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Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 20v

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. 21r); this page is its left half.

The machine reads it as

  1. At sumuna omnum A
  2. quoum
  3. Esto curva ADC. cujus od ordinata ABp, X. EC
  4. BC, y ⊓ AE.
  5. Erit X, a
  6. d
  7. a quad. Hop +
  8. 2
  9. et X p ad
  10. a +y
  11. ay axtyx.
  12. quorum
  13. a + y, H
  14. aequilibrii
  15. Summa est mongutum figurae AECDA ex HE axe _E
  16. aY2 que pendet ex qu ad cunte
  17. a2+y25.
  18. aequlib
  19. est momentum figuiae AECDA ex v Axc AB
  20. jum ut quaram, y, ita procedendum est, ex aequatione figurae
  21. fiet:
  22. y X - a y - ax sive 3 - a y, - a sive
  23. a ax, unde +9 + = a a -x Unde patet Toliter
  24. y- a y + a
  25. deau figuram a sa=x dm pendere a quad ypervolae. Nam si ipsae
  26. Y pendent a quad. Hyp. aufer ipde ipsas a
  27. Hyp. etiam a Y a -x pendebit a quad Hyp. Ejus vero centrum
  28. gravitatis pendet a quad circuli nam si ducatur in X fiei: a Sa-x
  29. quae est homogenea circulo, si Ducatur in se, fier: a- a x quae
  30. habetur absolute. Habito ergo figurae cintio gravitatis ex datu circuli
  31. quad ratura, quaeramus aliesm ejus alterum ejus indeterminata, fiei
  32. a at - a X B Y X, erit init ordimant X + S X + du 5 4a
  33. unde X +3 Y y+ aua figura paltit ex quad Hyperbolae
  34. plag. 10 Ergo et yt+ a pendoit ex quad. Hyp. Ergo a X - ex quad Hyp
  35. sc
  36. sive a = ax = y, CaX + y. Unde aYa p y. cujus ordinata
  37. ex qu. momentur ergo omnim y ex axc eorum ex quado circuli.
  38. Sed _ sasa X H y. quae tigura pendet ex quad. Hyperbolae
  39. Sed Xra Sa- pendet ex Quadkaturu circuli )) Invenim
  40. tit ad figura; nostram redeamus
  41. in ea BC, ess momentu
  42. AB
  43. figurae ex AE AB AECDA ex AE pendea ex quad circuli quia
  44. a quia ay Xy a2
  45. a
  46. momentum i vero
  47. figurae ex ABCDE, ex AE, pendet etiam ex quadratura
  48. circuli, quia X y +a Juae x 4a quia inventa est
  49. YY + a Yae-X
  50. a ideoque cenerum grantatis figurae pro
  51. positae pendet ex gro quad circulii ergo atu
  52. a - a x + 2a2 ae X + a
  53. 7
  54. quad circuli pendebit.
  55. aty, 1
  56. et per consequens
  57. x + at
  58. Sed ista exitum
  59. item
  60. 24 a a- F ex
  61. parte
  62. Ejus nomentum Hujus figurae quadrat ordimatar
  63. y habentur absolute, sed y ex X dunt a
  64. et
  65. 2
  66. us
  67. fus
  68. X
  69. ias
  70. 4 ( 2 + a
  71. 1 Laeay, et X, VSaeraega
  72. vide
  73. pag.ul

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 20v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068022:0040?run=73