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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 15r

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: 0.80.

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The machine reads it as

  1. yA- A V aequandus quodrato.
  2. sit e: a = fg: aa = hi: aa
  3. Y+B-D, insia y - vr - 1 = img: a
  4. 3to = nh: a 9- v = ni: a
  5. Z2- aabt = EL
  6. L
  7. cosab -v
  8. fint ist v
  9. aqpondus
  10. 2y = m f+g, m: a 2v = f - 9, m: a -,
  11. 29 = h+I, n: a 2V = h -1, n: a
  12. m: n = hti,: s+g = Hh - I, : f- g
  13. superest i = fg:h, et fiet
  14. hae
  15. omnet quantitases
  16. tih +f9 Lihh- 1g, et tand extuberde in inagus
  17. h. f+g
  18. h, f-g
  19. et tandem (hli s). ihg + st gE Fgg (hbs t lilus 5sg P sag
  20. fiet . tih =0 seu h = + f. Ergo 1 = +g
  21. et fa +s +8 = +5 +d. 4
  22. Et tandem hls- hhgs + Hg - sgg = -1, Shh litgs . ftg. fgg
  23. titif. ( - -1) - lihus (1+ Y- 1) + fg (1 + - 1) - 99t ( - L. 1)
  24. hf (hh - ggi - f. 1) 5 = s lita (hih -. 55) (1 + f. 1) )
  25. hh = f59 (1 1-1) -fg9 (1 - Y -1) hoc in integis efficien
  26. um
  27. (1+ Y- 1)9 = (1 - 1- 1) f
  28. hh = f (. + 1. 1) - 9 (1 - 1. 1) =
  29. 9(1 + - 1) = f (1 - Y- 1)
  30. videtur posse fieri th: fg = b: a posita b constante
  31. et fiet f: 9 constans ratio et h. f constans ratio
  32. et
  33. h:i constans ratio, et m. n constans ratio
  34. Alitrri fiat Sd. f(it .1) - 9 (1- 5.1 = 5508vo
  35. etbs s
  36. su
  37. gg ag199 5 = + gvr + 9 V _)
  38. 3d= 5oC it no vol cpt.
  39. sit Z - nabb aequanda formula quadrato, fiet fiat G Z = a 3: _ fiet a y - aa bb I : 214
  40. dibet etust -abb aequari quadrato, sid _ sab = va, fiet a y - a aeq. quadrato vel
  41. tandem yt- vt debet aequani quadrato siat yy+ vo = mme:a et gy -on = nne: a et sit
  42. Ee e: a = fg: aa = hi: aa y + v. + -1 = mf: a et y - v -1 = mg: a, et 2y = m, Htg: a
  43. et 2v -1 = m, f- 9, : a seu 20 = m, f-g, : a -1 y + v =nh:a y -v = ni: a sy 2y -n, hti, : a
  44. et 20 = n, h-i, :a. Ergo ex duobus valoribus ipsius 2y fit min= hai,:, f+g Et similiter ex duobus
  45. seu m:n = L1y h- 1:, f-9 quas duos ipsins m: n
  46. Valoribus ipsius 20 fit m: n = h - 1, i, (f - g, : - 1)
  47. valores aequando fit f. quos duos ipsias m: n Valores aequando sit hti = s-1, h. 1, adeoque fiet
  48. pro i substituatur ipsuis valor fgih, fiat hh+ f9 f.1, lit B9, adeoque hiti s - tit g tts g. sgg chli J. s getihius Ggu sas
  49. h,5+9
  50. h, 5.
  51. et fit hh f (1 - + -1) = hhg (14 f -1) = -fg (1+ . 1) Tes + f99 (. - Y - 1)
  52. seu hh= F9, f (1+ + - 1) - g (1 - 1 - 1) g (1+ + . 1) = f(, - + - 1)
  53. ffggaa
  54. = = ht
  55. vv qu (9 (Hl. 1) -f (1 - Y- 1))
  56. 9 (1+ 1 - 1) - f(1 - f- 1) fiet f(i+ 1.1) -g (1- L.1), in, 9 (1+ . 1) - f (1- - 1) = fgaa: vv
  57. sat 592+ -1 - fgei 2f - 299 = fg aa: vv seu H+ gg = - fgaa: hvV
  58. sinliceret facere videamus an licent facere fgaa. Evo = Bfq + ax ab. seu aafg = 2β fgre + 2aaD vv
  59. 4 = dd =09 = 1699v + g9 a
  60. seu sg raadvo a 20 ff +2s dqon daa
  61. sed ita aciditur in priora
  62. 16 v2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 15r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0029?run=74