The Elements of Solid Geometry |
From inside the book
Results 1-5 of 16
Page 7
... plane which is parallel to PQ , and it will be perpendicular to AD ( 21 ) . But only one plane can be passed through ... angle ( 4 ) ; therefore DCF is a right angle . Then , since DC is perpendicular to CF any line in the plane xy , DC ...
... plane which is parallel to PQ , and it will be perpendicular to AD ( 21 ) . But only one plane can be passed through ... angle ( 4 ) ; therefore DCF is a right angle . Then , since DC is perpendicular to CF any line in the plane xy , DC ...
Page 9
... 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 intersect the plane DF LINES AND PLANES IN SPACE . 9 DEFINITIONS: DIEDRAL ANGLES.
... 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 intersect the plane DF LINES AND PLANES IN SPACE . 9 DEFINITIONS: DIEDRAL ANGLES.
Page 10
William C. Bartol. D A If the plane DE intersect the plane DF in the line DG , then F - GD - E , the angle between the planes , A F B B ' E is a diedral angle . DF and DE are faces and DG is the edge of the diedral angle . In the face DF ...
William C. Bartol. D A If the plane DE intersect the plane DF in the line DG , then F - GD - E , the angle between the planes , A F B B ' E is a diedral angle . DF and DE are faces and DG is the edge of the diedral angle . In the face DF ...
Page 11
... angle ABS is the measure of the diedral angle between the planes PQ and MN ... ( 30 ) . But since ABS is a right ... plane . Thus , as we see , the line BA drawn in the plane PQ perpendicular to the intersection BQ , is perpendicular to ...
... angle ABS is the measure of the diedral angle between the planes PQ and MN ... ( 30 ) . But since ABS is a right ... plane . Thus , as we see , the line BA drawn in the plane PQ perpendicular to the intersection BQ , is perpendicular to ...
Page 12
William C. Bartol. 38. The face angles and the diedral angles between the faces are ... plane mirror . Place O ' - A'B'C ' under O - ABC , so that A'B'C ' coin ... angle of a 12 THE ELEMENTS OF SOLID GEOMETRY . DEFINITIONS: POLYEDRAL ANGLES.
William C. Bartol. 38. The face angles and the diedral angles between the faces are ... plane mirror . Place O ' - A'B'C ' under O - ABC , so that A'B'C ' coin ... angle of a 12 THE ELEMENTS OF SOLID GEOMETRY . DEFINITIONS: POLYEDRAL ANGLES.
Other editions - View all
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.