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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 25r

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: 0.81.

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. 1v); this page is its right half.

The machine reads it as

  1. differentiali ad absolutam ita veniri. Aequatio differentialis est
  2. st. 2 = baD 2r OY - b a D. 3Y. pro D infinities infinite parda
  3. relatio inter tempora seu areas, et radios
  4. Si ponatur M = Aa: d ba dt. 3r
  5. fel : C ext a dr. rot a sa: 2 dr. r = db. et a Sa: 2 : = t et hoc denum
  6. scribamus posite et esse d a. et fiet.
  7. aCdr rB = at saro - bad 2 E s a S Sdr. r: Car -bad = + siquae est
  8. casu erunt tempora radiis pro portionalia. Unde eo casa quo temporum et
  9. rudiorum relatio haberi potest, patet aream curvae esse quadi abilem. Sed quando m
  10. se vis gravitationis est simplex, non aeque facile radiorum et tempoum relatio habetur
  11. Una ud hac aequalio est extigum, nempe 2G1N + 1N. G = 1G1L + iL 2G
  12. et iNIG= a dt: p- dp et 2G, N = (A) HK) - m
  13. et 1L2G = adt : seu 1N G - 1L 2G = 2G1 N - 1G1 L
  14. 2L 3G
  15. A autem it = A + K
  16. seu fict aataY. Y = du adF: r- dr - aedt. pr et fiet:
  17. seu dp + ddp + (k) - m
  18. aedt, (N= p+ Erdr d: r(. 2V dr + r di) = ( 2dp dd + cp + 2 c ( + 2at
  19. ( adum rddx n (t K) - 2K) im + n dp 2dp K K
  20. sit AB + BGy ert AC, h.
  21. Ge aciilited pro omni diquatione curvae
  22. erit euit r yy h- 2hx +
  23. CG= 4F
  24. erit Irgo’dr = ydy = Ghdx + Xax. sei de
  25. rursus sit ciculatio e fiet dx + dus = dr 4 et
  26. jum e = a at: Y fier dx + = dr + W : Y
  27. AN- n
  28. N = _B. 0G2 y AC = R h.
  29. =
  30. CQ ex L1G. EF
  31. CH. 1G2G = e
  32. estam CH: CT::d
  33. sursus CH, CG.. L2G:
  34. du Pir - hh + 2hX. X = hdx + xdx
  35. fiet q
  36. mulliplicatur pert sileax
  37. seu
  38. seu rar = sar +C = de .r - ho Lihp. X
  39. jum st = 2ax + ax. fiet r - G + rhX - X = 2ax + a p. seu sit a + 1 = 8
  40. et 2 X + q ) X trarit X + C a = 8. 4 + r. si
  41. sit 6, ∞ - se = 3 firc X + C: 2 = r + 3)
  42. dx = rar: Sr 13 et fiet rar = Sar +C- r dr 1t 2 5 (∞ t 43 rut
  43. +q
  44. 1 - h - h C - 0. 4 = h. + 26 a - 2h : 14 a - a + rah - h. 1 + q + a rasus a Mr uta Bl ua f
  45. g
  46. 1+8 = ah + rhaq = h2g 4 rtaq: q + 2q q + 2a9 + a
  47. seu a=4 intr 4 b9 seu in Ellipsit ahe- 4n. + haqe 4+a: 9+ a seu set
  48. hec a + 9 h + 2hag,; _ a +q
  49. Brevius (h) - hC = d: 4 (-3 =) O: 4 (F h) = - h0 - 0: 2
  50. h + O. 2 = (H) + = h + a (= h: 1+4, = at + a h + ga, : + 9+ a
  51. m si C sit umbilicu Ellipseas est et et erit et 9 dictantia centu a vertice primario
  52. semisdistantia focorur fiet h. 4 9 = f. se. fiet af. 4) a + 9 = h + 0:
  53. quod si mulliplire. fit ergso seu a jam a = 5-4
  54. rde = dr +C - p dr :r + 5 h +O: 2 . 2Yr +3 =,
  55. seu rdi = rete rd + _32r (Y d) + 3 de +e (rdr) af: a+q trr 5 12a
  56. seu d dr = e (D. 2srri +6, _ 14 + 3p 3. sranta
  57. 3 = a rah C
  58. h= 9 -25
  59. 2s qusts
  60. (el 9 + f vel qu f
  61. Ergo h - 4 = 5
  62. f = 9- b2
  63. jam bb = a q
  64. q+ aq
  65. 25
  66. LH L∞X

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 25r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0049?run=74