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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 19r

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.

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The machine reads it as

  1. Videtur casus dari, quo s rrcc - irs (rssu f5 XX
  2. 2YX = XX
  3. deprimi possit
  4. reddendo scilicet numeratorem divisibilem per nominatoris divisorem 2X-X
  5. nempe multiplicetur 2Y - x per nec +s hex ner + rpX, prodibit
  6. 2nYd = nIrX = rPXX ~ rrcc - 2rf(r+f) X + ffXX
  7. + 2IrpX
  8. X fit 2nP = rrce seu n = Cc: 2r Ob ex fit p = - ff: Y ob X fit 21f (21f) = ntr - 2rrp
  9. sen 25(Y+ 5) = nr - 2rp, hoc est 25 (r+5) = =cc + 2ff seu (Cc = qus +4- 4f.
  10. sime
  11. seu denique CC =2f, (S) V Adeoque ABaerit media proportionalis, inter f seu CD, et a bis
  12. est autem =a, ilem quod (C)d, posito C eadere inta circulum Ce
  13. Et c seu AB eritu media proportionalis duplum mediae proportionalis inter radium
  14. inter OA radium, su seu Y; et inter OC, seu f
  15. Itaque si inter C A si circa CA describatur Circulus; erg ejus chorda
  16. angulo recto ad CA transiens per O, erit aequalis rectae AB, _ et centro A
  17. radio qui sit aequalis dictae chordae, descriptus in cent plano
  18. plano, normaliter ad AC eductam, in B vertice quaesito Coni scaleni
  19. normali educam et angule,
  20. cto
  21. cujus superficies haberi potest. Itaque dato puncto C, dabitur conus scalemus
  22. superficiei mensurabilis, ei respondens
  23. prodibit ergo
  24. art -Ert(risIX + ffXX.
  25. 2YX = XX
  26. X - 2r dividat ffxx -erf (rts)X + 4Vs F ffX - Errf
  27. X
  28. 2
  29. +2rfsX
  30. 2rrs -
  31. sed hoc fiustra, nam
  32. chorda minor est quamfuns
  33. diameter Circuli ergo minorqua
  34. CA, ergo ex A noa poste potest
  35. pertingere dius
  36. ad rectam exc normlaliter
  37. edactu
  38. videamus jam, qua quadhatura haberi possit dx Carrs. Bx, : X) - de
  39. af dao: dx = f
  40. Fingamus r+F =O, seu B imminer ipsi A die urr+ EX
  41. 2rX - XX
  42. jam SSXX + CCrr = GX + er1-1, fx - eFY-1
  43. Sx +c +GX-2Er, fiet c = + t 2f: 8- 1 - b
  44. sed ita b constini non potest.
  45. pr X assumamus Z7, et vi si esset r+f = + c, haberemus
  46. etiam intentum, nam numerator esset extrahibilis
  47. Y+ f = CA, sed se E = AB c = BA, itaque
  48. sed BA et C A non possunt esse aequales, ergo nec r+f- +c
  49. videamus, quid fial si r+f = -c, fiet rr+ ff + 2rf = Cc=
  50. bb +rY + aar taa. Et sit. sed f- atr et fiat
  51. YD+ (aa rar rn +2 rat im = bb + (41 n (+ 4art aa)
  52. e
  53. Ob
  54. et fint b =0, quod est absurdum
  55. nam lonicam, methado illa altiore, qua possumus bx + xt ex +5) _rationalisandum reducere
  56. citoo b
  57. hl_V + hfsu + fe ab vi LabrvFabrr. = h∞ + ff + (∞ + 1 lb, hv+f-(ver) lab
  58. a, vv+ un ir
  59. X Ab XDC, sit X=
  60. ha ve+ alisu + ac vrae racw e urr
  61. ves thv + (+)C, lv- 1f + (V er) Vac
  62. ad est +gyrghus + rationalsandum. B

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 19r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0037?run=74