The Elements of Solid Geometry |
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Page 9
... called the faces of the angle . 30. Lines drawn in the faces of a diedral angle perpen- dicular to the edge and from the same point in it , form a plane angle which is taken as the measure of the diedral angle . D A If the plane DE ...
... called the faces of the angle . 30. Lines drawn in the faces of a diedral angle perpen- dicular to the edge and from the same point in it , form a plane angle which is taken as the measure of the diedral angle . D A If the plane DE ...
Page 11
... called the vertex of the angle . The lines in which the planes meet are called the edges of the angle . Those portions of planes which lie between the edges are termed the faces ... called face angles . 38. The face angles and the diedral ...
... called the vertex of the angle . The lines in which the planes meet are called the edges of the angle . Those portions of planes which lie between the edges are termed the faces ... called face angles . 38. The face angles and the diedral ...
Page 12
William C. Bartol. 38. The face angles and the diedral angles between the faces are called the parts of the polyedral angle . 39. Two polyedral angles in which all the parts of the one are equal to all the parts of the other , each to ...
William C. Bartol. 38. The face angles and the diedral angles between the faces are called the parts of the polyedral angle . 39. Two polyedral angles in which all the parts of the one are equal to all the parts of the other , each to ...
Page 17
... called faces . The intersections of the faces are called edges . The points in which the edges meet are called vertices . 52. A prism is a polyedron whose edges are all parallel , except those formed by two parallel faces cutting all ...
... called faces . The intersections of the faces are called edges . The points in which the edges meet are called vertices . 52. A prism is a polyedron whose edges are all parallel , except those formed by two parallel faces cutting all ...
Page 26
... face and two parallel planes called bases . The bases cut all the elements of the cylin- drical surface . If the bases are circles as in the figure , the cylinder is said to be circular ; and if the generating line is perpendicular to ...
... face and two parallel planes called bases . The bases cut all the elements of the cylin- drical surface . If the bases are circles as in the figure , the cylinder is said to be circular ; and if the generating line is perpendicular to ...
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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.