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Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 9r

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: 0.79.

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. 8v); this page is its right half.

The machine reads it as

  1. Quid si sic breviorit calculi causa
  2. Xia = s, dZadv - dodaz,: d bdZ
  3. y: a = du: du dy: a = d7a d v - d vddq, : d2 q
  4. et duyi= sed ita fieret dy. dx = dZ: dv, quod nonhies
  5. An sic g: a = dv: dzue et d X: a =sddz: dz. fit dy. ax = (l 3 llv - dvllz B,. Ax dy) : (217 24
  6. ob . y: a sumtam = dv: di Z
  7. sit sit in aequ. data dy : dx = (X: a) = (V: a) et
  8. ex 3 et g fiet (ddv: dd Z) = dv: dz = spad Z: dz) (= dv: d2 sit constans deo = (B) dZ dd y: da
  9. seu dis dyndx 2) (dav: dd Ze) - dv: dZ
  10. S6 fiet dZ: d = (D5 ddZ: dz et ddz: deo = d dZ: az seu dco = dZ et daz = dev
  11. av = dZ (1 = B) Ergo ya foret constans ratio, quod absacue
  12. sit ergo deo = ) dz dd v: dazue et ex set 6 fiet dc: dZ = 5dd Z: dque et deo ddz: de dz = ddz. de
  13. et dZ = do + dco Ergo P E.se ex
  14. quod rursus absurdum. An ergo sic:
  15. dco= d dz: dav, et exs fiet
  16. da vadv: adzue db
  17. = dv: dz= d = das: dx quod est absurdum
  18. et davddz ddv : dco= ddZ 2d
  19. Cdv + dZ) ddv: ddZ v F S SdaZ: dZ = dutdzue: deo posito (dv + dZ) ddZ: ddv = dee
  20. sed ita fieret dav: ddz
  21. 447: dZ = ddo = daZ,: deo. unde dd zidz = dd v + ddz, ddao: (v + d2) dazue seu fiet
  22. dv: deo fadzue: d
  23. Ergo - dco,
  24. et fit ddv: ddque = dv: d2
  25. ddx, do + 4 = 4 + 1 +
  26. hanc Methodum non procedere, quia scopus
  27. daze ddiZ (dvtdZ) = ddvddo + lvdaz, aZ fiet it
  28. D (( +
  29. est, ut ante pro quadrabura inveniatur ado: daZe per do: dZ,
  30. ddo: ddz
  31. sed hoc
  32. ergo calcu Methodus pugruae praecedentes quam hactenus
  33. invento patet ex bb 1 et 3 habitum iri dy: Ax per y: a
  34. sed video generaliter
  35. seri da
  36. apaeramus fantum exemplum tractatu commodum
  37. et y. a L) 5ddZ. dZ fit dy: dx = du: de sit aequatio data
  38. quae est ad sectionem sonicam in fine pagnae primae huus plagulae, nempe
  39. Retinende est
  40. dx: dy =14) 1y: dx = (4) t _ y: x - a:y et fid dv: dq Glq: deg: Solaz. dv - 1: (daZ. Z
  41. reprobare non licuit
  42. Ed= (dZ: du) ((da Z: d2 - 1edd Erro ddz: dz = daz: dv Bvaq - d q lav) sclib. 13. 1)
  43. sit ge X: a = ddz: dv
  44. seu dque (dv dd Z - di daZue : (a DitZ) d velv:, du dazue- d27 cax = s ddz. dz. ubi non licet ponere
  45. adv = 0 et generaliter in hac methodo id permissum non est, nam alioqui haberetur
  46. Cdd7: d7
  47. foret constans quantitas
  48. et haberntur do per do: dZe sum
  49. assumatur dco = di dav: duZ et ex ea fiet
  50. habereturque praeterea sine quadraturis x aequatione
  51. Aco dZ, v. dZ): (d- dqe B(d v. d) (a0 - dzue. H av: du)): aede dv - deo = sadz: d
  52. evanesceret, et ddz
  53. seu dodo dz de ique dudo - d vdzue : d Z duaz = deodz = 5 ddZ: dz
  54. video difficulter assumi posse deu
  55. siet aosd (dvdq . deo dq doddo - dxtaz- didax) - (d vao - eodi B, av altztay auo - do t) daz
  56. Se C2 (vdod ddo = avavd z a X - du d 3 dz ddv E.l cod Z lv lo + duvtrar at deduly dam
  57. 2), dodz - dco dz
  58. = dudiqu duavazu dao evar
  59. dvavardaquet dvuez tav duaz aeo daz
  60. et pro deo substituendo valorem ethaliqua absolvendo fiet
  61. (2), dudz - dcodZ
  62. + Z d Z lZ ddv dax (ctd2) - 2 dZ dzue dx dd v dd veld Z
  63. do3 ddz
  64. Av do dZ (13) ddqu ddzue - 2 dvd lavaiz + d. d dldvado
  65. Az davao - 2Z dv ddvddav - d vellaz adz = dvar, due dazaaz - 2rddz av da XF dey delvaldx
  66. dento ee t
  67. daqe cu
  68. seu dar
  69. Et fiet Lud
  70. d (r2
  71. et seu d dez=
  72. d + dos
  73. d st + 24Z1 7 lv C az rd v)
  74. dodv (21 (dz + dv)
  75. de +2 d 7aZ + dz Ld 2d Z + 2 dod Z + 2d0 dv)
  76. 2d2dZ C a 1MavBE a +do)
  77. d7+26
  78. d 12
  79. etti X
  80. etq + 2dxdo)
  81. v
  82. xdz + dodo
  83. dv, dody d (1+(1 + 2. 4
  84. d
  85. ilo hotis- quadratu, C
  86. Avaro - dx s( + 2du +2
  87. +dodg et fiet do =
  88. ag =) des des - q dqu. 17 d2 =
  89. 12 (1- 4 12
  90. Edvdv) = (d 12
  91. ita reducta quadratura foret ad rationatem
  92. et latd+
  93. M 19dg = d2a2,: at
  94. 2 1 -a 12)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 9r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0017?run=73