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Leibniz-Handschriften zur Mathematik LH 35, 6, 7, fol. 10r

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.

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The machine reads it as

  1. n
  2. C
  3. C
  4. centr gnravitatis semper habemrus proprietates abundam
  5. larndovas
  6. si scilicet fingamus lineas quae silas esse calenarias
  7. suspensas seddifformis gravitatis. sic enim
  8. L
  9. quovis data linea
  10. produpi potest. Sit scil. elementum curvae guive in ratione aliqua p: at et fiet
  11. dementam momentam ejus ex axc. f SpyYax+a et TA distantia centrigiaioitalis
  12. euit
  13. et
  14. carvo
  15. S (1)
  16. y ax +dy: AAprdx +du=
  17. 2
  18. s= AT s C Rursus y - t: X :: dy: dx
  19. (2)
  20. Fit: seu FB X dy ger ydx - t dx = Xdy. seu tdx = Cy tx - X dus
  21. (4)
  22. seu t = y = x dy: ex en dt = (dy) = X d. dy: dx ( dy
  23. etgo
  24. Aursus A ex Y est by Sdx + dst = t p dX + au + Sp Ndx + dg at et -
  25. sit. PVax +a: (PSax+du dt: + py ax + dyt: t (podx ra l
  26. 2
  27. en perine
  28. Spyida ta
  29. se2
  30. sed in aqu. G sobsuento calorem te sit: ipsius f sit py ta et propat due ponendo n
  31. fit y dn = + dn + n dt sen (y an = +n quod constat ex aequ. 1. Et
  32. pro t substimendo ociorem fit: (y dn Z (y ard = Xdu an: dx = nX d dy: dx
  33. per 3
  34. e si
  35. divisione facta per rsit X sit an: n = -dy ddy: dx: sg: dx. Ergo
  36. fit dy: dx = a: p assumia constante a, ad implenda legem homogenectum
  37. Eegue seu an: a = dx: dy sit dys constans fiet du: a day: dy
  38. 2
  39. parsus
  40. nius ope tollatur _, ex aeg. 5, et fit ydu f an + adx: du at. et sallendo det
  41. at fiet (Y du) = y dn) = X dy: ax an D a a dx: dy X d dyi de sec ila tantum
  42. s
  43. l
  44. lq
  45. redditur, aequ. I1. Ergo quia n: a axidus faciamus dus constantem, et fiet.
  46. 1167
  47. du: a dax: dy. et sit = jam dn= pax + dit et ddn= dp rau tdus +paxdlx: tad
  48. Et etat
  49. se 15
  50. Si in aeg. 15 substituaes tollas dx per aequ. 11. fiet: du p dus n +a: a
  51. video non esse opus supponere dy esse constantem. Hinc si p detur ex y sen
  52. habetur lineut
  53. si constet quomodo pondus catena varietur pro recessu ab axe,
  54. Ergo si detur p
  55. est
  56. et rursus quia tollento du, fiet: d dn = p exernn + aa: n
  57. ex x seu recessura vertice. Atidem habetur solutio. Nam data n per x aut y+
  58. e
  59. utique solutio quadratoria habetur, pet 11. Rursus ex 14 et 18. sit
  60. fit dax a: dx= pdus Snitaa :n ubi si tollamus n per 11. fiet arqualis quaedam non bene tractabilis
  61. 19
  62. Eix gy. 16 se collamu ex et dap. per aeg. 1t. et 4 fiet Ean dx dn:p + Bady: a dndus: a : dh:p
  63. c.
  64. 5
  65. per
  66. seu dan: dn F ap: p ppn du: dna si poneretur staneet log. du= tn dy: ar
  67. A esset, p= 1. fieuet ddri du) ex dex. Ergo per 14 fieret. Cin = dx dy: a. seu du= Xdy:a + dy
  68. sad in aeg. 1b relento p. si pro plolx substituas vatorem ex 14, fiet: cia = Apdn: p + ppdx: du Andy: a sed ita
  69. si
  70. res non aque procedit sed et sine dius summa obtineri pt, cum B datur ex X sit cmm
  71. nam
  72. Pax
  73. du: Suntaa. Ergo spdx = AAnn + aa +d. sed si _C praeter aegu. 11. et 15 unde
  74. (22
  75. uit ceg. 1b. daretur e simul per X et y. imo fate at simul er dx ty uo posset ex his haberi lice bit s
  76. rem abtentare per aliam bram sit. cb. data peradbxa seu callundantia
  77. oterento plur puncta us albi
  78. promotio
  79. Catenarie
  80. ad satenam
  81. difarmem
  82. pondere

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 7, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068052:0019?run=73