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Leibniz-Handschriften zur Mathematik LH 35, 6, 1, fol. 13r

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.

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The machine reads it as

  1. HGK
  2. si super curva HGH immota, velut basi revolvatur congrua et
  3. 2) C,) patet situm earum esse amphidextrum respectu langentis
  4. (C) 2(C)
  5. communis GR, patet etiam trochoridem tali provolutione desciptam
  6. nullo negolio posse haberi. Sit enim haec descriptio a puncti constantus (C
  7. et ileud
  8. motu, cui responde puncto (C) respondet fixum c eodem modo
  9. C fixumtens
  10. litura respectu tangentis GR quo se eas immotum, ad eam situm
  11. situm est, ergo silantum dR normalis ad GK
  12. e
  13. Ergo SF + CF
  14. et
  15. Ergo si tantum Cm
  16. ducatur normalis ad GR, et producatur ad HC) donec fiat M. (C) aequ
  17. CM, habebitur il) locus in curva quae sita. Haius tangens 1c7
  18. foret parallela.
  19. porro icT, normalis ad GiC erit curvae cetangens
  20. ut ex trochoidum natura constat
  21. ux
  22. ponamus C incidere in A
  23. GFV. AB X B(C), y
  24. F Y
  25. BF, E.
  26. GC sen g-G.C
  27. ob triangula similia RFG, et RM C; fiet RC: CM i: RG: GF datur
  28. ergo CM = A RC, GF: RG ergo datur C (C) = 2RC, GF: RG. porro
  29. ob triangula AM C (adeoque RFG,) et 1(C) BC similia erit angulus
  30. c 1(C)B = angulo GRF. Ergo fit 1CB. C 1(C):: RF: GR. Ergo
  31. C. B = C. (C). RF: GR. seu 2RC GF. RF = GR = 1C B. seu
  32. y = 2. F- Z. V. Y : vDtEr
  33. Ergo XX+YY =
  34. CB: C. 1C =: GF: GR seu X~ e e
  35. Z VVI WV+rI
  36. 2RC. GF=: GR seu X
  37. XX + yy = (C. 1C)E =) 2. F.Z. vV:, vet
  38. se CB = C, 1C. GC = GR
  39. t
  40. Xx tgy = V 2vC caperest una ad huc
  41. aequatio
  42. E supersunt duae adhuc aequa
  43. b
  44. tiones, una relationis
  45. X + yC = Y- Z XV + y = Y-
  46. eG = Rm + nG. inter Z et v altera valoris ipsius Y, seu ipsius
  47. d.v. de =r porro superest adhuc aequatio pro 1C. Y tangente
  48. Nempe ipsa GrC normatis ad curvam producatur, dum ipsi FC ai eccurrat
  49. CM in C ∞C =- G (() in C9. Ergo (g = GM. C. 1(C). G. 1() CG
  50. ipsius curvae (C) 1(C)
  51. in p.
  52. st. A
  53. X
  54. = G
  55. et
  56. LG + Fp = F p. CZ. F
  57. seu (GF9) + F p FG1 Fp
  58. 1
  59. G9
  60. da
  61. Ge GZ + (GP seu) GF + F N, CZ Fp. FG ut fiet
  62. GZ scu GF, BF p = pp C∞ 1FG + G8 2FP Cq. GG
  63. vt
  64. ex G ad B iC) agatur normalis, ipsi
  65. FpCg. G) FC occurrens in N. cum G G. 1C) sit
  66. normalis ad curvam ( (6) (C) erit GN: N.C):: B. 1(C) : B,
  67. 15
  68. GFGCFZ FG C9 seli ex est autem GN = 2+X et _. (C) = y. v et fiet: Z+X: y. B = y.: t.: ty.
  69. t autem Gi C)= GC, ergo fit ec e2ty (GN+ N 1e) (it X2X ∞- 2vy
  70. seu X+y 1Vy-

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 1, fol. 13r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067956:0025?run=39