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Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. -

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: 0.76.

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The machine reads it as

  1. ns
  2. 2. Tet 2 = v, Men Z ( = 1
  3. = v. v, buc Z 7 +) ta t2- 29 tig + t
  4. F9Zγ + y + ~ + x = 2 Zp x Z YY + x + X1
  5. erso 2) + y +. t , = X X + )-
  6. Z
  7. CASE HI.
  8. 3. Tet X = v, Meno F o = =1 ). jia
  9. EZ) X + 9v + ~ 9 - xy X ZD~ + yu + ~) = 1 Z
  10. Crom erhence ailes q) -+ y -. ) 2
  11. X ZV~ + 9 r + ∞y - 1 q - 23 = = v.
  12. ASE IV.
  13. 4. Tet 2= = 0, chen v + v = 21 2)
  14. 2 F 2
  15. un
  16. 9 + ry - 9 9X + vy - y
  17. yX + xy - y = - +
  18. x2 u
  19. 1x +
  20. 2, itience Z
  21. y onatry - gi - 1.
  22. x Z
  23. Z = v.
  24. CASE
  25. Latis, Tet Z = v, ihe Fluxion oF y =
  26. ∞ 9 v ut 1 = 1 y - g; ergo ve have v-
  27. y = 2: V
  28. 4 ny ~ L 0 - 1
  29. .i magaii -15
  30. ti-
  31. Fy = qgi t 2 = 9- Z; ane chence is
  32. plain, ehac v = - y i + - 13
  33. i ay t - - 1 - q
  34. Next Forthe Dule Inversetr, c0 snd che Flowine
  35. Ouantier belongine ro rhe Fluxion ot any POrer
  36. Whether Perfect or Imperfect; procced thus.
  37. J. Pate He Fluxionary Letter or Letters ont or
  38. the Equation.
  39. II. Augment rhie Index oF the Fluxion by F. OF
  40. Uniey.
  41. TII. Divide che Fluxion by che Index oF irs
  42. Porver lo increased by Onitr.
  43. Lxamples.
  44. Onity, ic Will be 3 x x x. Then diridins ic by 3,
  45. ins non lausmedred) index, che Quorier will l
  46. xa, che Plorins Ouamis reguised.
  47. tatins avar che Fluxionary x, ic will be
  48. =1: By ausmemins che hudex bs Dnies
  49. m
  50. (i. e. tatine avay - 1.) ic will be x: Anc
  51. lasr, BY diridin8 che remainine paecolche Fluri
  52. on by Pretixed 20, or Mulciplied inco v, ihe
  53. Ouorient will be x n: Whict is che Flomine
  54. Ouancier Couehr.
  55. Tou will sind Framples enoush oE ihis lnverse
  56. Method: The Caloulus Integralis, Ox Summatory
  57. arichmeriele, in M. HaysS B00L OE Fluxions,
  58. Soct. 4.
  59. Some Instances of rbe Proporrions os Fluxions in
  60. Various Curves, by Mr. EL. Diuon.
  61. Texx and v express Abseisses, y and Z che Cor-
  62. respondemr Ordinares univertally. Ttien in ihe
  63. Ciecle we have ;: 2: . = = x rv = v
  64. ane supposine che Abscisse ro don unitormiy, aud
  65. consequemly x = 0, we tave y: Z: : rZ = x Z.
  66. ry = 0y : : r = x: 3 That is, che
  67. Fluxions C e, Ei, are toone anotter aS BO, 10
  68. O; che Points beins ever determined by che
  69. Perpendicular h 8. let Fall trom h che Incersection
  70. Of che Radius OC, Wwich che Line Dh.
  71. Tis cerrain chat 5O = , 7 = 2, trom che Si-
  72. milax Friansles C F O, h8O; sor b8 = D B
  73. =9, and Z: r - v: : g: 1 v
  74. AC = +
  75. AB = x
  76. CF = 2 HI i =
  77. DB = y
  78. AF = v Cc = y OB =
  79. Again:.
  80. da
  81. Suppose x x a Fluxion propoled: B;
  82. ec
  83. ClBC MC A S F. II.
  84. EF 3 X X X evere propoled; by catins avay x
  85. In che Parabolick Curres, purcins P ee Pata.
  86. metet = 1, cheny = 2, and Z = v, chen y:
  87. a
  88. c
  89. Z: : n x
  90. nonid..
  91. it Will be 3 x x; and by encrealing its Index by
  92. Theletore

Cite

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. - . Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/806933011:0344?run=74