A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying: Adapted to the Method of Instruction in the American Colleges
A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying: Adapted to the Method of Instruction in the American Colleges
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. 1854 Excerpt: ...the two ends, there may be drawn in each, such a number of small rectangles, that the sum of them shall differ less, than by any given quantity, from the figure in which they are contained. And the solids between these rectangles will be rectangular prismoids. Ex. 1. If one end of a rectangular prismoid be 44 feet by ...
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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. 1854 Excerpt: ...the two ends, there may be drawn in each, such a number of small rectangles, that the sum of them shall differ less, than by any given quantity, from the figure in which they are contained. And the solids between these rectangles will be rectangular prismoids. Ex. 1. If one end of a rectangular prismoid be 44 feet by 23, the other end 36 by 21, and the perpendicular height 72; what is the solidity? The area of the larger end =44x23=1012 of the smaller end =36x21= 756 of the middle section =40x22= 880 And the solidity =(1012+756 +4x880)xl2=63456 feet. 2. What is the solidity of a stick of hewn timber, whose ends are 30 inches by 27, and 24 by 18, and whose length is 48 feet? Ans. 204 feet. Other solids not treated of in this section, if they be bounded by plane surfaces, may be measured by supposing them to be divided into prisms, pyramids, and wedges. And, in.v deed, every such sobi may be considered as made up of triangular pyramids. THE FIVE REGULAR SOLIDS. 56. A SOLID IS SAID TO BE REGULAR, WHEN ALL ITS SOLID ANGLES ARE EQUAL, AND ALL ITS SIDES ARE EQUAL AND REGULAR POLYGONS. The following figures are of this description; 1. The Tetraedron, 2. The Hexaedron or cube, 3. The Octaedron, 4. The Dodecaedron, 5. The Icosaedron, whose sides are four triangles; six squares; eight triangles; twelve pentagons; twenty triangles. Besides these five, there can be no other regular solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are together. less than four right angles or 360. (Sup. Euc. 21,2.) And the least number which can form a solid angle is three. (Sup. Euc. Def. 8, 2.) If they are angles of equilateral triangles, each is 60. The sum of three of them is 180, of ...
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