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Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 14r

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: 0.84.

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. 13v); this page is its right half.

The machine reads it as

  1. f
  2. Hinc estum haec austica proprietalem alterius habet quod nempe per suam
  3. quolutionem aliam sanstram describat sibi similem.
  4. sit Parabota AG9, (figs. 6) cujus vertex A axis AH in quo punctut
  5. est datum B., quod radios BG, Bgenibsit, qui reflexi constibuant lunvam saustica
  6. determinandum est eiut punctuma. vel invenicna est longitudo GL sit paramete
  7. a + AB,b. AH, r. HG, + = sar BG, y = Y (rY - rb + bb + . Ergo GS, ax.
  8. Ai 9, adr: 2aY. addantur eorum quadrata adrdr + 4 drdr, : 4+ = Gg. qu.
  9. est autem dy (seu 90) = 2Td 2r - eb +a, dr a ( 2 t(rr - 2rb + bb, + ar). adoque
  10. G9. qu. = 9Dqu = Gd qu. = abb arK a Lb- r) dedr: rearr. syb + 4 bb +4ar
  11. dx dx constanti.hlujus itaque quantitatissumendum esset differentiale, et aequandum
  12. nihilo. sed quia universalitar solvere niius prorixum foret samemus casum specialem
  13. sit igitur b =0 id est ponatur B in vertiee erit caetens ut prius, BG, y-Y(eY + ar)
  14. G1, dr. gi, adr: 2Var. G9qu = adrdr Farardr,: 4r et dyd2ra Falar:
  15. 2Hertar). ideo G9qu - goqu seu G0 qu. = adrdr:, 4r + a) = dxdx constanti
  16. ergo differenticindo, si adx =0 fit dar = drdr: 2(r+ a). Et ddy erat -aa ardr F
  17. modit ddus = = aa dar +2rY aer Far, drdr 4(rr + aY) err+ ar). quia
  18. +Z (2ddr + addr) pr + ar), : 4
  19. ergo dxdx + dys dy = drar (a + 41): 4r erit ydxx + ydydy, :, dxdx + dudus 2yd
  20. = + 4Y) ((e tar) : 3a =GL si ergo fiat 3a ad BG ut a + 4r adquartam
  21. erit ea GL. cur si addatur recta BG proveniet 4 (a + Y) (er +ap): 3 a pho
  22. valore curvaelausticae AL. sputium cansticum AGL etiam quadrari potest
  23. oronidis loco ad jumgemas determinationem causticae in cyclorde vulgari
  24. agradiis axi parallelosum reflexis sit (ycloides
  25. linea Avulgaris AB verlex (, axis CE, circulus Gentor CFE, radius
  26. quae causti ca generetur
  27. incidens GB, reflexus BH, cujus consitudo quaeritur. sit (E, 2a. CL, Y. Arcus
  28. CF5. LB F = 5 + SEar -rr). peripheria CFE = AE = p Erit AG = p -s
  29. - ar -1r) = X. et GB, 2a = r = y. ideo dx = - dr (2a=F : Y) qui a.
  30. autem dx constans, ert ddx = a drar: r((2ar - YV) - dar Y (2a -r: Y) = 0
  31. ideoque der = a drar :, 2a r = rr. quia y = 2 a+ 2a = Y erit dy - - ar 80
  32. EArdrtadr) Cirer faer)
  33. Cddus =Cer+ ar) Cer car Fedrari adius
  34. serdr + adr) (2Y ar Fadr)
  35. (+(rY+ar) (2r+ a) ddr
  36. (rrar) ter ur)
  37. ad (a tar: r) sta
  38. Quae non consentiunt, Ergo est
  39. tota AHE, est dupla diameter EC. spatium ABH aequale subdduplo semisegiento AG
  40. si LBtransit percentrum circuli eut H omnium supremum. CausticaA AE
  41. (r tar) r +ar) et
  42. =rrC2aD
  43. nrtam Terrtan)
  44. error in caleulo, alterutio
  45. ddyu = - ddr = =adrdr: , Ear - rr. Itaque pro dxde + dy du, : Eddqu (+ pato - 2day)
  46. fiet 2a -Y = y = BG = BH quaesitae. Hinc curva AH est dapla BE, et
  47. prartaur, trr ratrarn
  48. est etiam cycloidalis, cujus circulus genitor est etio sub quadmplis circuli EtC
  49. dar
  50. virtur
  51. traar
  52. My-) car-aa
  53. et ar
  54. et
  55. fi abk = d2. 21p
  56. pro hocloci ex pumeratore
  57. videtur exfigum trD 2aV
  58. scribendum C
  59. seu dignna dxdr( arar +Erta) adrisia
  60. sit
  61. atat)t or
  62. et posito det = dTdr: LCr + a)
  63. fit 2drdr + (2r + a) ddr = Grai dr
  64. 3 a drar F 2x drar a arar
  65. ar, rta, 1(ertar
  66. in Zarr = 3aaY, 1, 4, 1
  67. seu dily = arar, Saar - 5aN - 2a3- 2Y,
  68. rrtar, ia, Crtan

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068089:0027?run=73