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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. Compare chese tvo Series, wrich the rive
  2. Tet ehere be anocher Nuiiber i I - y: There
  3. OE che Theorem, and YoWH And a = 1, b = 0, Fore us Losarictim ill bC a Y F b y 2 -- cy 2
  4. 641 d = 0, = 4042s=0, 5 = n, b=0
  5. 6421 k = 0, 1:
  6. Hence Z = ny.
  7. 4041, m = 0, ec.
  8. 64: 32, ec. OF n y
  9. 2X34= ) A, Bc. Supposins A co denore the whol
  10. proccedine Term, wtiich vill De chie same Series
  11. 2o MI. Nermcon has tiest Eound:
  12. On che larme Mectiod chis Beneral Pioblem mas
  13. besolved.
  14. The Abscissa correspondins 10 a certain Area in
  15. any Curre beins giren, co sind etie Abseisa, wtiole
  16. Noi il 1 F 2 = r- - y, it Sollons,
  17. That a Z. F b2 = c2, etc. : ay 1 bgr f
  18. C73, ec. :. n: r.
  19. Thac 15, a Z- b32 cZ, eC. = n ay-
  20. n b92 = n cy. ec.
  21. Thetehote ve may ind ehie Value ot Z. exprese
  22. by che Povers oEy.
  23. apain: Since 1. + Z = 2 - y; cherelore
  24. = + - g - 1.
  25. Thacis, 2 = ny = x - 9. + X
  26. n - +
  27. n.
  28. correspondins Area Mallbe co rtie tust in a siren = X
  29. Ratio.
  30. Theresore q is doubly exprest by che Pomets ox
  31. The Locarirtimick Series mistir also be Pound y: Compare chese Wvo Values rogertier, and rhe
  32. vichout borromine any ortier Idea, rtianthac LO8a= Coesficients, a, b, c, _cc. Will be determined, ex
  33. richns are che Indices ot Povers:
  34. cept che Arst (a) Which may be cakten ac pleasure
  35. Let ihc Number wtose Loearichi inc imagine, and sires accordinoly all ehie disserene Species of
  36. ver Y Z; suppose is L ogarictimi 10 be a Z b2 Losacietims:
  37. 623 dic.
  38. redmeto Publish:
  39. The follomine Convergins Series for the L. s at ne o) The LOOES O) au quatiOnS, nhe-
  40. cher Simple or Adfected; the late Mr. Wastellof ihe Navy. OHice, senc me; and desi-
  41. A = Wdars Ablolure Number.
  42. n = to ehe Exponent ot ans Porrer.
  43. hP, q rySy e. che several Coesicienes in ans Equation.
  44. Then in ans Equarion it will be
  45. LX 4 = pX Xn - 1 = 9X . d - 2 p X r n - 3 = 5, 8c. = 4.
  46. And we have Unirertally,
  47. 2 fY n = + F gXn: 31In = 2F p X n 4Y n = 3+ BC
  48. FKnN = 1 = p Xn - LH n - 2 = gXn - 2R 1 - 3 = rXn- 3N 1 - 4 =, 3C.
  49. In irticti Series oblerre,
  50. L. Thac ehie lalie SIBA IH che eiven Lquarion, mult Ve in he Theorem OE Series respectirely.
  51. II. Any Term urhichis vanvine in che Equarion, must be omitted in che Series.
  52. III. The Oucrient at everr Operation, mustbe made a Ne N.
  53. IV. Thac ie terminares in che ROOr, Or Calls inco a Series, is it be a Surd.
  54. V. Suchi Series will be praclucee (in Nubes os Places) By a Ceometrical Proeretion Scom Unitr;
  55. Cirtiole Ratio is tw0) each Operarion.
  56. VL The nearer N is eaken eo etie rue Roor, ihe Pooner il Will Converse ro il.
  57. Ane in his Pdicion oE Passoni s Arichmerick, Docke 2. Cbap. 21. Vou may see a Cariher Accounc or etis ses
  58. sies, and che lame exemplitied in Numibersi
  59. Let id dus tumber allumed.
  60. n
  61. EA LAANONDANE

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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/806933011:0322?run=74