Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 277
... trihedral , quad- rahedral , etc. , according to the number of the faces . 482. DEF . Trihedral angles are rectangular , bi - rectangular , or tri - rectangular , according as they have one , two , or three right dihedral angles . 483 ...
... trihedral , quad- rahedral , etc. , according to the number of the faces . 482. DEF . Trihedral angles are rectangular , bi - rectangular , or tri - rectangular , according as they have one , two , or three right dihedral angles . 483 ...
Σελίδα 279
... trihedral angle is greater than the third . S A D B Let S - ABC be a trihedral angle in which the face angle ASC is greater than either angle ASB or angle BSC . We are to prove Z ASB + Z BSC > < ASC . — In the face A SC draw SD , making ...
... trihedral angle is greater than the third . S A D B Let S - ABC be a trihedral angle in which the face angle ASC is greater than either angle ASB or angle BSC . We are to prove Z ASB + Z BSC > < ASC . — In the face A SC draw SD , making ...
Σελίδα 282
... trihedral Draw D'D making the S - ABC trihedral △ S - A'B'C ' . Then DSA , DSC , and DSB equal . Z D'SA ' = LD'S C = LD'S B ' , ( being vertical of the equal & DSA , DSC , and D SB ) . Then the trihedral △ S - DCB = trihedral ≤ S - D ...
... trihedral Draw D'D making the S - ABC trihedral △ S - A'B'C ' . Then DSA , DSC , and DSB equal . Z D'SA ' = LD'S C = LD'S B ' , ( being vertical of the equal & DSA , DSC , and D SB ) . Then the trihedral △ S - DCB = trihedral ≤ S - D ...
Σελίδα 283
... trihedral angle . 9. Cut a given quadrahedral angle by a plane so that the section shall be a parallelogram . 10. Determine a point in a given plane such that the sum of its distances from two given points on the same side of the plane ...
... trihedral angle . 9. Cut a given quadrahedral angle by a plane so that the section shall be a parallelogram . 10. Determine a point in a given plane such that the sum of its distances from two given points on the same side of the plane ...
Σελίδα 291
... trihedral A = trihedral ( two trihedrals are equal when three face A ' , $ 492 of the one are respectively equal to three face of the other , and are similarly placed ) . Now face AD = face A ' D ' , ( being the two bases of the oblique ...
... trihedral A = trihedral ( two trihedrals are equal when three face A ' , $ 492 of the one are respectively equal to three face of the other , and are similarly placed ) . Now face AD = face A ' D ' , ( being the two bases of the oblique ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume