Key to the Course of Mathematics, Composed by Charles Hutton
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Key to the Course of Mathematics, Composed by Charles Hutton

Key to the Course of Mathematics, Composed by Charles Hutton


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About the Book

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1818 Excerpt: ...ro be the surface of the water round the ball, the cone being per-At fectly upright; and let Hki be a horizontal tangent at K to the sphere immersed; Fzg a line parallel to Hi from c a point of contact of the globe and cone, D the center of the sphere, and Dg a radius at right angles to Bc the slant side of the glass. Join Ab, an, ai; and from c draw Ce perpendicular to Ab; Ce passes through the points K, D, and bisects Ab in E. By the Question Ab=5 inches, Ec=6 inches, and Dg or Dk= 2 inches; also, by the last example, the slant side Bc=6'5 inches, and Dc=5'2 inches. But, in. in. in. in. As 6-5 bc: 6 ec' 5-2 cd: 4-8 gc. Likewise in. in. in.. in. As 5-2 cd: 4-8 gc:: 4-8 gc 4 43077 ac. Consequently, By subtraction Ck=32 inches, and -k= 1-23077 inches. And.. in. in. in. in.. As 6 ce: 3-2 ck:: 5 ab: 2-666 hi. Now the ungula Jiog above the level ro is equal to the cone abc above the same level; wherefore, if Q be put for the Diameter in inches, and R for the Altitude in inches of a cone equal to the given cone; also s for the solidity in inches, of the cone abc; it will be maX-7854xac _ a2X-7854XR _ 3 3 S That is, substituting numeral values, in. Const, dee.) in. in. (Const, dec") in. $ (2-66 x:7854 x 4-43077)-(2-9242 x-7854 x 3 509), or cnb. in. cab. in. cub. in. 8-2487--7-8543=-3944 the content of the cone abc, or of the ungula Gno. But, As Cone am: Cone abc:: ak3: ams. Hence a7-=-6S4 of an inch. (Key to Vol. II. jiage 865.) Quest. 56. Let Abc (as in the two pre-ceding Examples) represent the conical glass, rao the level of the water before the sphere is immersed, and Fkg its surface after the ball has sunk; alio let D be the center of the sphere, bi a radius at right angles to Bc, and ab a line parallel to Fg or ro from tbe point of contact ...


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Product Details
  • ISBN-13: 9781130797923
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 40
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130797929
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 91 gr


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