Leibniz Legible

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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: 0.90.

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The machine reads it as

  1. Then mulciply che Mra Rigure inco che le-
  2. cond, wrtich takten cogerher make a; and write
  3. S. Square the chird Fipure, and subleribe its
  4. Square 25 Betore in (Step. 3.) chen ad d all inco one
  5. in Produet dont rvice as betore (in SceP. 2.)
  6. The Frample Collonvs.
  7. 133225 (365
  8. 133225 == Square OF 365.
  9. From which Mechod oF compotine a Square
  10. crill be easie eo understand the way t0 Fxtract
  11. rhe Square RooroF ans Number siven,
  12. AS SupPOlC 133225. FOF,
  13. 2. Beginnine ac Cheriphr Fand, make a Pointover
  14. che Arst Figure (5); and aster chat over every ocher
  15. place alternatety. Which Poins me rou che
  16. Number oF Places in che ROOE.
  17. 2. Find che nearest. Square ROot to the srst parE
  18. 13, Wrhich is 3, urite ic in the Ouorient, and
  19. then place irs Square (9) under, and subtract i
  20. From 13. Ihis Roor is a, and che Square a a.
  21. 3. Toche Remainder (4) brine dovon che nexr
  22. Square 32, wrhich will make 432, and will be c.
  23. qual eo 2 a b -) = b b, in the last Scep oF all, els
  24. alvars bisger, and is called che Resolvend. Them
  25. double che Fisure (2) in che Ouorienc, and make
  26. it a Dirisor 20 all ihe Resolvend, excepe the last
  27. Figure rowardsche rishr Lland, enquirins hour of
  28. ren you can hare 6 in, 42, and place che Antver 6
  29. (FOr cho you can have ic 7 eimes, yer must noc
  30. bo caken, because ris 100 large) in che duorient,
  31. andalso atrer 6 in che Divisor. Phen multiply che
  32. thus augmented Dirisor by 6, and vrire the PrO-
  33. duct under, and Subtract ic trom che Resolvend
  34. Torhe Remainder 36, bring donn che next Square
  35. 25, and chen rou hare 3625 For a new Relolvend
  36. Fhen, as betore, double rhe Ouorienc 35, wtich
  37. akes 72 == 2 a, For a new Dirisor, and enquire
  38. ho otren rou can have 72 in 362, vrrire che An
  39. PIVer 5 = a in che Ouorient, and alo afrer the Di
  40. visor; and mulciplyins che ausmented Dirisor by
  41. ic, ron will hare a Product 36255 = 2 a b- 1 bb
  42. wtrich suberacted From che Relolrend, leares no-
  43. ching and (oche Work is over, and the true ROOt
  44. tound robe 365. TE chere had been more Points.
  45. che Work in chis chird Scep must hare been repea
  46. red ril all ras done.
  47. 432 = Relolrend.
  48. 396 = 2 2b -- b
  49. 3625 = Besolvend.
  50. 3625 = 24b.- b
  51. 0000
  52. Dut when a whole Number hach nor 2 Square
  53. Roor exactly exprestible by any rational Number,
  54. chan eo approach intinirels near che exaet ROOI
  55. Proceed chus.
  56. Place a5 many pairs oE Cyphers on che riehe
  57. Fland of che Remainder, as rou vould have Deci
  58. mal Places in che ROOr, and work as betore, di
  59. Rinsuishrins ehem trom che Incesers by a Comma,
  60. thus: IF FhC SguarE ROOEOF r2 be desir d tochree
  61. places in Decimals; annex 6 Cy phers 10 12, and
  62. cwvill stand etrus:
  63. 12, 000000
  64. Whose Square Roor beine extracted, is sound ie
  65. be3, 464, OF 3. ∞686 bur because of che Remain-
  66. der, ic must be chac 3, 464 is sels chan rhe crue
  67. TOOr, and 3, 465 greater than iE; Vet nOc wanuins
  68. the 200S OF an Vnit OF rhe true ROOF.
  69. The SquAsE ROBE OF a Vulgar Fraction, is
  70. thus found.
  71. Firs, HE che Praction be nor in ils least Terms;
  72. ler ic be reduced ro che least Perms; chen exrract
  73. tHC Square ROOF oF the DonOminaTOF FOF a neW
  74. Denominator, and of che Numerator for a new
  75. Numerator; ehis nem Fraction Mall be che Square.
  76. Root ol the Fraction propoled. Thus the Square
  77. ROOE OF 2 18 2, OF. = 15 3.
  78. HFche Vulgar Fraction siven, be incommensura.
  79. ble FO irS Square ROOL, boch in che siren PerMSs
  80. and also in any other Terms chac it is reducibleto;
  81. chen reduce the Paid Vulsar Fraction into Decis
  82. mals, consictins ot an eren Number ot Places; and
  83. chen extract che Square ROOr thereoF bY Approxi
  84. mation, accordins ro the Preceprs already delir
  85. rered.
  86. Thus: IFthC Squaro ROOF oF = De required, irs
  87. equiralent Decimal is 75y Wrhose Square ROOE,
  88. 86602, 690. Theretore che Square ROOT OF 3 15,
  89. 86602 ferc.
  90. HEa Mix d Number wete given For Fvrraction,
  91. Wohose Fractional Parr is exprest in Terms ot a
  92. Vulgar Fraction; ReduCCiE IntO an ImPFOPeF Fra-
  93. ction, and (it commensurable, extract the Square
  94. RoOE oF the Numerator and Denominator, (25 bC
  95. fore;) obserrins to reduce the Fractional parE OF
  96. the Mix d Number, (Or che improper Fraction e
  97. quivalene eo che Mixd Number) inco ies least
  98. TerInS.
  99. ThuS: THC Square ROOF OF 5 = I5 2 2, For etie
  100. improxer Fraction equiralene 105 3, is 13, and the
  101. Square ROOF OF 13, 183, Or21.
  102. 22. b = 66,
  103. 2 a. F b = 125
  104. Sum, and repeat ehis Procels as otten as there is
  105. Equied.
  106. occation; che last Sunt e au l M tue Square
  107. Thus.
  108. 160.

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/806933011:0776?run=74