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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: 0.88.

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The machine reads it as

  1. V. or. Suppose von vould Square chis Surd, :
  2. 22; because the Index 4, is compounded ol 2 anc
  3. 23 V: 12. is chetrue Froduct, or rhe rrue Square
  4. Olthe Surd ROot Y: 12. 50 20 theSquare OF V: 10
  5. i5 V: 1C
  6. The Realon ot ivhich, is plain: For suxpose cho
  7. : 16 = 2 Were t0 be squared; irs square in
  8. Surds Will be expressed thus, V: 16 == 4
  9. Bur woten a simple Surd Ouanciry, whosc Radi-
  10. cal sign hach For ies Index some Pernaer Number
  11. oreater chan 3, 25 6, 9, (9c. And tis required t0
  12. Involre rhis Surd Cubically. Then only pretix
  13. betore the Ouantiey a Radical Sign, wich an In
  14. dex, wtiich is one chiird ot cheformer, and ris done
  15. Thus, IE V: 64, were 10 be Cubed, ic will bC
  16. V: 64, and the Cube oF V: 522. 15 V: 512, 00
  17. al(orhe Biquadrare oF V: 5. I5 25 (25 being thC
  18. Square ot che Square ol Y: 5.) And ihe Cube ol
  19. V: 81, Wvill V: 8Y OF 9.
  20. In the general, tosquare, Cube, Rc. any Surd
  21. Root, is ontr ro Square or Cube che Power, re
  22. cainins che lame NoreoF Radicalier; bur ris vet
  23. ter where ic can be donc, tocake one halF, pare
  24. 59C. oF ete FXponent oFthe ROOr, as is abore Mewn
  25. inthe last particular Rules.
  26. Onthe contrary, it vou vould extract che Square
  27. Cubo, Or other Roor ot any Surd, rou inust double
  28. oxtriple, (090. che Exponene ot che Radicalier. Thus
  29. che square Root OF Y: 16 is Y: 16. che Square R00
  30. oC V: 27161: 27. 90.
  31. Division of Simple Surd RootS.
  32. I. IF che Surds are Similar, Flomosencal, Or0
  33. the Came kind, divide onc Number, Or Ouantity
  34. by anocher, and prelix che common Radical Sisn
  35. coche Ouorient: Buris cher are Lererogencal, Ot
  36. noc oE che same tcind, ehes mult be reduced besore
  37. they can be divided.
  38. Thus, V: 9d Y: 326 (V: 64 = 8. And
  39. s: 5
  40. C
  41. 35 (Y: 2
  42. The Demonstration oF wotich General Rule, i
  43. the Camie as thac in Mulciplication; for from che
  44. Nacure ot Division, che Diritor is toDnity:: a
  45. ihe Dividend eo che Ouotient. Therctore in our
  46. sirst Instance, V: 9. V: l: : V.: 576. V: 64
  47. buc 25 chese Roors are, (0 Will cheir Squares bc
  48. That iS, 9. I : : 576. 64. and chac chese Number
  49. are cruly Proportional, is apparene; because the
  50. Rectaneles oF Fhe FXtreamS and MeanS are equal
  51. WVheretore, V: 9. V: F: : V: 576. V: 64. anC
  52. consequemts 64 is che true Quorienr.
  53. TI. YF any Racional Ouanrier be ro be dirided b
  54. itS Square ROOT, the Square RoOrwill BetheOuo.
  55. tient: For it a b bc dirided by V: a b, the Onori
  56. ene mustbe V: ab: And if 50 bc dirided by v
  57. 50, the Ouoriene Will al(obc V: 50. AIOit, any
  58. Rational Ouancier berobe dirided by a Surd, cha
  59. Racional Ouanciry must sirst be reduced 10 cho
  60. Form oF 2 Surd, bY Rule F.
  61. LII. Dhena Surd RoOE havins a Rarional Ouan-
  62. cir prefix d belore Il, 15 lo be divided oy lne Surd
  63. parr oFic, the duoriene will bethe Rational Ouan-
  64. Eier. ThuS, il 5 V: 9, betobedirided by V: 9
