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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 72r

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: 0.70.

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The machine reads it as

  1. alem X, y, Z aebent fache quadhatu ex non quadintis,
  2. X=mm X = lenm
  3. 14
  4. 4 4
  5. y- Um X Umn y = lmmn Z = lmnn, fit 1 mn
  6. An sic X = Im y = In Z = mn fit xyZ = ummun. Ut servetur ex homoque crectum; sit
  7. ete qu+ha = lm
  8. Av. + hb = In hv + he = nn
  9. h sit unitas
  10. seR Ca C = n: V = ln: h = b. Ergo fit In - hb + ha = lm et ln - hb + hC = m
  11. et fit e lnn -hbn L han =(Cmn) = Un = hbl + hel, seu
  12. sit
  13. a
  14. ulet
  15. ubi si facias quaeras n per l pervenies ad
  16. radicem quadraticam, quae non cedet quae si lae. Ergo
  17. LMM
  18. c
  19. Ergo fiat hv + Ra = Impp ho hv+ hb = bngq
  20. E2∞ + EC = MMYY
  21. quem ipsius tix valorem ex media aequatione sumtum
  22. _ AV = ln9q - kb. Ergo Inqq hb +ta substituendo in pnabus extr emisfiet:
  23. langger - sibn rr + hangqrr = (Ima pprr) = leg9p = teblapo + ucpp
  24. aeret Ranrr help: llnpp -hblpp lnner + bbneY
  25. 99
  26. re pp: rr faciamus g9: hh, et fiet h an -t a h Cggl:, Uggn hl au gglln - hbgsgl- hhlun + titbbn qu
  27. aplicemus n per L faciendo n = 1ol + rh, et ita videamus an mudponi, denominator per numeratorem
  28. de
  29. divisibilis reddi possit. ita enim ae res reducta esset ad desederatum: ot nec tantum 10 et 11, sed etia in g)
  30. +
  31. apy 1
  32. crbutraria erunt.
  33. 15
  34. C
  35. Effici posset si han hC gy( ficret CfL; et seu si frecel
  36. cgge: tea A = th st + cggl
  37. Ergo oportat ut faciendo BEan = hC. 99l = hS f, seu, R= hhfC + cgahhf+ cg9) : ha
  38. das+hage
  39. se
  40. s
  41. AA
  42. ta tollendo R, tam iumerator quam nominator, divisibilis erit per L, et F evanescet l in
  43. C
  44. numeratore manelutque solum U, l et l in denaminatore, quae est formula aequanda
  45. a
  46. e
  47. a
  48. quadrato, quod semperr fiegi potest
  49. =anrr = seblxp = Rburr = teclpp: Unpp = IYr
  50. seu 99 = Krr (a - b)n K pp (C. b)L,: Unpp lnnrr siat p: Y = foh ubi a, A, Y et ) dive 6, l, p permutantur
  51. id est si rubique pro a, n, Y ponas respective C, l, B prodit idem
  52. quod nate et n ge 20t +21h, etate adi tollere simnl
  53. g4 = B (a- b ) F hi3+F1b-c) l: H nor t fIn - hhat nin Explicavi per 10ta + 1A
  54. Sit p. r= H. t.
  55. et uet explicatiorum factam tentavi tollere aint go
  56. et
  57. eo
  58. expcemus
  59. 0+
  60. A sed non licuite
  61. sit set (a b) n + f (b-C) l = hhgl adeoque numerata erit divisibilis
  62. per l, jam et nominatorem, hoc modo per divisibilem esse praevidemus. Fit n = Chhg - ff 1b- c)) l, : (a - b) hh
  63. piat. hit b)na
  64. intiltminatu non ibit ultra quadratam.
  65. vel per compendium n = el: R et fiet g9 = thgl :, s C ppes
  66. seu 99=
  67. 1
  68. ata pp
  69. ppll ell. h) et BC (3t h
  70. ., PCl - heell. et g= t ut
  71. Lf h ihg , lV (hppe- hhee)
  72. i

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 72r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0143?run=74