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Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 21v

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: 0.74.

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The machine reads it as

  1. seu explicando:
  2. anurr raantimm. + aaIl rr, mull
  3. 2UImm + aa IIrr + aammunvanner L-8a lmni =0
  4. 12U InM + 2aa lrY + 2aammnn- 3a nurY
  5. 1
  6. 16a mar
  7. c
  8. Nulla quae duae exunteris cequationes sunt solvendae, nulla loteraram
  9. pon polest aequalis derhuo.
  10. Si ponatur aa urr = 8 a lmur seu Ir = dmn
  11. e
  12. sit: 3 Umm + aa inmnn = 3a nurr = 0 seu - 3. 64mn aammurr - 3 a (nnr-
  13. et 60- c2Uum + raammun - 3a nntr = 0
  14. sed ita coanesante hacebitur
  15. inquacble
  16. tar tatius est sinc ulla Hypothesi facere solvere duas aequationes
  17. et
  18. raaller Faammuna lmur = Cumm+ba nurr = 12Umm + 3a narr
  19. Ergo seu siet: 3a nn rr 6Uum seu a nurr = Zunm
  20. seu anr - im s2 seuar = (m 52 : n
  21. sed ergo fiet aatr na 2aalm + a m nt -8Sal m n = 3ummn + b allnn
  22. 2
  23. d et divisis omibus per m, fit: l+ an = 3+6a + 8Aa ln
  24. 1
  25. 4
  26. e
  27. seu l + a n + 2a l’n = 3+ (~ + 8(2+2a Unn
  28. seu Utann = In 10 et 1+ 2Ba + ann = (8+ 2 a ln
  29. et l + 11 In + LO un = = D = a nI
  30. seu l + On = n Y L O- a
  31. Se. l+ L On = n Y3+ saa +8T2F1a
  32. ergo problema foret solutum
  33. falerum ergo
  34. et quia d y
  35. E d = O+ d0
  36. (7
  37. talem formam du f
  38. M Cn
  39. a + βV
  40. V+ dY
  41. fiet dy = (mrV + IY ( mrD+ mn
  42. m v + C
  43. rv + n
  44. = a ∞ LB A
  45. r2v +2pnV + un
  46. Ergo curra Hype holae (idem est de Ellipsi) invenietur per summum
  47. 1
  48. 1
  49. ta
  50. a 4 (3V
  51. 7+ 1D 51D - B+O: m
  52. enavae figurae cujus monata est d Talis formae
  53. + dv. nn∞ = + 2nX V.
  54. per, ca quadratirem
  55. It de sequitur posse inveniri Curvam Hyperbolae
  56. Hyuibol seu per rogarithmos. Eadem Methodus etiam
  57. ac Ellipsia et Hyperbolam quamlibet appercari potest.
  58. bis tam ex una quam adsera
  59. aqualre unde pt prodire

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 21v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068001:0040?run=73