  65. the Ouoriene must be 5: A5 it 5 V: 9 had beei
  66. dirided br5. che Duorienc voula be V: 3.
  67. IV. Wrhen elie Diridend and Divisorare che Pro-
  68. ces et C Macteut Ludnririe; mulriplied seve
  69. Fally into one common Surd; Or wlien cher are
  70. Cctclus 6) Cl Lultotat Pdet et CC DLIOE, atic
  71. ertiar reluls, is the ue Suortel.
  72. LMuS, IF 8 V: s bc dirided b7 2 V: 5; chc
  73. Ouorienr will be 4, and if 8 Y: 7, be divided by
  74. 4V: 2, che Ouoriene will be Onif 2.
  75. V. Buc vohen che Diridend and Dirilor are rvo
  76. Racional anciries, or Numbers, prefix d io rwo
  77. unequal Surds; rhen ron must diride, noc only 25
  78. betore, che Rational parr oF the Diridend By chat
  79. Ot che Dirilor, buc also che Surd part; and chose
  80. eivo Cuorienrs connected rogetter, (0 as the Ratio-
  81. nal pari Rand on the Lefe Lland, are the erue Juo:
  82. tient Coughr.
  83. Thus, il 4 V: 15 vere co be dirided by 2 V: 5.
  84. the Ouotiene Will be2 V: 3 (= V: 12.) and il
  85. 4V: 12, Were 10 be dirided by3. J: 2, cheu0-
  86. tiete will BC V: 6.
  87. T. YVHeN HNO Ox more Simple ana Lguat sutas
  88. are to be added, mulciply one oF chem by che
  89. Number oF them all, and the Product is the SuMI
  90. required.
  91. Thus, The Sum oF V: 5, and V: 5, is che
  92. V: 203 because V: 5 mulciplied by 2, che
  93. Number ofche Surds, chat is by V: 4, sires V:
  94. 20 cheie Sum. AlCo che Sum OF Y: 7 F Y: 3
  95. V: 7; becauseche Surds are 3 in Number, i5
  96. s: 189; Because Y: 7 mulciplied b7 3 (1. c.) che
  97. Y: oc 27 mates Y : 189.
  98. TI. BUE iF 2 nequat Simple Surds OF the lame
  99. tind are ro be added cogether, or it orie ro be sub
  100. eracted From the other, vou must sirst ery Wwhethee
  101. cherare Commenturable; and it cher De, chatis.
  102. it wten cher hare been dirided by their grearest
  103. common Divisor, cheie Ouorients are Rarionat
  104. Ouancicies, then rou must Mulciply the Sum ob
  105. chose Rationas Ouanciries by che laid Common
  106. Dirisor, and the Produet will be the Sum ol the
  107. Surds propoled: Or il chie Ditterence oF chose Ra-
  108. rional Ouorients be multiplied by the Common
  109. Dirisor, Thenthe Product willbe the Difference ot
  110. che siren Surds, when che lels is ratcen trom che
  111. Sreater.
  112. Thus, IF che Sum or Diserence OF chele tvc
  113. Surds, V: 50, and v: 8. Were required; becaule
  114. they are unequal, L ery sirst, Whether cheY ArC
  115. Commenturable, or nor, by dividing cach by the
  116. sreatest common Dirilor V: 2. And che Ouotients
  117. are V: 25 and V: 4; chac i5, 5 and 2, Wtich are
  118. Racional Numbers; and cheretore che Surds arc
  119. Commenturable: Then cheir Sum 7, or their Dit
  120. ference 3, mulciplied by che common Diriser S: 2
  121. Produces 7 V: 2 For che Sum, and 3 V : 2 EOF
  122. che Difierence ot che durds required.
  123. TIT. TEche Commensurable Surds proxoled, hac
  124. been Fractione, oe Mrine Wuribere, reduced re che
  125. Focu
  126. Racional Ouancules Pren d Detore one Comnion
  127. Surd; then diride ehe Rarional parr oF the Diri-
  128. Aadition and Subtraction os Surd Roots.

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/806933011:0792?run=74