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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: 0.88.

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The machine reads it as

  1. 2
  2. Suxpole Xy = 20 any R ectanole made Ox encrea.
  3. Sed br a Perpetual Morion ox Fluxions ot cichet O
  4. che Sides _ Or y, along the otter, and let tHC MIO-
  5. menis, ox Fluxions of che Sides, Be x and y. By
  6. I. From ihe Flovinz Ouantity siven, 10 finct
  7. the Fluxion.
  8. II. From the Pluxion, to find the Flomins
  9. duantity.
  10. AS torhe Formet oF these, the L eared Dr. W al- wrhrich e undersland che Velociry wich wtiich ei-
  11. lis, in che place abore mentioned, (romM. Nem. xher Side mores r0 Tocus ine Meclalis C.
  12. tons Papers) sires this general Rule,
  13. Pet each Ferm of the Lquation be Multiplied sepa-
  14. rately by theseverat Indexes of the Povers of all
  15. the Flomine Ouantities contain d in that Term:
  16. And in every such Mulciplication let one ROOt or
  17. Letter of the Pover be chanced into its proper
  18. Fluxion: Sostall the Aegrezate of al the Pro-
  19. ducts connected rozether bytheir proper Siens be
  20. ehe Fluxion os the L. quation destred.
  21. And aII ehie Cases oF ir are demonstrated by
  22. MIF. Tsaac Nemton in the Lemmata abore deliver-
  23. ed, Wotrich L Mall exemplisie by parricular In-
  24. Rances.
  25. T. In che General, 10 express the Eluxions oF
  26. Simple rariable Ouanciries, as was laid betore,
  27. vou necd only use the Letter or Lerrers Which ex
  28. prels them, wich a mall Poine over their Fleads,
  29. chus: The Fluxion OE x is i, and the Fluxion oF
  30. yisy, and che Fluxion OF x ] - y - v -) Z i5
  31. L
  32. v
  33. 2 8C
  34. And (Inversely) ehe Flomine Ouantities in chis
  35. cale will bc casly had From the Pluxions, by on
  36. ly uvririne che Lerters withoue che POints Over
  37. chem.
  38. N. B. FOr the Fluxion OF Permanent Onanti
  39. cies, wohen any such are in the Equation,
  40. Vou must imaeine o or a Crpher; For Cuch
  41. Ouantities ean have no Pluxions, propert
  42. speatins, because they are wichout Morion,
  43. or Inrariable.
  44. TI. T0 And the Fluxions oF the Products ol
  45. evO Or more Variable Or Flovins Ouantiries:
  46. Multiply the Fluxion of each simple Duantity, bs
  47. the Factors of the Products, or ibe Product os a
  48. the rest, and connect the last Products by theit
  49. proper Siens, the sum or Asgresate is the Fluxion
  50. Soueht.
  51. Thus che Fluxion OE X y is x y - X y, andche
  52. Fluxion OF X y Z, i5 x y Z - ] = X y Z F X. y Z, ane
  53. the Fluxion OF x V y Z is x V yZ - F X V7Z=
  54. X Vy Z-= X V y Z, and che Fluxion OF a - X X
  55. By b = y (ihe common Product beins a b -) - b X
  56. ) a = X 7) wvill beb it - ) a = v y = x 3
  57. Erom che Sides subduet the hale Fluxions of
  58. chose Sides, anel it will Mand chus; x - = anel
  59. Mulipir chese onc ino amorher; and che PrO.
  60. duet wilt BC r y - 7 X - X 7 X 1
  61. Thencoche Sides add che hals Moments Or FIuX.
  62. ions, and ic will be thus; X ]- =, and y-]- 7:
  63. Wtich mulciplied also inco onc anortier, will pro-
  64. duce x y -- 7 X X y x y
  65. Atcer which, Suberact ihc former Product trom
  66. this last, and che Difference will beonty x g X Y,
  67. the Fluxion oF. x y, accordins co the Rule.
  68. The Inverse oErhis Rule finds also (in chis case)
  69. the Flomins. Ouantiry From the Fluxion, viz. IF cach
  70. Member oE che Flixion be. dirided by che Fluxi-
  71. onary Ouaniey Or Letrer, or by changins the
  72. Fluxionarr Letrer into chac proxer Elovvine Ouan
  73. ruy oF wvhich ic is che Fluxion. For chen ihe
  74. Ouores connected by cheir proper Siens will be the
  75. the Florvine Ouantities CougtE. Ontr il che Ler-
  76. ters aIl be exactly the Pame, che Flovine Ouan-
  77. tiey will be a Simple onc, Wwhole parrsare noc tobe
  78. connected rogether by che Signs and -, a5 in
  79. che tirt chree Examples oF chis Rule.
  80. III. Fo Hnd che Fluxion ol any Fraction. Mut.
  81. tiplus the Fluxion of the Numerator by the Denomina-
  82. tor, and aster it place (with the Sien -) the Fluxion
  83. of the Denominator into the Numerator; and Divide
  84. the whole by the Square os the Denominator.
  85. Thus che Fluxion OE = ; x y = = 7, (0r
  86. Cuppole 4 = 2. Then Will r = 7 2: ntiea e

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/806933011:0340?run=74