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A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids; Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids; Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges


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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. 1815 Excerpt: ...of AB is equal to that produced by the revolution of ab. And the surface produced by BD is equal to that produced by bd. Ex. 1. Considering the earth as a sphere 7930 miles in diameter, how many square miles are there on its surface? Ans, 197,558,500. 2. If the circumference of the sun be 2,300,000 miles, what is his surface? Ans. 2,495,547,600,000 sq. miles. 3. How many square feet of lead will it require, to cover a hemispherical dome whose base is 13 feet across? Ans. 265J. PROBLEM V111. To find the Solidity of a Sphere. 70. 1. Multiply the cube of the diameter by.5236. 2. Multiply the square of the diameter by of the circumference. Or, 3. Multiply the surface by of the diameter. 1. A sphere is two thirds of its circumscribing cylinder. (Sup. Euc. 21. 3.) The height and diameter of the cylinder are each equal to the diameter of the sphere. The solidity of the cylinder is equal to its height multiplied into the area of its base, (Art. 64.) that is, putting D for the diameter, DxDx.7854 or D2 X.7854. And the solidity of the sphere, being-of this, is Dsx.5236. 2. The base of the circumscribing cylinder is equal to half the circumference multiplied into half the diameter, (Art. 30.) that is, if C be put for the circumference, CD, and the solidity is JCD. Therefore the solidity of the sphere is f of iCD-=DsxiC. H 3. In the last expression, which is the same as CD x JD, xve may substitute S, the surface, for CD. (Art. 69.) We then have the solidity of the sphere equal to SxD. Or, the sphere may be supposed to be filled with small pyramids, standing on the surface of the sphere, and having their common vertex in the centre. The number of these may be such, that the difference between their sum and the sphere shall be less than any given quantity. The...


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Product Details
  • ISBN-13: 9781155015804
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 84
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1155015800
  • Publisher Date: 06 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 168 gr


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A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids; Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges
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