The Elements of Solid Geometry |
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Page 11
... lie between the edges are termed the faces . 37. The plane angles lying between the edges and hav- ing a common vertex , are called face angles . 38. The face angles and the diedral angles between the LINES AND PLANES IN SPACE . 11.
... lie between the edges are termed the faces . 37. The plane angles lying between the edges and hav- ing a common vertex , are called face angles . 38. The face angles and the diedral angles between the LINES AND PLANES IN SPACE . 11.
Page 17
... termed oblique . 57. The altitude of a prism is the perpendicular dis- tance between the bases . 58. Any section of a prism perpendicular to the lateral edges is called a right section . From the definition of a prism we readily deduce ...
... termed oblique . 57. The altitude of a prism is the perpendicular dis- tance between the bases . 58. Any section of a prism perpendicular to the lateral edges is called a right section . From the definition of a prism we readily deduce ...
Page 18
... termed right or oblique according to the conditions of Art . 56 . From the definition the student may readily deduce the following : - ( a ) The opposite faces are parallel . ( b ) Any right section is a parallelogram . ( e ) All right ...
... termed right or oblique according to the conditions of Art . 56 . From the definition the student may readily deduce the following : - ( a ) The opposite faces are parallel . ( b ) Any right section is a parallelogram . ( e ) All right ...
Page 25
... termed an element of the surface . N F B M D E CD is a moving line always parallel to NM a given fixed line , and continually touching DEA , a guiding curve . The guiding curve and the given fixed line lie in different planes . CD , FE ...
... termed an element of the surface . N F B M D E CD is a moving line always parallel to NM a given fixed line , and continually touching DEA , a guiding curve . The guiding curve and the given fixed line lie in different planes . CD , FE ...
Page 26
... termed a right circular cylinder . The axis of the cylinder is the line joining the centres of the bases . оо 85. A right circular cylinder is called a cylinder of revolution ; for if a rectangle be re- volved about one of its sides as ...
... termed a right circular cylinder . The axis of the cylinder is the line joining the centres of the bases . оо 85. A right circular cylinder is called a cylinder of revolution ; for if a rectangle be re- volved about one of its sides as ...
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Common terms and phrases
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle EDC-O equal with respect equivalent faces is called feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA lune MN and PQ mutually equal O-ABCD oblique parallelopiped parallel planes parallelogram pass perimeter perpen perpendicular to MN plane angle plane MN plane PQ polar triangle polyedral angle prisms whose bases radii radius regular polyedrons regular polygon right angles right circular cone right prism right section SCHOLIUM sides slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tetraedron THEOREM triangles ABC triangular prism triangular pyramids triedral
Popular passages
Page 48 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Page 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 4 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Page 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Page 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 56 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.