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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: 0.81.

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The machine reads it as

  1. To Fxtract the Square Loot, accordine 10 the Methoa
  2. Suppose a a = c = 2.
  3. For a cate anx Binomial, 25 suppole r - ]- 5
  4. is best Eo maker == 1, (1. 0.) toche trst ROOF, Or
  5. Side, ot rhe siven Square, becaule chen d will con-
  6. verse rhe (OOneT.)
  7. Then wilt rr 1 2r5 155 = a a =
  8. Reject the Porver oF S, as beins ot lmall value
  9. Then will rr. F 275 = 0, Or2r5 = c = r7
  10. Divide all b7 2r; ard etien S =
  11. eohich is che standins Theorem.
  12. Suppose hereforer = L; then = c = 3
  13. Make 2 n che Divitor ) 1,0 l, 5 = 5
  14. To obviare wtich, eis much bercer ro. use etze
  15. tollowins as, whichis Mr. Ward S.
  16. Wtence atises chis Thectem,
  17. dividins all Br r. F 25.
  18. 9
  19. Pet chen (a5 betore) che SquATE ROBEOLZ = C
  20. a an be required.
  21. First, Takier = 1: Then talve che Resolvend
  22. = 1: And som it rake L r r =. 5, there
  23. remains. 5 =D. Make
  24. Tochehcr = 3, adet ,3 = 5, For a secondr, in = 2, che Divis.) . 50 (4 = 5. subseri. = S5 - B under
  25. order For a new Operation.
  26. Then L,5 ische newr, che Square oF Wetich, is
  27. 2, 25 ==rr; Trom which Subtract 2 = c because
  28. 2 i5 lels char 2, 25, and vis Aand chus.
  29. 48 = r5 ] = 5S Eche Cypher
  30. Di. = r L 5= 1, 4) 20 (20 (1, =5
  31. 145 = r 5 ] =55
  32. Let S beFOr == 2, 2nd r -]- 5 = a.
  33. Are AI by 2; chen ris : r5. = 55
  34. C
  35. of Convergins series.
  36. Y = 23 23
  37. da
  38. Themrr I 215(55=
  39. iie lcten, al 10 2d
  40. 27 = D, ic Dividend.
  41. 11. - 8 1 5 = l, 4 11 5500 (3 = 5
  42. 4234,3 = rd 2dd
  43. 2r = 3)0, 25
  44. Which mustbe dividedbr 2r = 3, and che Ouo-
  45. tiene will bc--. 083 =S; erhich havins a dese-
  46. etive sien, must be subcracted trom the last
  47. et ae 14l3) 12633010
  48. 113072 =r5 F :55
  49. r = 5 = 1, 4138) 1347800 (9 = 5
  50. e
  51. 127246, 5 =75 7255
  52. 2,41389) 7533500 (5 =5
  53. 9069462,5 = r5 )= =55
  54. 38:
  55. 2341
  56. 25 5693. 40403133 d
  57. ies Square beins 2,007669 =r r, (as beloe8led
  58. cex Mhan 2 = c.) Lalie 2=c tolu llllo.
  59. Lhis ROOE a == 1, 413895 ditters ton ne 1O-
  60. met RoOr Found, bur by 0,000022 (a lictle more
  61. TalI 2050 3) FOr no exaet Roor can befound by ei-
  62. Which will Be a neirr, For a chird Operation; anc
  63. 2,007883
  64. cher waz.
  65. Flere also, is more exactnels had been required,
  66. ehe Remainder enelcaleuo) Csptiers, migtie have
  67. been inade a ne Diridend, and 1, 4r3895 a new
  68. Divitor; and (o rou may proceed on a5 Far 25 YOU
  69. Lcablo. 607689 = 5.
  70. Wrhich beins divided by ervice chelater, = 2,654
  71. sives in che DuOtIeHE =. 002783 = 5; and chis
  72. S subrracted trom che last
  73. Former, any one ill soon sind chac rill eer borh.
  74. 19 4l7
  75. 30278:
  76. chir HC.
  77. The vast Adrantase of ehis Method aborertic
  78. 2,414217 = a
  79. An Lxamole ofsus, in a true square uet
  80. Wrhich sires the ROOE +0 7 placeS AE FhrCC O pera.
  81. FIONS.
  82. Buc if more exactnels be necellarr, call ic a
  83. nerr, tor a tourch Operacion, une procced julta5
  84. betore.
  85. N. B. This Method, which iS MT. Raphson S,
  86. is very precer, buc ic labours under cvo Inconre-
  87. niencies, viz. The creaness of the Divisors, andihe
  88. bigh Involutions; especiallr in extractins ROOrS OuE
  89. OE hieher POWerS, aS che Cube, Bequad st
  90. Foret, a.
  91. ThCSquare ROCC O 133LL3, noLeScntCla,
  92. 66612,2 = = C.
  93. 43 5 =
  94. =r == 3) 216 (6
  95. 198 = r5 ] E5S
  96. 0) 1812,5
  97. 1812,5 =75 ] -55
  98. 0000,0
  99. Therctore, a = 365.
  100. SQCIARHIC

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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/806933011:0777?run=74