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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 253r

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. 251v); this page is its right half.

The machine reads it as

  1. X + m + m X + n = pX + qX +r
  2. X F 12m X + 2 n X + mmx + 2MnX +nn 1 =
  3. - p X = - 2pgX = 2prX
  4. = 9q X = 2gr X = YY
  5. X x bx4 + cX + dX + ex + f
  6. fit AC m= 2b - L pp n = LC + p9
  7. Yr(E nn-5) = q CC + 209 + 4 pp 49 - f
  8. 94 - L bb ab pp + 1 p 2p s ce + repus a +ppgu - f - d
  9. rursus rr = _animun- amne + ee,: qq = mmun-ane teC, :nim -2p
  10. seu er =. bb - 2bpp + pt _2, cc + EC P9 + 4 ppgqu = b. pp C + apqu e + ee,: qq = cet repqi ospus
  11. hX + lX + mX + n = pX + qX + rX + s
  12. hh X + 2hlX + 2hmX + 2h nX
  13. + U X + 2lmX +2lnX
  14. = ppX + 2pX + 2prX + ap SX
  15. + mnXX + LIMX X + XN
  16. +X t vX + WX +y X + ZX + CX +9
  17. pp = 1 + hh p = hl ergo 1 + hh = ht HI
  18. 2hlr + gq = b + 2hm + H
  19. 2hl5 + 2gr = c + 2hn + 2Im
  20. 295 + rr = d + 2ln +mm
  21. 225 = C + 2mn,
  22. Ss = f + nn
  23. =
  24. + 9q X+ + 29r X + 295X
  25. + rrX +2r5X + 5
  26. 1 X + vx + bx + CX + d X + C X +5 _
  27. t
  28. +M + y. +Z. + β +G
  29. h = 49 - b - 1, : Em - 2 1r = c + 2lm - 2gr, : 2l5 = 2n
  30. G 49 - b - 11 2l5 = In a = 2m - 21r. C+ 2lm - 297
  31. seu n = q9 - b - l 2l5 = 2m - 2Er C + 2m - 2gr: 299. b- d
  32. rurus n = 295 +rr - mm - 3 : 3l
  33. et n =, 2Y5 - e: 2m
  34. aequando duosposteriores ipsuus R valores fit
  35. Am 295 + rr - mm - d = l Ers - C 1
  36. et aequando priorem posteriori, fit qq - b - H 2lsm = m Em - EIr C+ elm - 29r = 49 - b EYs- e
  37. harum duarum aequationum ae fit 5 = D. m + dm = e l = mrr,: 29m -2Y
  38. et rursus s = n. Em - 2r E + ulm - 2gr = e qg - b - H : 9 - b - H. 2l m - 2Y
  39. qui duo valores ipsius saequandi sunt inter se tet p = e amm + 4r
  40. rursus hh = 1 : H - 1 = q9 - b - u: 2m - 2lr, quae est ceq. f
  41. Rursus nn = 5s -f = 4rrss- 4rse f ee: 4mm, habemus ergo novum valorem
  42. ipsius, S quem aequando uni ex prioribus nova prodibit aequatio e
  43. Nns aequationes D, 8, et resolvendo eva prodibit equatio calculus opinor satis ulte
  44. (pergamus in exemplo proxipur aq. 5. erit ay L ax +XX. Ejus differentialis esst- adu = adx+ 2x ax et fit.
  45. assurget
  46. dy: ax a+EX, : - a aequando aeq. 4 sit aa + 3aX+2XX- da, verum hi valor non consentit priori
  47. jam invento, nec hos ducit ad inveniendam e; jam supra ex 5 et 2 fiet ( 2X: a + X: aa= e-X
  48. quos duos valores aeq porio XX +Z ax Zaa= _S aa seu X = 15 : 2 = 3:2 quo valore
  49. substituto in aeq. 4, habetitur et e e = XS X: aa + 2X: a + E s lgcunde aretum ad
  50. pariter 8 ceptrum circuli, qui Logarithanicam osculatur, simulus punctum osculationis
  51. videamus. Mothodi bonitatem. probemus in casu jam noto, nempe cum parabolam osculatur circulus
  52. sit x sit ra yu et qyyl yy- caxt XX ft 2aX FXX = va
  53. et sit H) centum circulit et HB ∞ (et BC et ABLX et AH = b, et AB = b - X
  54. et latus rectur paribila 24) Hit at caX = gq bbL ∞X
  55. fit 2ab- raxFyy et py + XX= exprore eg fit adeL yay
  56. utamur solis 2 et 3 ex sit 29dy x ax seu ay du x X. y ergo
  57. ex 3 et fit x9 d.
  58. en xa
  59. rabu 2ax Bt rabo ExI XX = yy
  60. fit in parbola a
  61. X
  62. et pacg Ex Isii quex bad eyaus
  63. seu atx -q. r:: a. y seu ay+- 9y
  64. es at ae a
  65. et ex 2 fil dy: txL= x 9. et
  66. r. BP, a D: ga PZ: ZR:. 4: Y
  67. et, adque +. Xdy +y dx - aay = 0 et ly: x. 4: 9:: y: g- a -
  68. n Re AC. AQ, q
  69. ZR
  70. A a= a g = 3F su P. = 4u a, 3 fit
  71. 6

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 253r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0501?run=74