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Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 33r

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: 0.83.

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. 34v); this page is its right half.

The machine reads it as

  1. antur 8+ d equa d+c 1s eed pponatu equ
  2. et puendo d+c+ao d0c rd seustacer c
  3. sed pamo
  4. non licet au
  5. d’aequ nis drC +2de aequ. m3 17 + 1- 2cd. seu daeaqu. m
  6. c-C- 2de - cd equ il+cd. faciamus d aequ fcC
  7. fiet: cte-2fe ef d n ret
  8. euesqu
  9. 1c
  10. Datum cubum oblitri partiri in duos
  11. d’+C3 aequ. hi3.
  12. seu d-
  13. seu d.
  14. cubos.
  15. haequ. m d+c. Ergo d + c- cd aequ m, d +cq ud
  16. 3- 2cm
  17. 1- m3
  18. 4
  19. elcet
  20. =c - 2c m aequ. f
  21. E 1- m3
  22. Equ. 4 (2) c. Eem + m31C
  23. etrcm aqu. sC. m4 +C m) m 2C m + m
  24. 21 - m
  25. 4 = B M + 4 mo
  26. tc + 2Cm aqu E Y () 1- Dem - 4(3) , - m
  27. 2 - dre
  28. sed difficili. paulo est efficere ut -7 +16m B8m+ 4m sit quadratque
  29. la problema aliter aggrediemur, unde apparet multum
  30. interm
  31. 2)
  32. d+ C’ aequ. h. Ergo d’+C + 3dCd Hc aequ. h2 + 3 de, dc
  33. ponatur dac aequ. l. fiet. l’aequ h3+3 de dc. sive l - k aequ. 2 de dtc
  34. fiat: d+C aequ. m 1- h eritue P+ h + hl aequ. 3dc m Nam.
  35. nimirum in aequ. 5. pro d +c ponendo valorem ex aequ. 6. et utrobique
  36. dividendo per l- h.. jam. per aequ. 6. est a aequ. m l - mh -c
  37. quem valorem substituendo in aequ 7. fiet:
  38. l+ h + hl aequ. 3m d - 3nch = 3mc, et ordinando.
  39. (10)
  40. P+ ti hC
  41. s- (h -13 - el
  42. N+I +lh
  43. seul = h3
  44. h +I R + lnsmetgnie aqu. l’ +olmer guic, +, 2ni le - 12 me
  45. + 3uc
  46. (11)
  47. quod rursus ponatur aequ. l + lcn + c21.
  48. aequationes, una: ha lorvis aqu L + ca
  49. Tende oriuntur duae
  50. 13)
  51. L + 1h + 1 46mic + quie laqu. + len + eri, seu h + mC aqu (1+ cn
  52. F3nC
  53. (14)
  54. (12)2 12
  55. et: (17 +6 lm C +9m C (4 12 m. 1d = 12 mC aequ. (17 + 4 len + 4c
  56. divisisque omnibus per C, fiet: 18lm +9mtc - 12mc aego 4 ln + 4cn
  57. supra autem habuimus: d+c aequ. ml - mhr. Ergo pro tribus
  58. literis. d. c. C inveniendis, habemus tres aequationes.
  59. Nempe per aequ. 13
  60. sit: C aequ. het 2h. per 13. et C aequ. 4ln = 181m ex aequ. 1
  61. n - 3m
  62. et duos ipsius Cvalores aequando fit:
  63. 18)
  64. 9m + - 12m = 4n
  65. laequ 2h, 9 m t - 12m - 4n
  66. denique. d aequ. Emh, 9m - nm - and = mh 2h n - 3m. 4 - 18m2
  67. n - 3m, 4n-j m
  68. dere
  69. n- 3m
  70. (19)
  71. Unde jum d’ye esse aequ. h3, substitutis valoribus ipsarum d et C.
  72. verum ad huc debet esse aequ. d+c per unde ex aequ. 6. fit: aequ. ml- inh
  73. q nh qui vator aequandus est valori reperto in aequ. 18. ubi
  74. m- 1
  75. patet primum destini h. datam quantitatem. ubi sx poneremus
  76. 2+ m - 1 vqu0 fieut, n - 3, 4n - 18 aequ. 0
  77. 35
  78. id est.
  79. (25)
  80. ponendo e in aequ. 1 et n aequ. 3. vel n aequ. 9 35
  81. erit problema solutum. Tantum videndum an numeri, d. c. fiant atigmatir
  82. ed vndeo rem non procedere feres enim per 20. Claro ip 1g0. 0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 33r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0065?run=73