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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: 0.83.

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The machine reads it as

  1. Z
  2. quor just boil, and chen prets it hor chro a Cloch;; in ererr Memiber bB, 2b AC, 3c A Bd 4
  3. altex ehis, craporare che siltered Liquor to iis due ehe Sum of che FxponeHE OE he Capital Letters
  4. Consistence.
  5. 15 4. (Phere ic mar becaken norice, ot, Thac b
  6. THus are the Fxtracts oE Rhubarb, Centian, the Exponent OF a Letter, is meane the Number
  7. WorinWvood, (9c. made.
  8. erhich expresses irhat place ic has in the Alpracl
  9. LXTRA Fudiciat, in Lam, is irhen Judo- Thus a is che Lxponent ot che Lecrer V.) Elend
  10. ment is giren in a C ause or Casc nor dependins inis derired chis Rule For tindins che Capical Lerrers
  11. thac Coure where such fndsmenris siren, or Where. OF all che Members char belons ro any Porer.
  12. in che Fudge has nor furildiction.
  13. EXTRACTION, is a separarins oF Etie subrle
  14. Parr oF a mixed Body, Trom che more srols: FOF
  15. Fxample, When che Scrensch ot any Medicine is
  16. Fixcracted by Spirir of Wine, thac wrhich is lete af-
  17. rer the craporation oE he Menstruum is called che
  18. Fxtract.
  19. EXTRACTIONof Roots, in MachemarickS, is
  20. the method ot tindins our cherrue ROOEOF any
  21. Number orOuanciey siren. See Square Root, Cube
  22. ROOt, _CC.
  23. In Philos. FranC. DF 240. The Ingenious Mr. ABF.
  24. de Moirre sives thefollomins method os Pxeractine
  25. ehe R00t os an Insinite E quation.
  26. PHFOR P M.
  27. 1E aZ F b3 Y c2-F d5 + ez
  28. _c. = 5y By2 - i 92 ) k yt. 1gr +
  29. _c.
  30. Then Wvill ZbC = 5. y 1
  31. i - 2b AB =c _,, ,. L =bB =2b 4
  32. =30 A B = aA, , 1 = 2bBC = 2bAD
  33. = 3C AB. = 3cd. C = +d N B cA
  34. m= 2bBD = b CC = 2 b AF cB:
  35. ScABC - 3CA D = 6 d A B = 4 d A
  36. C=3e A B =5N y ec.
  37. Combine che Capical Lesters as osten as gou ean
  38. matee the Sum of the Fxponents equal 50 the In-
  39. dox of ibe Porer co mhich chey belonz.
  40. S. That ite Exponents ol ihe lame L etcers whicti
  41. are irricren betore ihe Capitals, exprels hion mans
  42. Capicals chere are in each Member.
  43. 6. Thac che Numeral Figures ox Vncia charoceur
  44. in Thele Members, exprels che number oF Permu-
  45. cacions Wrhich the Capiral Letrers oF each Member
  46. are capable ot.
  47. For rtie Demonstration or ihis,
  48. Sippose Z = A y L By C y 3, a
  49. Substiturechis Series in che room oF Z, and che POW
  50. ers oEchis Series in che room of the LoWetsel L
  51. there rill arise a new Series, CHEH CdKC The LO.
  52. + 2), Xc. and the C O. etACtenEs A, B, C, D, (30
  53. Will be tound much asis derermined in the Theo-
  54. rem.
  55. This Theorem mixhr hare Bech made muetimore
  56. general, by suppolins
  57. a2 =b2 402 2+ 2, ec. = 8 h +
  58. L 1g2 ec. Then all the POerS OF chC Se-
  59. sies Ay + By = Cy, ec. designed by etie urii
  60. versal Indices must hare been caken successirelr.
  61. This Theorem may be applied contiat is called
  62. the Reversion of Series; Tuch as tndine etie Numbet
  63. For the understandins ot ehis Series, and in or- trem its Losarichm siven, elic sinc trom ils arse
  64. derro conrinue II a5 tar as ve pleale, ir is ro be che Ordinate ot an Flliplis From an Area sirentobe
  65. oblerred,
  66. cur trom any Poine in che AXIS.
  67. I7 Thacererr Capital Lerter is equal to che Burromatre a parricular Application oF ic, we II
  68. Cocficient oF cach precedins Term: Thus the suppole chis Problem as to Besolved; viz. The
  69. Leter B is equal eo the Coefficient h= b A=
  70. 2. That che Denominator ol each Coetsicienti
  71. alvaySa.
  72. 3.Thar che tirst HembeF oF cach Numerator.
  73. is alwars a Coeficient ot the Series z y ) - B y
  74. L iy, ec. viz. The Arst Numerator begins ieti
  75. the Coesicienc e, the second Numeraror with che
  76. second Coefficiene h, and (0 on. nioi
  77. Chord oF an Ark beins siVe Wo nd he Lhora
  78. oF anocher Ark, thar Mall De rorhe trlt aSn FOL.
  79. Lec y bethe Chord eiven, Z The Chord requis d;
  80. non ihe Ret belongins 1o che Chora, i5 y. L ∞ d
  81. 39
  82. 10 t = 2 4s au che Ask beloneine 20 che
  83. Chord 2, 15 Z = 64 = 404F 1124
  84. the FrE OF these Arts, is co the 2d as iton; theres
  85. q. Thac in every Nember alter che srst, the Pore mulriptrins itie Fxireams and Means cogertier,
  86. Sum oE che Exponens oF che Capiral L erters is al
  87. ways equal ro the Index ot the Porver eo which
  88. ehis Member belongs: Thus considering the Co
  89. iciene L= bB = 2b A C - 3CA B = d A
  90. retiet belonso 10 chc Poee y, ve hail sec ac
  91. ve Mal have chis Equarion, Z = 68. 40de
  92. +
  93. +
  94. n aer de = n7 + a
  95. 5n 3, 8
  96. 112.
  97. 1
  98. 10
  99. efFICIEHES WIIICH DCIOMS CO The Sereral POrVerS OF
  100. correspondins Co. Culens e inc Settes 8) L B7
  101. in ehis neir Series, and make them equal ro thé
  102. Com:

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/806933011:0321?run=74