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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: 0.82.

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The machine reads it as

  1. Note, AIL3 LhatenC Sut et an
  2. FixpOnentS AV. This beins well understood, chere is chio
  3. ot ervo Pumbers or Ouantiries, in any Creotie
  4. trick Progression, makes the Exponent et
  5. Produet os hose tuvo TermS.
  6. Tmis JV S or at is che var ol exesline
  7. che Product oC x inco v, and +
  8. X is the Product OL X 3 into x .
  9. AICO X F 1 3 Or X : is che Product 0
  10. xinto ic selt, or che Square oF x
  11. And ihe DiserencC Berween the ExpOnent Ot
  12. any vo Terms, ische Exponene ot che Ouorier
  13. arilins by Divilion ofche grearer by rhe lel5.
  14. TImS, x= SOF X Is the ExPOnenE OF ch
  15. Ouorient ol v b7 vt, 930.
  16. LeE p RCPre(CnE TC ExPOnent OF N any Numbe
  17. ac pleature; and lex P = 1.
  18. Then Will N = N : N P F = N, ana
  19. = N3 NPF 3 = N2 30.
  20. Or it p = 3.
  21. Then will N = N3 and XB = 3 = N6.
  22. Bc
  23. And Negativety,
  24. N =V = N = and N = V + =N 3c.
  25. Also, 25 0 is an Arichmerical Mean Beroeen a
  26. Postire and a Negatire Ouancity equally distant
  27. Erom ic, (1. C.) - 6. 0. 6 are Arichmerically
  28. Proportional: 50 is r. a Geomerrical Nean bC
  29. civeen an Aftirmatire and Nesatire Porver, at c
  30. qual distances from ic.
  31. Thac is, N P. 1. NP -:
  32. Trneretore, + = N = P X NP. And dividine
  33. al by N P = = N
  34. Sochac 27 is all one wich N
  35. t
  36. X ~ F = = + X ∞ 5 = v
  37. And = dirided by = vill sand in chis Ne
  38. Cion. cus. ): . (= - -.) 5 (-.
  39. = (∞ =7 = 1 Xx
  40. General Rule For rhe sindins the Fluxion ot any
  41. Pover, Whecher Perfect or Impertect, viz. Mulei
  42. ) the Pover (first brouehr one Dezree lover) by ibe
  43. Index of that first Porver; and then, That Productby
  44. the Fluxion of ihC LBI.
  45. 2 X X, ecc. and che Liluxion ol x will bc 3XXX
  46. ThaE OF x Wwill bC 8 x X, _C. Or it m expressche
  47. Index oF any Pover, as suppose xn. Then irS Flu
  48. rion Will Bem ~ = L X OE M X r = =- . FOF X H
  49. brouche onc degree lorver (m beins a general In.
  50. dex) must be x = 2: then thac x by m che Index
  51. mates mxm = , and ehis last by che Fluxion ot
  52. che ROOT PrOduces m n = 2 X.
  53. IFche Pouex be produced Fromr a Binomial, C3C-
  54. 25 suppose xx 2 x y y Y, ies Fluxion will be
  55. 2 X X F 2∞ y -F 2 Xy L 2yy, By workins ac
  56. cordins co chis Tourrh and the second Rules.
  57. Eche Fxponent be Nexatire, as suppose
  58. Or =, ies Fluxion will Be = m X X = m : Oe
  59. il rou moula doit by way os Fraction =m
  60. (For rhe Square oF xn iS as Wel x 2 m 25 ∞e n2) OF gC.
  61. cordine rO ME. Nemton SWay, Which is vet MOr-
  62. mX
  63. ret, mot 1. Sec Casc 4. P. 252. 0s bis erim-
  64. cixia.
  65. And co add some Lxamples os Musciplicarion
  66. and Division in chis Way,
  67. ui
  68. che Pover be Impersect, i. c. is ils Fxponene
  69. be a Fraction, as luppose V: X: Ox in che orter
  70. Noration x . Let us suxpose X n = Z. Then
  71. it vou raise up cach Member ro che Pover ot n’il
  72. vill Randthus, xm = 2. The Fluxion ot which
  73. will be, by ehis general Rule, m xm = = x = n
  74. ma.
  75. 2u i. Wheretore L willbe = n Za = - (by
  76. diridins boch Parrs by n X - 1: aud mrno-
  77. n7 2
  78. m X Or Y: x n - by purine in
  79. Aead oE n n = = its Vatue n Xm-=. S0 chac 10
  80. sind che Fluxion of any kind oF POver, you muse
  81. procced chuS.
  82. Mulriply the Pover eiven byits index or Exponent,
  83. and then that Product by the Fluxion of the Root es
  84. the Pomer siven, and afcer this Subduet One or Dnity
  85. fromthe Index of the Pomer.
  86. AS For the Fluxions oF Surd Onantiries, WIr.
  87. Frayes pires che followins Examples in his Frearise
  88. OF Fluxions non in the Prels, Which will mahe the
  89. chins plain co anx omechac will render himsellready
  90. aectie Practice oF this AI.
  91. Or
  92. Thus he Fluxion OF x x Will bC Z X N, SOP X L
  93. = X X X, buc The LIUXION OL H R X = X X X X
  94. LROL

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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/806933011:0342?run=74