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Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 2v

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: 0.83.

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. 3r); this page is its left half.

The machine reads it as

  1. sint circuli ordinatim datri, quorum
  2. Centra in curva V(V), et, dalo puncto curvae i,
  3. inte Horum circulorum intersectine
  4. formetur curva Y (3
  5. Exnatura cioculi AX, X
  6. CyV v. VVOr. ZZ E=X + y -o L) rr. et pro
  7. concurtu circularum (2 - X) dX + (y- 0) du rar Et ex
  8. Circuli langentit, (Z- X) dx + (y- V) dy =0 seu Ddx: dy=
  9. Z-Y
  10. soeiitis
  11. 3)
  12. v.y fat sit jam aequatio data: Ax: dus = t: a
  13. Z- X9:, v- y (6to) F: a. jam ex aqu. 1,F, 1 et 2, inveniantur
  14. X ot Y, et substituantur in aequib Rursus jam ex aequ. 1. et 2. Invenians
  15. E
  16. X et y, fi et substituantur in aequ. 6, habebitur aequ. inqua
  17. solum Z, v, Y, dz dv, dr., Nempe ex 2 est
  18. v
  19. y - v = Y ar - (Z- X) ax, :dv = 1(rr -(Z -X) 2) et seu
  20. YX(drdr: d vdv) + (Z- x) 2 (dX dx: dvav) C 2Y (Z X) (drdx: de dx) rr-β X) =
  21. seu (Z-X) = - 2rd rdx (y- X) + erdrar dede guextrrade + rrdrardudx
  22. qdx+ axdip
  23. 12) (ax X+ dvar) ( (dx dx + dvdv)
  24. BY, drax + savire L + dB Fararae 3
  25. et fit R Z-x = s
  26. 10
  27. seu X = Z = Y
  28. Cardx + sevdv (de d3 Favdn fF ardrdZaZ) x de + dudx
  29. az dz + dx do
  30. et parijure V -g = Y ardio + fl 2de C +dvdu) + arar av ilo)
  31. az z+ av du
  32. seu y 0 - Y. drdv + (ddqze (d2A Z favdr) + drar dudv)
  33. dz d2 F dudo
  34. g, et 1I, fiet
  35. et fit et ex aequ. per
  36. + (3) araque + Y (do dv (d Zdz +do dv) + drdr dzd2)
  37. a
  38. in aeg. 13 drdv F Y (dZdZ (dZ +Z + dvdv) + drdr dvdv)
  39. Et quia explicando per X. a, y: a et ex datis secundum aequ. 5.
  40. et in aeq. ut fiat aequ. 14 et in ea pro X, y, substi tiendo valores
  41. ex aequeo 10 et 12. habebitur aequ. inter Z, v, du, dv, r, dr,d
  42. si si b + a expli compendio sid r d Z + (+a (d 2 1Z+ dvdr) + ardr dezu) dsu
  43. et idem permulatis solum dZe et de sit, = (16) dgdus et dZ dv + dv dv sitsos) - dede
  44. fiet ex 13, t: a = (18) afdf: dgclus et = 10, X = (19) Z - Y (fdf: dede)
  45. et ex 12, y = (20) v- r (dydg; dece) aequatio data 5, t: a Xxtgy,iaa
  46. Au (22
  47. seu xx. per 18, XX+yy, : aa=dfds: eg dodus, et fice et ope
  48. e +rdsErZede d, dodo =aa dsaf de 4+
  49. Edg+ Zero Eyd9s c
  50. aegg. 19 et 20, ex aeq. 22. fiet
  51. videamus an licuat facere (24) df =0 seu de
  52. seu ex
  53. 15, Card raz d2) = dZ dz (d ZdZ+ Lodo) dr+rdzdZ et fiet
  54. vel dZ du Ya quod est impossibile, vel aq
  55. seu ex eg. 15. Cdrdr dz d2 = dodo (d2d, + dodo) (+ drardydu
  56. adeoque de = dz f- 1. sed ia fieret et de=. unde praestaret potius
  57. onservare df. sed video posito de=o tamen huc tandem veniti d
  58. aliter = faadtas XXdgs idg , seu Ly = Ma d fa sde - 27d0. 2Er dedeatat
  59. 22
  60. :dg = v - r(dgda: dede)
  61. si loco aqu. 22. fuisse
  62. fieret ex ig et 20, Z- 2+ ZEde +rrds - 2Zr dededsls rta: +X
  63. 24)
  64. vode-rrdgt +vY dydegus d agag=na dfils do +
  65. ubi faciendo Z v = 0 fiet YYdf4 - rraq, dodus = aa d fd+ dC
  66. Ex 24 sit dZ = dv
  67. et dfdf. per 15 = C 17) draz + de N(2 dxd +drar) = (28) iudusddb. Et ex aequ.
  68. 25 fit redes rrdSE er de sed ob aeg. 29. in ipsa 25 dvavescent Omnia, et
  69. fiet af sel de =0, de non dede = 0 non licet Ergo fiat df =0 sit ita fieret y=0
  70. et X -Z et y- X. quo non licet facere

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0004?run=73