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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: 0.84.

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The machine reads it as

  1. Since cheretore OurhrredS Theoremm, 25 is Tev-
  2. Fior 12, Their Summ, caken trom 90, che summ
  3. cd abore, is, Fhat SS = DD = AR. Where oEcheir Squares, lcares 7B; and added 10 27, cheir
  4. Core, : divide all b7 +: 55 - DD = R 5 Xet
  5. YR De made a Fangent ro the leNer, Or 2 RiglIE.
  6. sine ro the srearer Circle, as rou sec in the Figure
  7. accordins a5 D, Ox S, is siven: And deaw alsorhe
  8. Hrporhenuse II. Then Will che Base ot the Tri-
  9. onsle be d. And HHI - d d = R (b7 47. C L.)
  10. That is,
  11. DD
  12. P. Wheretore BY Fran-
  13. Cposirion, IL FF = R. j- d d, and cheretore HI =
  14. : R -= d d. And consequentir, il ic had been
  15. in the sirst or Second Forms, Wvhere d and R evere
  16. siven, EI vill also be Found. Or it II had been
  17. diren, and d required asinche Third Foem. Since
  18. AHI = R - ] dd: Theretore, LIHI -. R = d d,
  19. And V: HIHI = R = d: And harins thus found A
  20. and a, the = Sum and = Ditterence oF the trro ROOrS.
  21. Then HI = a (-= 0 p) Wvill bc che Greatex ROOE a.
  22. and II a (= p n) Wvill be che lesser, wtich vil
  23. be Afirmarire or Negarire, according eo the Form
  24. and Circumstances oEche Equarion.
  25. A Ouestion and Problems in Adfected Quadratick
  26. Equations.
  27. QVESTTON.
  28. Euo Mlen have each a certain Number os Cronns
  29. ohose sum Subtracted from ehe Sum of their
  30. Squares, leaves R =78: But their Sum added +0
  31. males 39 = 5.
  32. ITon mans Cromnshad each:
  33. For the untenoun Sum os che Numbers put 2 a.
  34. And For their Disserence 2 c.
  35. For then ehe Numbers may be thus Nored
  36. e = = and a = c
  37. Where = and =siexisie che prearer aned lester
  38. C
  39. Then,
  40. 2 a a = 2 C e = Sum Ot CCH AI.
  41. 2 4 4 -] - 2 cc -= 25 == R. byche
  42. Srare oErhe Ouection.
  43. 2 -- 2 3 a a - ec - a -. 39. =
  44. S.
  45. by TratP. 41 59 ad a = cc. WMCH SuP
  46. Dy Tranc. 1
  47. e
  48. Wwill ac last help ro And c.
  49. a a = ec - = 2 a = 5.
  50. Their
  51. eroduc added ro their Sum.
  52. a a - 2 a - 5 =
  53. ee
  54. 39 = a a -) a = a
  55. OY TratIP. 8(18 = 2 a 4 - a
  56. 3) a 4 - = a = 3 = S, Whic
  57. Ouadrarick oF hC HIILLOLLIL
  58. Compl. 10 a a - = a 17 25 = 39- 25
  59. 221 et 1. 37 1 260
  60. Rectans, makes 39.
  61. Let ci cooLtuldtosoltieus lillcead et a and
  62. The Difference of both the Less of a
  63. Rishransled Friansle beine siver
  64. from the Hypothenuse; 10 find the
  65. Sides and the Friancte severally,
  66. and to Form it.
  67. Tetthe Difterence ot thelellet Side Fromthe LIy.
  68. Pochenuse be (b) and char oE the grearer (d.)
  69. For ce Prearer, Side Conehr pur (a.)
  70. Thet vilt,
  71. a-) d = Fyporhenuse, and
  72. a- d= b= bc thelesser Side
  73. a a -) 2 a d - d d.=
  74. 2 a a
  75. 22d 2 a b- 2 bd.) d d 1 bb.
  76. a 2 - 2 a b = 2 b d - b0 = 0
  77. by Comparison and Transposi-
  78. tion oEche laA Scep
  79. a a = 2 ab == 2 b d =- b b. votrick
  80. is a Ouadraricke Equarion oErhie
  81. Second Form.
  82. tdus de te blcalet dide toul. d Co be C
  83. 2
  84. 7
  85. LV. B. By this Method oF purtins a l C aliet d = e
  86. c as I he Common was; many Ouestions
  87. producins Adtected Ouadrarick liquarions.
  88. Fspecially vrtien the sum and Diferenc, or
  89. Sum or Disterence ot che ascates et lle Man-
  90. rities Touslie, are amons ThC Data.
  91. otien etiat ar manae d, mas be solred as ca
  92. SilY, and in the mannet ot simple Equations.
  93. e.
  94. - 2a
  95. D+ 2a
  96. L ICOBL E M I.
  97. a a = 2 a b - - b b = 2 b d.
  98. a =- b = v : 2 b d
  99. a = V. 20u- b.
  100. Geometrical Construction.
  101. Trans
  102. Comp
  103. Find a mean Proportioras Betleen d a, Woset
  104. Iet DC DF: xo Which, place at Righranoles FC
  105. EOD F, and cuF Of II D = GD. Then wil
  106. produced eo C (Corhar C H = F. D) will give CD
  107. AC) che lesser Side oF che Priansle required
  108. FOF a - ) d- b = L. Draw a Semicirele on C B
  109. And (a) beins knOn, the ralue OF (e) ill and axpir A B FIB. Then drav A C and rhé
  110. Lhanele is tound, wrhichis AC B.
  111. 2 a =- ~. 39
  112. 13lLhetetore 2 a = 22.
  113. Number aS a e, Thatis 9; and the lesler Was
  114. =e; charis 3: Which Numbers 3 and 9, vili
  115. Antiver the Ouestion.
  116. bo found trom thefourth Scep. Where e = 2
  117. NTou, by our Supposition al Aest, the GrCateF

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/806933011:0683?run=74