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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: 0.87.

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The machine reads it as

  1. A A Z
  2. rent trom thar wrtrich was deduced by e for- that when anY Line, 25 FC, F6, (9c. is coin-
  3. 2y u = 0, arid here rIS ly u = d Zn =0
  4. buc chat thele F.quations are exaetls che lame, il
  5. cidene ich P F, which Limagine c0 BC a Nor
  6. mal ro the Curre in che Poine B, From che lame
  7. Poine F; chac chen che intercepred Line, F B.
  8. F FI, (90. is coincident wich the Subnormal FD.
  9. hus casilys discovered. Because i = -, and) and consegueneix upon che decerminins ol an
  10. = Zi, ereo u: 2: : 7; trom whence
  11. 1: n: : 2u: uZ, bue (by whar wene betore
  12. i = 272 F d27 - 299u erxo 1: n:
  13. dy22 = 4227 - 2712: v J. Tiom hence
  14. Extremum, che Invencion OF a Pangent natu-
  15. FaIIY FOIIOWS.
  16. Totorm che General Equation chat is to serre
  17. in this Bulimls, ve hare, trom che Rectangular
  18. Lriansle EBC, ZZ = = n n = 2 n X .
  19. X 3
  20. L yy; Or on the ocher side P, trom he Prian-
  21. Sle GHTF, 2Z = X X - = 2n X I n n - yy3
  22. OF FOT AM EXtremum, 2 X X -= 2 n r F 2yy = 0:
  23. In Whrich Eguation, iE in ThC rOOM OF 2 y y We
  24. substiture ies Value from che Equation of the
  25. in MII. NeimentiirS Fquation, viz. ly u = d Zn Curre, che Subnormal ill be discorered
  26. o Substimmrine chese Ouantiries in the room Fx. er. Suppole the Curre Were an Pyper-
  27. OF L’and n, ro vrhich ches are proporrional, ve
  28. have u Z2 a y - u 27 7 Z = u u 22 y7y
  29. bola, Mhen 27i = r x + 2 r X Z: Theresore
  30. =du ZZ = 0, or diridins all by 1 Z, and mul- ( 2 X X = 2 n x F r -- 2 Y X X = 0, and 2 n X
  31. tiplrins by yy, and rejectins Contradictories,
  32. we have d 27 y - 27yy u = 0, chac is, d Z = 2 X x -- r x 2 rX ~, andn = x ]
  33. - 2y 2 = 0. d. F. D.
  34. These Examples may serve 10 illustrate a Y g = FA, erBO FD (Ehe Subnormat)
  35. a Rule wrhich is in ic setf rery plain and obri-
  36. OuS.
  37. AS For the Dse and Application oF the DO-
  38. ctrine de Maximis C Minimis, perhaps ic may
  39. Y 9. 8. F. L
  40. Suppose the Curre a Circle, in which Cale
  41. De a5 DTetul and Noble 2 one a5 any, 20 Men (2yy = 2r X = 2 x x; then proccedins as Be-
  42. hon trom hence all Tors oF Curres may be cur
  43. at Righe Angles, (and consequenty the Inven
  44. tion ot che Langenrs isro be pertormed.
  45. FOrC, We have 2n X = 2r x, and n = r, and
  46. ergO F D = r = x; wrhich Mews chac P is
  47. erer in chis Curre, the Cenere ic SelF. In chc
  48. Common Parabola, rX = 2 y y, and Cheretore
  49. n = = - x, and (OFD = =. BuE Eis NOL
  50. ontr in chese Conick Sections, buc in any otter
  51. Curre whatsoerer, char trom chis General Equa-
  52. tion by a due Substiturion of che Value OF 2 y y,
  53. the Tangene, or (which is all one in eHect) the
  54. Subnormal will De discover d.
  55. MEAN Axis, in Opcicts. Sec Axis.
  56. MFAN Diameter, in Causinz, is a Geometri-
  57. cat Mean between the Diameters at HPead and
  58. Buns in any close C ask.
  59. MEAN and Extream Proportion. SeC EX-
  60. tream and Mean Proportion.
  61. MEAN, in Lam, Gonites the Midele Berween
  62. EVO FxtreamS, and chat cither in Time Or in
  63. Digniey. As in che First, Ilis Action Was Mean
  64. berwixe the Disseism made eohim and his Re-
  65. coreer, that is in the Interim, (OF, 25 we laY,
  66. in the mean rime.) OF che Sccond, there iS
  67. Lord mean Or mense, and Fenant mean. Sec
  68. Mesne.
  69. HIEAN Motion, Or Meam Loncirude of the
  70. Sun, in che Prolomaicte Hypothesis, I5 an ArK OL
  71. he Pcliprick, reckond from the Beginnine ot
  72. Aries ro che Line oF che Suns Mean Morion,
  73. decoumcins accordins ro cho Order OF the Signs.
  74. Rod re alo res voulual 10 cal are
  75. mer PrOcCIS: There the Equation WaS d Z
  76. Tet A C C BC any Curre wtcre rertex is A
  77. AXC A TT, iES Ordinates E D, C B, CFHI: Let
  78. any FOMH, 25 P, be caken in che Axe ac liberes
  79. att Lom chence che Lates LC, LL Le DC
  80. atas Co che Curre.
  81. TeE A F = n, A B, AD, AEI = X, TIF
  82. F FD = n = X, ED, BC,
  83. n = X,
  84. OFI = y, FC, F F, FC == Z. The POInEF
  85. beines catien aus vohere ac Ubecer, io evident,
  86. HE AN

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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/806933011:0500?run=74