Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 175r

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. 174v); this page is its right half.

The machine reads it as

  1. Invenire
  2. Hujus problemalis osanna non nisi unum exa
  3. porut vid. Dian
  4. 690.
  5. anver
  6. 3 jil 1t14 A
  7. eactem
  8. Ut Triangulum Rectangulum in numeris, ut summa aboruta id lalentus
  9. sit cubus. Tiranguta Latera Trianguli Rectanguli sunt
  10. 2ab, 4a - bb aa + bb. Horum cub 32 a Cubi collecti dant
  11. 2
  12. 14) 162 (17
  13. 3ab + a =3 at bb f3a a b b + a (3 a b0+ 3aa b + b = c
  14. (3
  15. 2
  16. seu 8ab +2a + 2b = C3. sit a= cd et b2 ce et fet
  17. sit c aa + bb + d et fiet 8ab u + (2b (a) + 3 ab + 3a b+
  18. + 3 a bd+6a bd + 3abD+ 3aa dd, + le dd + d3
  19. sit c = 2ab + d fiet (8a b) + 2a + 2b = (8a b3+ 12 a bd +6 abdd + d
  20. jam aggregatum duorum caborum semper est divisibile sit X3 +13 dividi potest
  21. per, XX - xy + yy. Ergo et a + b dividi potest per a- aabb + b+
  22. sed nescro an sic rucremur prastat aequavem reducere
  23. (2)
  24. problema ad simplius, e nempe sitr a = d et b = e, fiet
  25. eab + a 8 de + 2dd + 2 ee , C faciamus eru d
  26. c= fd et e c= fe, et d = ge et ReY
  27. 8gec +299eC+ 2eC L f3C3 et divisis omnibus per ce,
  28. fiet e= 2+ 8g + 2998,: f3
  29. 63
  30. 110)
  31. 63. Ergo tantum
  32. dpus est 2 +89+ 24g aequare cubo (5b3 seu) h
  33. seu 99 + 4g. = 13. 2- in seu 99 + 49 + 4 = b: 2 + 3
  34. V(II
  35. unu uende 9 +2 = Sih + 12. 2
  36. seu fiet 2+
  37. (10)
  38. itaque opus est 2+8G + 299 aequare cubo, (f3b seu)
  39. et fit99 + 49 +4,
  40. ∞2)
  41. (1) Dxh - 1 + 4 seu g + 2 = S2t + DE : 2
  42. ergo seu a: B3 4Y t3+ E2 B. 16, :8 Ergo re
  43. (74.
  44. huc redit ut V4 St+i = 16 sit numerus. Ante omnia
  45. ergonh3+ 12 aequetur quadrator in definite seu nm videamus quomodo
  46. formemus 12 ex A. H + un + na + n U + tm + mn = 12
  47. I + m 3. m sit latus quadrati a et fret
  48. h1) amm (F 12) + ginim seu mmh = 4m + 9
  49. fiat aef. n -2 et m pt2 Ergo ex aequ. N. fie b
  50. n_ - 6n + 121 = 8 + 12 = pp p + 4 Unde sit
  51. l1ct)
  52. +94s
  53. Ergo se sed ita oporteret = 12 +89 + 1299.+q aequare quadrato
  54. Et ita nihito facilius hoc est pri aeque Isi
  55. prastato rec
  56. uideamus quid fiat, si redeundo ad aeq. I1 pro g Rbnamus
  57. pro9 seu a:6, faciamus r3. et siet.
  58. 2 + 8Y3 + 276 = h quia autem
  59. habemus unum exemplum 3, 4, 5, fiet tunc a = 2, b = 1, 2 + C = 6 d = 8 C = 1 f =
  60. V
  61. 6
  62. = 8.
  63. AY3 + 4
  64. Error fuit in calculo reassermam

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 175r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0349?run=74