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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 21v

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: 0.78.

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The machine reads it as

  1. Hinc apparet modus aequationem hansfeeo mulandi in difficliorem, quod ulile
  2. aa hay + mydx + G n dx ex y fiat svax et pro dy fiat vdx et
  3. pudibil hrdx + M RVdx + msvdx dx + ndx = o seu hv + m sedx +n = 0
  4. inde differentiando fiet hav + vdh + mvdx + am (vdx + dn = 0, et
  5. pro sodx substituendo valor, - hV -n,: m fiet mhav + m, vdh. + nim bdx, ndn hvdm
  6. seu nih. do +
  7. hv dm
  8. Sit ponamus log. bi a esse 1.
  9. f
  10. eam
  11. maecedente fine paginae, etiam gradus fit
  12. attior
  13. egut alyamania ny + ap- aseu per cumpendium ag+ nytap= o, unde diffeccaliand.
  14. ag de. b + Caadque b t ndy +yan t adpX? jau B = = ny ap,: a9
  15. ddaqs
  16. et siit agnysde tagapde + aanydus +da ap dg. nag ) aaydn- aaga dp
  17. a9 b: a)
  18. et explicando regnu trapusse qu
  19. vill
  20. reanyduscgndus + a p dg
  21. a
  22. 9 aep
  23. Fn
  24. etrsus dm=m
  25. sit aequatio aydys + aβdy + Jydx tad ex = 0 quae multiplicaliper 2Cgn + aeq dabit 12gcd x sat a . ad
  26. gyan
  27. 2aFgnydys + 2a (Bgnydy +2CY gnyyex t Za cbguis + R B9dy + a 9AX
  28. fi Ex gyydx fit dl = 2c) dx: aa ex dus sit n g = gpl - agn, : aB = grul - augnri aa B
  29. +a) Gy x
  30. unde ex ydys fit ant + 2 a Cp = 2 cBndpl: B - Bn: B seu p = apl 2BB+a seu p p rantndra
  31. + aq ydy
  32. e
  33. aat - ZaBC
  34. Next te sit m blypaxagnabgnax-aa gnpaapdus argneaa gupta ac a
  35. Ex ax fitBBdm Bepdus Ha ap = Dt opdX- abgn ax Unde habetur
  36. -2aBpac dgndx - aApae VyxaX + afea ondx=
  37. et proppouendo valaen nia frit aa BVnx- Dsgap ax- a Brtipag- a B pg5 an- a para Crrpnal
  38. at Brundus-2aβCBrgunax Ng pnaX + Vr gunax = ernat gun
  39. si q et dg
  40. Et potest compendii causi fier
  41. luas et 2
  42. cyytalyrnaai nytap =o seu aqs thyrap: ofit a de b randytajant auap
  43. Ubi illud pulchre evenit,, ut posin ubique non extet
  44. et pro be substitiendo valorem fiet any de undq ayan-a =. junde- rcgag ratsrag lacem
  45. nisi n et an unde habetur an, d. Y
  46. aq
  47. Resumatur calculus:
  48. acep y ds + a lpaus raangyal + ea pydm
  49. y+ a pam
  50. Eydu - aide
  51. et f zaenyydy f caralydus +
  52. sit aequatio ag dus + aβdys +V ydx+ ab ax = quae multiplicata per re ny t aaque dabi l
  53. ndy
  54. 2aCnyydus + 2aβcnsLy + 2) nyydx + 2ac bnydx
  55. +aq qydx + aBgax S
  56. Unte per - yy dx est dl = 2C. aa) B Vdx seu l = XC: aa) s)ax. Ex hyfit 9 = lp - an, : C
  57. +aqydu +aBgdu
  58. unde ex
  59. iy dy fit, aut Bl a βIn + 2 aβCp = 2βBCn + aalp= Bn fit p. n = aB l- 2BBC + a) :, aal- 2 aBc
  60. Ex de fit mat
  61. E Ex ex fit arnam,agran- astr - a BIrndx - a Bn ax. seu dm = ad Brda + aa Bn di + B lynax -accDn dx
  62. i et quia ljam inventa est potest compendio dici p = In: a et ap = rdn + nuY,: a
  63. a Brn
  64. Restat gux unefini ata an + BaadF+ aa bl ax-aa aa Bdx paur XI( a B du) - 2 ac CD ex r f-)a dx
  65. am =, agHn: a) tadm F at rn dg - agden) N- tgrn a on Dil gn dx u na Degndx,
  66. in dm = (- a d9) + den, O dx -ad dx
  67. Yn
  68. a
  69. pursus am = 2acd 1x + aa g Y dip A duf B dg.
  70. aegl
  71. aa (5
  72. vil
  73. a
  74. videturres haberti
  75. sed verorne sit enor
  76. sane habetur san et satn
  77. rn

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 21v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0042?run=74