An Introduction to Solid Geometry: And to the Study of Chrystallography ; Containing an Investigation of Some of the Properties Belonging to the Platonic Bodies Independent of the Sphere

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author, 1820 - Crystallography, Mathematical - 140 pages
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Page 4 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center. The radius of a sphere is a straight line drawn from the center to the surface.
Page xii - XIII. is now in the Press, and will be published in the course of the present year.
Page 3 - ... alike in form. What is their form ? Yes ; they are all triangles. How does the number of triangles on each compare with the number of sides to the base ? Yes ; there is the same number of them. Now I will tell you, that all solids of this description are called pyramids. Can you describe a pyramid ? A pyramid is a solid, having a polygon for its base, and as many triangles tapering toward one point (the apex) as there are sides in the base. The teacher has to add, that according to the number...
Page vii - ... Mr. Travers on a voluntary action of the Iris, which was published by Mr. Travers in his work ' On the Diseases of the Eye;' and an Appendix to Larkin's ' Introduction to Solid Geometry and to the Study of Crystallography,' in which Dr. Roget demonstrates the ratios subsisting between the volumes of solids composing the artificial series, together with the various inclinations of their faces. In 1821 he wrote "Observations on Mr. Perkins's Account of the Compressibility of Water," in the 'Annals...
Page 112 - ... number of faces, similar each to each, and similarly placed. Any two homologous tetrahedrons are similar. Two similar tetrahedrons are to each other as the cubes of their homologous edges, and two similar polyhedrons are to each other as the cubes of their homologous edges; therefore, similar prisms, or pyramids, are to each other as the cubes of their altitudes and similar polyhedrons are to each other as the cubes of any two homologous lines. Similar cylinders of revolution are those generated...
Page 80 - ... and described in schemes or diagrams upon a floor, sufficiently large for all the parts of the operation, has been called DESCRIPTIVE CARPENTRY. In order to prepare the reader's mind for this subject, it will be necessary to point out the figures of the sections, as taken in certain positions. ALL THE SECTIONS OF A CYLINDER, parallel to its base, are circles. All the sections of a cylinder, parallel to its axis, are parallelograms. And, if the axis of the cylinder be perpendicular to its base,...

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