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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 177r

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: 0.79.

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The machine reads it as

  1. y, 1. X, 2 (,3
  2. riangulum Rectangulum in numeris invenire
  3. cujus cuborum a lateribus summa sit cabus.
  4. 471
  5. 4
  6. 2. 1. 2
  7. e
  8. Latera quaecunque Trianguli rectanguli possunt sic designari, Xy, Exy, Xty
  9. Htorum cubi erunt X - 3X + 3Xy - 8Xy, X+ 3Xy+3Xyt
  10. summa cuborum 3xb +6Xy + 8Xy e aequanda cubo xe Adeoque
  11. 2.8
  12. 2.(9. + 6. 4. 1. +8. 8. 1
  13. 8. 27
  14. (
  15. (2)
  16. 2X +6y +DXy = xC
  17. 32 16 + 16 = 2. 27 -5G
  18. Explicemus omnia per y, et sit X = et troy 01+ 10y et e= 20+10y, et fiet
  19. 2X+ = 72. O1 + 2. 401. 10y + 2. 6. 01. 105y +2. 4. 01. 1037 +2. 10 y (e = 20 +3, 20. 100yr 3. 20. 100 y11107
  20. 6 =
  21. ... - - ---
  22. .--
  23. +16 2
  24. + 0 1 + 109
  25. . . . - - - - - +8. 01. 1 + 8.10. 25) +,o y 4 3 1oddicoy 19 , 0 3. t 10100 G
  26. +8xy =
  27. Xe = fO1. 2= 10203y - 3. 1a 20. 1001 4 3 1020 ve P 1o 1 s y (F 1 20 + 3o1 1 . ) 3. 31 b 15 + 01 10
  28. 16(7
  29. =3. 91. 20.100y 4-3. 01. 20 1004,2+ 01. 1007 y
  30. Si fiat 10 =2 et 100 =3 evanescit At.
  31. aqu. 0. unde ut evarescat ist, fir 2 - 5. 848-27,:54 01
  32. seu 20:01= (45: 54 =) 5:6. Restant termini Y y, y.
  33. t qui explicati dabunt: +2. 6: 52. 26 +1b 6: 5 26 y +48.6: 5 26 y
  34. (10
  35. - 6:5 20 = 82. 2037 - 18. 28
  36. = 96: 5. 28 y - 27. 6.520 y2
  37. sit jamaequatio m + mq y + ng y
  38. in + ny in p+97
  39. nBy
  40. =0 ubi dividi possunt
  41. omnia per
  42. ubi fi (20 = mq + np, :, 16. 6.53 - 2. - 9. 6.5 seu qqundio 20 = ingerpi c
  43. fit mp + mgy +nqyus
  44. +n p
  45. 2c
  46. ob ysit (12)
  47. et 29 = 48. 6.5 - 18 - 27. 6:5 seu per qend n9= f
  48. sesit (14
  49. 65)
  50. Et ob y fit mq + 2mugp + n p, per (2. 6: 5 - 6. 5 seu per) 9 = cemm
  51. et tollendo n per aey. 13 ex aeg. 16. siet W F Mq + 2M fp + s= cemm: 9
  52. sit mgq p + f D seu m qp A e sit p ArH et ex
  53. 19
  54. aequ et ex aeq. 17 sit in qeamsans coterimqu cm . 9
  55. (20
  56. quae equatio diveltatu in duas mtamsq ce m q. g, lus qsm
  57. E
  58. ot
  59. seu m= 25 g c 9 et r 2h. Erpo p2. h pr 13 et 9
  60. et aseramsrs
  61. b
  62. sit p= 1 + Y et 1: g = 1+ b quae est cognita ut g.
  63. 8
  64. (20)
  65. fiet xg. 17. n g+ Emfgtamfar+mfgr+ - Cmq +em ab
  66. quae aequatio divellatur in duas, ambas deprimibiles nemper
  67. e1
  68. mq +2mgf+ 54= eniqu et amfrtmr = mb
  69. unde fit m g + f = +C m 9
  70. fit m= f: fq - 49
  71. et 4fr + 2fr = eb m
  72. et m= +frt2FY,: cb
  73. (
  74. et sit cb= 4cqr + 2c9fr- 44gr- 29q r, ubi fuciendo qr = Xc
  75. fiet ctf 4 ac 1 rc fiet cbf - 4cco + 2C frco- 4gco- 2fco
  76. quae divelli potest in duns: cbf∞ t fr et - 4.
  77. cbf t Cgr + 2C9 frY et 49yr 299 fer=0 simo non licet utiq
  78. aeg. 2a nam ficiet
  79. a
  80. (29)
  81. et fiet q Obsgi aY+2fr et (Y = - a. -(0)
  82. quae divelli potest in duas: +2c9fr2 - 299 fr = 0 et ebf = + 4cqr- 499r
  83. unde ex 28 fit g = fc et ex 29 fit Y = bsg: 4c - 4c quod absur
  84. est
  85. s
  86. 16
  87. 48

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 177r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0353?run=74