The Elements of Solid Geometry |
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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 If the plane DE intersect the plane DF in 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 If the plane DE intersect the plane DF in LINES AND PLANES IN SPACE . 9 DEFINITIONS: DIEDRAL ANGLES.
Page 10
William C. Bartol. D If the plane DE intersect the plane DF in the line DG , then F - GD - E , the angle between the planes , Α C A G C B B ' E is a diedral angle . DF and DE are faces and DG is the edge of the diedral angle . In the ...
William C. Bartol. D If the plane DE intersect the plane DF in the line DG , then F - GD - E , the angle between the planes , Α C A G C B B ' E is a diedral angle . DF and DE are faces and DG is the edge of the diedral angle . In the ...
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 ...
... 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 ...
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 is a polyedral angle of three faces .. LINES AND PLANES IN SPACE . 13 ...
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 is a polyedral angle of three faces .. LINES AND PLANES IN SPACE . 13 ...
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Common terms and phrases
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting called centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle equal with respect equivalent feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA line is perpendicular lune MN and PQ mutually equal O-ABCD oblique parallelopiped one-third the product parallelogram pass perimeter perpen perpendicular to MN plane angle plane PQ polar triangle polyedral angle prisms whose bases radius regular polyedrons regular polygon regular pyramid right angles right circular cone right prism right section SCHOLIUM similar slant height sphere spherical angle 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 30 - The lateral or total areas of two similar cglinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each, other as the cubes of their altitudes, or as the cubes of the radii of their bases. Let S and s...
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 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.
Page 29 - The lateral area of a prism is equal to the product of the perimeter of a right section and a lateral edge.
Page 61 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...