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Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 28v

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: 0.75.

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. 29r); this page is its left half.

The machine reads it as

  1. fiet: (quaeramque surita AH pro absussa at DB pro ordinata, equaeramus
  2. D7 pro intervallo langentis quam vocibim . nempe fiei Xa7 saque V fXA
  3. a
  4. sive A; hujus aegreationis pricti junctae ope tollamus
  5. X +) terminum Z. dempe primum qu, pro 4q2, substituendo ejus
  6. 62 sive
  7. diva
  8. volorem ex priore, qui est. X - 2a7. 1 0 fiet: (a Z) + x (aZ B Xd. et eris
  9. ZY X = X 2, et 32
  10. aequatione substitati fiet:
  11. 214Y - 2a+ = X + 24 X A - f H A2 qua
  12. X
  13. aequatione exprimitur, valor ipsius A. aequatione tati: 2 a x - 2 ad = X + 2 X A - xd aX
  14. itam effeciem sed revius forte ita rem obtinebi my
  15. Z2
  16. = 26Z + b B b - x et +Z + b p, 5b- X, et ZH + A + b
  17. pro Z fuestitucudo X suestituendo X +(B. fier: Z F propima Z p f S62 . 1. B a
  18. auferatur illa ab hac, fei: + Nb2= XE = 2∞ - p)
  19. 1b- , B () unde
  20. + b2 - X) - 2x B - B2 - 2 (b. - p - 2 2 - ( br = ( bZ ∞) W
  21. sive b 112 + 2+ B ( B, b 2 +( b2= X. sive.
  22. WW4 + 4Xβ V + 4 N B
  23. 64 - 2
  24. 262 - 2X V = 2 xB = 1. WV2.sive:
  25. 26 - 2X = 2yβB = W p 2F.. et quadrando utribique
  26. 4b 2 b X - ob x B - 4b.u2
  27. e
  28. (-8b X 4X +). -8b 3X + A8 X B.. e quod si jam
  29. addatur ad W. addatuo β, Tadix summae reprae sentabit etiam crementa
  30. llipseosi sed haec quoque compositiora quam velim.
  31. exitu, quia ibi A habetur jura
  32. ope tamen ipsius A facilius habetur
  33. satius ergo erit ad raligus propedi aequationes. Sumamus scilicet aquationem. 6- bx t.
  34. et quaeramus EA 3. e HX, ponendo AH, BX prfordinata; et D pY pro
  35. absca nempe fiet, - Yb Xh p Fy, et
  36. BT W
  37. b- b
  38. hp-
  39. Xu a X, sui W (t x
  40. 62- b 22
  41. addatur (, et producti radixo fiet:
  42. figurae
  43. Y6-LX
  44. bg2 = b 7
  45. E42
  46. b--
  47. ejus quadrato
  48. lX b
  49. superest ergo ut hujus curvae dinrensionem tentemus b aX2
  50. Nimirum aequatio fit:
  51. b2XV + b- b
  52. ficit
  53. 250 g0
  54. 6- 2 42
  55. Hinus figuiae momenta g habentur ex quadratum Hyperbolae. Ejesdem etiam
  56. habertur ex quadilum Hyperbotae fit enim g
  57. quae pendet ex quad. Hyp. At
  58. br -
  59. vel inculi si
  60. 8) fit pus
  61. aua est quantitas
  62. bqu
  63. -k +E9)
  64. hyperbolae si negativa. duo ergo as
  65. curvae harus momente habemus rum figmae ipsarum 9t
  66. fiet: mno mentam omnum g ex vert
  67. summae ipsem _ X, d cinquiu fier:
  68. b2 X B = bx
  69. e
  70. puncto ultra vrtieri
  71. BX
  72. 1∞~- BXVF 1.
  73. quae pendent ex quad.
  74. ducantur 9 in b + xb
  75. versus vesticem, Bmmetum
  76. aux. + b + XI Cb - X B
  77. Curva Hypeib olicae homogene homogenea est hoecfinura. Sa +
  78. XS
  79. postenor similis facile reddi potest homageneae curvea Ellisti . dividendo per d. cognitam:
  80. Elementa curoa Hypertalicae ex posteriore etiam sic enuntiari possunt.
  81. 1X
  82. ai H 1 +
  83. per partes.
  84. in nfinutus facilimus ita +
  85. ∞7 1 +
  86. 2Z+
  87. v
  88. Item haeci Sex +a quae
  89. Si.
  90. (1.
  91. a+X
  92. a taa Uurur si licet extractione
  93. er sed ut prgessio frat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 28v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068022:0056?run=73