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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 321r

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: 0.82.

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. 320v); this page is its right half.

The machine reads it as

  1. V vib, vrC = ito
  2. v = i Hm L 123 Imn
  3. _V = +EUlum + BL 14. 1123. 123Im An q Hac quantas
  4. iss unumta 4. ter ns rem.
  5. +a vo = 1e af lm
  6. + 2. 112. 13af M B SIn
  7. + rapus An
  8. siet sit aq m fiet p = Et 3. 12. 13lmm +2. 112. 125 mM. + 112. 123 afm
  9. + 1122 125 aesfmm +
  10. aequ. 12 gulmm + 6. 12. 125 4glmnn + 12 afg glim + ae994
  11. e u ore
  12. 112L mm + 6. 12 15 nm +ag
  13. opsitet jum ut 9 possit haberi rationaliter
  14. etamsi non integre
  15. compendio sit e q9 + a5. =0
  16. fiet q- argu r aarr-darrs
  17. seu qq = ar + aarr -5),:2
  18. Ergo Ex his patet si l, m, n sint integri simplices, etiam q fore talem, nam quia ipt valoris
  19. 1a mar at
  20. iis gu in integris, inventi non alius esse potest dirisor quam , qui non est ratiopelis. In, qui non est
  21. otitit
  22. dum per in potest dividi numerator
  23. Hinc i a pro aequ. et effi-
  24. cienda tantum oporeet, assumer l, m, n, g per X ratioraliter integre simple
  25. =3X + 3a q= 40X + g1 a ubi sunt et habemus hincliteras
  26. adeoque oporeet q fieri rationalem integrum
  27. sine lileris artiligrias 8. sed aequato hocrndo explicata ascendet ad gradum X adeoque opus est
  28. si imalimus p quoque esse integram, cumque assumere pro duplice, manente a simplice, potnissemus
  29. aequationibus destrnctitiis Z, ut aequatio fiat identica
  30. in ob irrationales ascendentur ad
  31. dX et opus esset aequationibus
  32. rationalbius comparatitiis 5 in summa novem sed litera praeter 10 supra dictas accederea
  33. identitasfacere duas aequationes, quibus termin omparantur et
  34. tres ex valore ipsius p pens nempe soxx +st ax +S2 aa = ap itaque videtur salis affore
  35. X, opusque esset comparatitiis aegqu. 4 ob ratiorales ascenderetur
  36. literarum arbitratiarum.
  37. pah tak sin extr sit extrahibilis
  38. B = ak : 2Y et aXK+ 47 =4 In = 4 aehV
  39. btih - aXL seu 2YY =aussaa hih . A Kla) + a t
  40. Aliter videamus quibus casibus formula
  41. ssit 2, a (3 + V sin L taa ββ + 2 a β) An fit
  42. In
  43. +e diu
  44. strisamus conpentio u apret ag W2t H 50. 240 X = 40 s0 X + 40. si a XX + 40.5
  45. compericus sintums
  46. noo redeamus ad cum modum qui rem red
  47. _n ln = WUX 10. 20XX + 10. a
  48. aax + 41 s2 aa
  49. Lnrjaa la mn = 20 30 XX + 20. 31 ax + E1. 31 aa
  50. rntionales integer
  51. sed valar debet es
  52. po. 125 Um = 11E qul1 min l. 1 112. 123 mm = 99. seu 9- + 2. 112. 123M
  53. -4. vi. 135 m pt a 4. 12 123 a fmn 4 115. 123 auffrum 4 123 ggmmnn + 123 af. g9mn + agqu
  54. t destruatiu ubi U, et habebitur
  55. Senquin q - 7m. fini
  56. 4.112 25 mEp + 4. 1127, 123 af m + gt - 6. 112. 125 49 mnn + 112 afgum
  57. =4. 12. 1236mmn - 4. 112 12 a fmmn -112. 125 aa f + 125. 7 mmun + 123 7agma. +. 7a.g
  58. 4. 112 125 mnn F 4. 11E. 123 uf F mim - 6. 112. 125. 7 mun ( 112. Zaf m
  59. mmn mnun mun mn nd
  60. 4. 115 923 afmC 112. 11X 193 afm connescit
  61. et 2. 12 123 mun - 6. 12. 125. 4. 112. 123 my = - 20. 2. n a mmn
  62. et ( 4. 12. 125 tuml - 512. 125 mmul= 123 mm n + 125 as mmon-n antuzasmn+ ag. t. aass
  63. sit ergo jam m = 10n + Ua et l = 20n + 2la
  64. cd hoc praestari non sb in rationalibus interus simplis, quia mmnt ninus assurgit
  65. Ergo redeundo ad aeq. explicemus dia per m
  66. a = 20m + 21 a et fiil + 4. 12 125. 112+ I M + 4 12. 15
  67. huut sepem aequationes ut destrnatur
  68. Me, M mt n m n, m
  69. liferae 10711; 20, 21; 30,31;
  70. ubis ex ipsis, 6, an atolli poles
  71. Itaq rspes ad huc est successe.
  72. la. = 6. 112. 123 In qq
  73. -6. 12. 123 Igen mm
  74. =112t uumno
  75. e extrahibee
  76. aili durit gaeis dclet al
  77. datur m, quaeruntur b et c. fit at = bbb + cem et g= 2bC. Vanur a, so
  78. vilitur ast semlit prdit ab
  79. vel potius in integris
  80. n es aar qua ubi cem ducto facunt am
  81. af abb+cem, diodo per n, socisque donec residuum quotiens sit quad alus et
  82. quid si hoc loco, ubi omnia debent esse rationalia procedatur, more Vietao ad imutatiorem numerosae ptotestatum
  83. solution
  84. residuus etiam quadratus quorum latera invicem
  85. at +029) B4. 1. n Pn ex ita non denominato
  86. ex frahendo nocet
  87. m umtum au )u ga biltinibi und u viaetu. quod ede
  88. dacere suetimman rere dili tntonatum e tau cotiet
  89. vider jam, si qdebet esse rationalis
  90. atiam aque deberese
  91. b q ab+ csum = acbb m +2abc Jam = as taagtam
  92. lietaeo extrahamus. Ha
  93. luu pomudsa et bistars. sid quae pisto altus asingit calido
  94. nn intigre simple

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 321r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0637?run=74