Solid GeometryMacmillan, 1913 - 107 páginas |
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Página 243
... square piece of timber a portion of which one end is to be perpendicular to the lateral edges , while three given lateral edges are to be 3 ft . 6 in . , 3 ft . 4 in . , and 3 ft . long , respectively . Show that these measure- ments ...
... square piece of timber a portion of which one end is to be perpendicular to the lateral edges , while three given lateral edges are to be 3 ft . 6 in . , 3 ft . 4 in . , and 3 ft . long , respectively . Show that these measure- ments ...
Página 247
... square of the diagonal is equal to the sum of the squares of the three edges that meet in any vertex . [ HINT . The diagonal is the hypotenuse of a right triangle whose sides are one of the edges and a diagonal of one face ; the ...
... square of the diagonal is equal to the sum of the squares of the three edges that meet in any vertex . [ HINT . The diagonal is the hypotenuse of a right triangle whose sides are one of the edges and a diagonal of one face ; the ...
Página 252
... square each side of which is 3 in . Find its volume . 6. Show that two prisms with equal bases are to each other as their altitudes ; and that those with equal altitudes are to each other as their bases . 7. A clay cube having a 2 - in ...
... square each side of which is 3 in . Find its volume . 6. Show that two prisms with equal bases are to each other as their altitudes ; and that those with equal altitudes are to each other as their bases . 7. A clay cube having a 2 - in ...
Página 257
... square base is 16 in . , the area of a section parallel to the base and 10 in . from the vertex is 561 sq . in . Find the area of the base . 3. The bases of the frustum of a regular pyramid are equi- lateral triangles whose sides are 10 ...
... square base is 16 in . , the area of a section parallel to the base and 10 in . from the vertex is 561 sq . in . Find the area of the base . 3. The bases of the frustum of a regular pyramid are equi- lateral triangles whose sides are 10 ...
Página 262
... square and its altitude is 3 ft . , how long must each side of the square be in order that the volume may be 16 cu . ft . ? 4. Show that the volume of the tetrahedron , all of whose edges are equal to a , is √2 a3 / 12 . [ HINT . See ...
... square and its altitude is 3 ft . , how long must each side of the square be in order that the volume may be 16 cu . ft . ? 4. Show that the volume of the tetrahedron , all of whose edges are equal to a , is √2 a3 / 12 . [ HINT . See ...
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Términos y frases comunes
acute angle altitude h angle formed Angle Sine angles are equal bisect circle circumference congruent Corollary corresponding cube diameter dicular dihedral angle distance drawn equal altitudes equal spheres equilateral EXERCISES face angles Find the volume formula frustum gent Chord Arc given line given point Hence HINT hypotenuse inscribed intersection isosceles lateral area lateral edges length lines are parallel locus lune whose angle measured number of sides parallel planes parallelogram perimeter perpen perpendicular to MN plane angles Plane Geometry plane MN plane perpendicular points equidistant polar triangle pole prove radii radius ratio rectangular parallelepiped regular polygons regular polyhedron regular pyramid respectively right angles right prism right section right triangle segment Show similar slant height spherical degrees spherical excess spherical polygon spherical triangle square straight line surface tangent tetrahedron Theorem VII triangular prisms triangular pyramids trihedral truncated prism unequal V-ABC vertex vertices
Pasajes populares
Página xxxv - If two triangles have two sides of the one equal to two sides of the...
Página 312 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.
Página 224 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Página 303 - 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...
Página 258 - Aa, and let k be one of those parts ; through the points of division pass planes parallel to the plane of the bases ; the corresponding sections...
Página 220 - If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to their plane. Given FB perpendicular at B to each of two straight lines AB and BC of the plane MN. To prove FB perpendicular to the plane MN.
Página 254 - A truncated pyramid is the portion of a pyramid included between the base and a plane not parallel to the base.
Página xlii - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Página 319 - The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters.
Página 308 - ... respectively equal to two face angles and the included dihedral angle of the other.