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Leibniz-Handschriften zur Mathematik LH 35, 1, 19, fol. 5r

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: 0.77.

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. 6v); this page is its right half.

The machine reads it as

  1. ve quacum vero cuilibet puncto curvae
  2. CC respondeat suum punctum, e nempe centrum maximi circuli curvam ineo
  3. puncto intus tangentis, seu convedinem metientis, operae pretium erit
  4. invesligare lineam centrorum, ED. Quod ex dictis non est difficile, exem
  5. pli causa, fi in foctione conica, quin inverrimus esse,
  6. 7 aequ. X + p + 4p, seu Zaequ X +a + ax q +X
  7. unde compendii ausa +a +q vocendo b et 29 +a vocando R
  8. fiet Zaequi LX + b. seu xaqu 29, bg
  9. seu xaqu. 4Z- Bq. b)
  10. Et quia supra diximus esse vaequ Zy- xy -y.
  11. a + ax
  12. - q
  13. erit
  14. seu vaequ 27 4Z744b7
  15. Yaequ. av fiet y aequ. va Faez p + a bv
  16. 1b - a-
  17. intor tatunc ut
  18. a + 4Z
  19. a
  20. as
  21. sed tevx
  22. t2bC
  23. et compendii causa pro a b scribendo f et pro h- 4+ a scribendo g.
  24. et pro b -f scribendo 1. fint y aequ ZV + f0. 97 + l
  25. Et inventos valores literarum X et substituendo in aequatione ad
  26. Conicam: X rax +q X aequ gy. fint 2247 - 2agb, + 949 + 2a9 bZ + 49 bb aequ. . .
  27. h hht
  28. aeu aaque vo t 2at zun +5fiv,: 9977 4 2.q I
  29. 1h
  30. ht
  31. ht
  32. quae est aequalio ad curvam EG
  33. si conicassestio esset parabola, fieret a aequ. 8. et baequ 4 g. et haequ. 29 et fag.
  34. et faequ.q et aequ. 9 et et laequ. +:9
  35. et ficret 2Z + a4 + _ f aqu aequ.
  36. aZ + a4 f a
  37. yy
  38. a Z + aq aequ. -aa ZZ vV Z3
  39. aqat E
  40. 44
  41. Y: Z- x p.: y. p
  42. ent vigu FCu 17 7
  43. si curva sit par ACC sit pambola erit AF seu Z aequ x+ta seu xaequ Z a
  44. erit _ PF ad BP seu ad _ a. ut
  45. In genere curvedinem cujuscunque sectimis Coniaem sis inveniemus Ducatur pen
  46. seu gy tpo +ov, ZZ 2ZX - ZP exX + 2xp+ pp equ e. qui quia dp aequ. + a dx
  47. fiat diferentialis aequatio 3 A7+ vause d Zdx +Z ax p X AX f a xAX Aa Xx + adx + xrq eadxaqo
  48. q B 1
  49. ydy + vdu q dx +22 tx 1 ad axx par f a p dx aeguro et quia veram repy
  50. fiet x. du 2 ∞3:
  51. 11a
  52. tiet Z.x aequ Z.x p + Z xap g. seu ap + p +x aequZ
  53. seu gy 129V+ ro + ZZ 2ZX + XX aequ. el. seu cujus differentialis yy + vdqus
  54. ydy tVdy 1Zlx + xdx aeq e ( Cyes se axel y rrez X : 3 g. p.
  55. Et quia ob Triangula PFE, PBC similia FE ad pF seu vadze X.p. ut BC ad pF seu ut y ad p
  56. fiet pV aequ Zy = xy - py. seu y tv+ y:: ZX.. p. Et pro p ponendor valorem
  57. a + ax firt. a0 43xv ay +GYV aequ. Ly x cujus aequationis aequalio
  58. differentialis est + avem tadu fantus aequ Zdy- x 4- ydy. seu Ret
  59. a dx: du in Y 247 y a 1 ap: x f 2 B At supra Lx dy 1. y: a + ax
  60. tiet za ya vaa aa v + a Z + a xu faa x - aa vx aequ xy t a ry
  61. q9
  62. seu p B+y aequ y. Z. X. et Es autem p aequ a + ax et dp aequ = a ax fiet
  63. deidys.
  64. :
  65. P dy + a dx vty aego Z. X dy ydx at dx aerio Zp Ergo firt:
  66. YY P + G q vry aequ Z. X = 978. ab Ergo paulo ante Y +y aego Y q. X.
  67. Ego per p + 3 v27

Cite

Leibniz-Handschriften zur Mathematik LH 35, 1, 19, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067981:0009?run=39