destruendis: +X sb
  24. als
  25. C: 4b
  26. + C. +b X Y + XX
  27. + C. b = AC
  28. 4
  29. seu Beb) + (C) y +cd) yG, = 0 Unde per aeq. 4 calculi procedentis
  30. per compendrum
  31. (5
  32. d
  33. habetur y. pro b, c, d ponendo valores ipsarum (6), (C) (d) ex
  34. ibi repertis
  35. comparatione aequationum 4 et 5, et pro X ibi reperto, ponendo
  36. et siet. +ZZ seu per compludium (6) + (C) Y +Cd) yy. 6 sua non quae
  37. ita x ita res redit ad aequationis quadratica resolutione
  38. sit ergo Faciamus X = 1. Z. Et ex 0g. 4 fiet
  39. 6
  40. +q sb + C: 5b Z y + yy = 0
  41. sed ob 229, video hnc
  42. huni non dari solutionem
  43. si jam voluissemus facere Xtb + c: ab - d = 0 seu determinare X
  44. + c: abZ2 = eZZ.
  45. res redacta esset ad solutionem determinatam. Sed pro generali
  46. = Z
  47. solutione cum sit sit pro compendium yy + Cs my +n =0 et fit
  48. yy + my Lnm: 4 = um- an : a et y = Vmm- qn = m,: 2
  49. ei debet min- an aequari quadrato. Et habetur formulaaquanda quadrato
  50. in qua extant 74. 73, q. abestantem absolutus; Et video nem
  51. successuram si absit terminus h simplex ita enim prodibe formula
  52. p2X Z
  53. Z, et absolutus. ut quidem si lnqullet face
  54. iliccris facere b =0, haberetur desideratum sed hocmonlicet si faciamus y- PZ+ Y
  55. aequanda quadrato, in qua sunt 2
  56. Puce
  57. Ileu Zet absolutum 17

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 174r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0347?run=74