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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 268r

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: 0.81.

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. 267v); this page is its right half.

The machine reads it as

  1. man
  2. M n . Cm abn +d, multiplicane per quantitatem, in qua M, et n non
  3. extent nisi dato gradu praeditae, e _ eodemque modo affectae, sint autem d. data, at c. et n. quaesitae.
  4. cM + b n + d in em + fn + 9, fiet: ec m + eb mn +gcm +gbn +gd
  5. fb n +fc
  6. +de +df
  7. fiat ec + fb. sive b, eC. rursus eb 1- fc sive b, = fe et Quod non
  8. procedit nisi f sit quantitas impossibilis, Unde etiam b fier impossibilis sed si omissis terminis
  9. m. n. reliquos examinemus, eb + ferjo sive b pp FC et gc + depjo. sue epp- de,
  10. et 9b + dfB0. sive bp = dt - FE sive ess ed fiet rursus absundtum,.
  11. sit b m +Cn + emn + d. Ho. ita multiplicanda ut prodeat qu mn vel mn, vel mn,
  12. aequalis datae quantitati hoc se ipso praestabitur. Ponendo b et c 10.
  13. Sit bm +n +v, + fmn + quiv + huv + d 1o multiplicanda per totformulam talem, ut
  14. in producto tantum restet mn + M V +n Sed hoc iredo impossibiet
  15. si essent equationes nn mv + ntv t9. mv FY
  16. m+ n v S.
  17. foret m + q md + rM + s 10. Et componeretur radio una aequationis quadra.
  18. ticae, ex tribus radicibus aequationis cubicae Haec si succederent valde commoda forent
  19. sed non video quomodo facile succedere possint. Habemus quidem aequationem m +n v
  20. et mux datae, unde fieri potest mr v Y. Sed habemus, mn+ mo +nvri datae, ut 4.
  21. quod turbat
  22. X X qX + rno. XH 1O Y + tXF4 + 1O 7- Y +
  23. Sro x ponatur y + p. fiet y +3p V + 3pE V + p B sit data aequalio; y + b st +Cy + d o. conferatur
  24. inventae, fiert PB) b et q c - .
  25. c
  26. 4 1
  27. + qu
  28. ir e r 4. + B ⊓ d + 2, b e
  29. d + 4 db7 - 2 dcb, + 4 b6 = 4 b + c262
  30. 4, 27
  31. 42727
  32. 27H - 3, c, b + 3C b+ - b0
  33. Ergo Y + q
  34. sive distincte scribendo:
  35. 27, 3
  36. 27,9
  37. X + 2, H
  38. 27, 27
  39. + d
  40. 4, 27,3
  41. 4,9
  42. = dch, cb, + es d + db- 8. eb +0
  43. 27
  44. 9,2
  45. 27
  46. Si alsit C, sive aninus pemultimus in data, fier y ( _ + B + Ae aB + s = + B -) , db
  47. relictis autem omnibus fiet VF 13) = d - cb + b
  48. Povamus jam b,22 Cr 2- 4)
  49. de - p
  50. 2n + Y = B d- .b + db3 +c
  51. 36 2t
  52. 0b7
  53. =R, 823
  54. -362
  55. et =H = R (+9823, - 22) + 224)
  56. 2
  57. 27
  58. ber 42, 2-885165
  59. debR 2 - 2R 4)
  60. +E, 1 2, - 3, 427 + 3. 1652
  61. 27 Si
  62. t
  63. = k + 25. 22+ a)
  64. 4 27
  65. Data aequatione quadrato quadratica, ut quam simplicissima
  66. habeatur irrationatium expressio utile erit tolli terminum
  67. X + rX +s B sit XH X + b.
  68. fier: yt + 4b y3 +6b2y + 4bY + b4 +0. Unde ut selent
  69. p. .. + 3pbe. +3pb. + p b
  70. 1296. + 96
  71. lenminus fiab
  72. negativus, erit
  73. ec 6b2 3pbr
  74. + Pb +
  75. 2P
  76. 16
  77. Ita enim statim redinet
  78. ad (ubicam, secundo bumco
  79. carentem resula Huddemi
  80. se lertium X + pX.
  81. 1
  82. erit - +

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 268r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0535?run=74