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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 214r

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: 0.80.

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. 215v); this page is its right half.

The machine reads it as

  1. 2 Maji 1696.
  2. Addatur shediasma praecedens 1. Maje
  3. dimensio Curva Conicae reduci posset ad
  4. Quadraturam Rationalem, si posset extra
  5. extrahibiliter deprimibilis reddi. hac fssml ex aula
  6. formula bX +. X +. x +. X. Hoc ut tentemus, sit bXx + ccx+ d3 intte
  7. Itaque re ut reddatur productum deprimibiliter ex trahibile puematur ipsius x
  8. valor talis et rationalis, ut nominator sit quadratus e non assurgens atera ju,
  9. Numerator vero talis, pariter et nominator, ut rxte non assurgat
  10. non contineat in valore irrationali nisi Ly+. y + y; et numeratir
  11. Et 2do valor vero ipsius bxx + CCx + d3 sit exhahibilis Hae–
  12. Haec ut assequamur fiat primum brevitalis eausa. X = lyy +m,:gu
  13. ila , prior conditio obtinebitur nempe a+ =tE+ y ( C) Vyt: y
  14. sed inu et posterior tentanda est fiet
  15. i x = buy + 2blodyytom ∞ fpssy trofyy + an
  16. Cc Ex = ccl. + ccm.
  17. = d:
  18. ergo bff = bll + ccl + d seu f= Sbll+ ccl +d3. b
  19. rursus 2bf = 2bl + cC sou f = 2bl + ec, : 2b
  20. Ergo bl F ccl + d3: b = 4bbu + 4blcc +C,: 4 bb. seu fiet
  21. GbbU + 4bl cc + 4bd3 = (4 bbH + 4bl cd + ct. sed ita evanescunt quaesitae
  22. et nihil est actum, nique adeo hac via obtineri ex trahibilitas depressica potes
  23. ot
  24. Faciamus ergo _ X = lyy+ m:, gyt mytun, et ita ert
  25. exte erit Setoyu + Ency + enn:, ytn.
  26. a yys tenye
  27. super est ut sit
  28. vel faciamus X = lyy + mmy+ n: gy fiet Sx+C = (t ejgyommy+n: y
  29. b yt Xx = bUly + 2blmmis f ibn yy
  30. + bm. + 2b mmay+br
  31. cc X = cel.. + cemm .. + cen.
  32. ..
  33. L
  34. bpe + 2479y3 + 26pV gy
  35. + b gt yy + 2699y + bp
  36. Quae frmuila aequanda
  37. quadcato a pyyty+n ducto
  38. in B, lyy
  39. ly t mms jus
  40. +2l pi tumon By + 2X py
  41. + lpp gs t mmpphs
  42. Ergo sit 49 Y6 = n6 et gu vel siplacet ro - n et qq = mm
  43. et p = 2bl + cc,: 2b = bu + ccL + d3: B. Funde (4bbl1 + abl cett E =(bb l + 4blcd) + 4bd
  44. ubo inciditur. in idem inconveniens quod ante: itaque faciamus,
  45. X = lgy + nmmus + 13: y+p, et ut interpretemur bxX + cc X + d, fint
  46. ypt XX = blly + Eblmm y3 + 2bl r yy
  47. + b n+. + 2bmm Ry + bn
  48. CCyt X =s cel + cemm. + CCM.
  49. +2cc lp +2cemmp.. + 2CCn p.
  50. + cc. Lpp. + cemmpp. + ccr pp
  51. dg. +4dp +6dpp. +4dp. +d
  52. per compend.
  53. aequ. quadrato a qu tryt
  54. ducto in a
  55. seu
  56. (∞ agy +2a9ry + ragtys
  57. art yt ra ly
  58. aeus i taggy + a hy + d a R ∞ agqust ragrus traq
  59. 13 = (+) 1 et rr = 15: 2+3 = (+) h: 2k3)
  60. a72. t at y ab
  61. un eex A+ +) 1g+CK + 9b -= 19b - = s’KS
  62. s
  63. Ebmmud + recrep= cemmept 4 D p3 SoulAd
  64. = +ce + (+) 2eH e + (4) Sh: qeK illium temim t rcclp. +ad, Son t Cp
  65. seu + (+) 4 ek g = 8 eeK F fh
  66. 2
  67. +2
  68. fit g = +e et 1r = f. 29 = 75: 2C 7 + BK = (X) etr vel 4(+) 5N = + eti
  69. (+) ek AAa
  70. seu 6. Ne autum calgulus Sit X- veo
  71. tit (+) ppIo = F C
  72. vet , adeK3: pp vocemus r
  73. quasi a
  74. tas perinde ac si l et l essent date. Iu f est y vel mon
  75. alit
  76. n
  77. EtG Endem itatabe
  78. inde derivatis aqualitaltina siumpitur ex hongeniorum ipte p oc im. Hine rilile pulo fima raons ris pt
  79. liter
  80. quar
  81. aqu
  82. Ns ac et i t eeS tontrad m da nbim

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 214r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0423?run=74