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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 71r

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: 0.82.

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. 70v); this page is its right half.

The machine reads it as

  1. ver. tim . A DE. a DE esse ut CD ad SD, ubicunque in figura ossumantur, faltim ess;
  2. nec implet conditionem. Curvas ergo similiter positas esse, est omnes earum tan
  3. gentes esse parallelas quod non fit nisi earum perpendiculares coincidant
  4. Eligenda est jam recta in figura, quae sit constans, si qua haberi potest. Ea
  5. dimidis
  6. autem est in Parabola ipsa GZ, latus rectum datum ea ergo data est simpliciter.
  7. cumque sit a ad b t , ut G8 ad AZ ut GH ad AB.
  8. ad
  9. fiet: ab = sa x + 2 a Z sxa, sive
  10. a+2x+c
  11. airic
  12. a
  13. s
  14. ab
  15. exa
  16. a +4ax+ 2ac + 4X + 4Xc + C
  17. sive a b ax + 4aX + 2aC X + 4X a + +X Ca + CaX.
  18. ab.=
  19. X 4X4 + 4XC4 + 4X + Ra + 2X aC + XAC et posita a +c-g
  20. X’+ aXg + Xg
  21. Similibus
  22. Nota in Puraboles absciste sunt ut appli ordinatae sive abscissae sunt lateribus rectis propor
  23. eut X- sic X- C vel i
  24. b
  25. lionales. Esto enim faX X=
  26. mas
  27. saxs st Cx bq
  28. , ita b ad y, sive b ad exa.
  29. 1 = e 2- 4 Ergo be sea
  30. 1Xa a sive na a
  31. XH
  32. bi X2
  33. sive X ab x = aeb. Ergo X = spb. (quod si ducatur in ab, fit
  34. vel 10 ab tiet 19a b = X, vel 10 a b = =
  35. Ergo ex Sive ex ab exhatenda est radie cubica, quod ex suj ex se suposita paratota
  36. gai data vota regula ac circino praestari pote
  37. In Hyperbola, posita asymptoton assumi pro axe, aequatio erit a= Xy = 0. vel
  38. = yb = 0. Ergo E = et y - a
  39. VX+ OL b.
  40. = 2
  41. Sositis jam duabus istis hyperbolis similibus
  42. rectansulo
  43. Ergo si hyperbolae sunt similes, idem est utrobique
  44. ai latus secundum quod possunt drdinntae ad aspagtotor
  45. Ergo
  46. a 8b -
  47. in va y Y 1d est si Hyperboloe sunt similes quadrata
  48. laterum rectorum simt proportionalia d lateribus homulii sive rectis respondentibus
  49. se eodem argumenta debam. Ergo =Eo
  50. horpola
  51. Y 4 inm X ad 8 (a2) est ut a (1 y) ad b. Ergo Xb - E , hir XbG a
  52. Ergo GJum ob raturum dyperbolae, b est media proporto-
  53. nalis inter AT- 2As = 27. = 28 et AZ - AC + CG X + G2. quae GQ setiam
  54. talis L7. media proportionalis inter 2X ipsam GZ. et 2C9- 2x, ideo GZ = Y a 2a
  55. a
  56. a et C+ 21 2a.
  57. ide. b, media proportionalis venter Z a - 22,=2 aeb
  58. sive b= Exc + 2x + 4X. si ba = 2X + 2XC + 4xa, vel
  59. ba = X + XC + 2Xa
  60. Aa soloi potest, problema in Ayprtota si ex curva non in ordinatam, fidusingtotem
  61. sed in diumltum cadant ordinate,
  62. b
  63. sin a
  64. ut 11it

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 71r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0141?run=74