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" The sum of any two face angles of a trihedral angle is greater than the third face angle. "
Schultze and Sevenoak's Plane and Solid Geometry - Page 333
by Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...coincide by superposition, but they are said to be equal by symmetry, PROPOSITION XXVI. THEOREM. 423. Tlie sum of any two face angles of a trihedral angle is greater than the third. The theorem requires proof only when the angle considered is greater than each of the others. Given...
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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 688 pages
...which the angle varies as the line in the plane revolves. The statement of Prop, xxii., 458, " that the sum of any two face angles of a trihedral angle is greater than the third angle," should be limited by inserting the word "convex" before the word "trihedral." The seventh,...
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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 1074 pages
...which the angle varies as the line in the plane revolves. The statement of Prop, xxii., 458, " that the sum of any two face angles of a trihedral angle is greater than the third angle," should be limited by inserting the word " convex" before the word " trihedral." The seventh,...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...projection on the plane than with any other line in the plane passing through the point of intersection. 2. The sum of any two face angles of a trihedral angle is greater than the third. 3. Define a regular polyhedron. How many regular polyhedrons are there ? Give their names and define...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...to coincide by superposition, but are said to be equal by symmetry. PROPOSITION XXIII. THEOREM. 487. The sum of any two face angles of a trihedral angle is greater than the third. Let S-ABC be a trihedral angle in which the face angle ASC is greater than either angle AS B or angle...
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Report

Rutgers University. College of Agriculture - 1893 - 682 pages
...proportional are similar. 6. The diameter of a circle is five feet; find the side of the inscribed square. 7. The sum of any two- face angles of a trihedral angle is greater than the third. 05) 8. Two symmetrical spherical triangles are equivalent. 9. The lateral area of a cone of revolution...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...dihedrals of a trihedral are equal, the trihedral is isosceles. PROPOSITION XIX. . THEOHEM. 91. The sum of two face angles of a trihedral angle is greater than the third. Notation. Let a, j3 and y be the three face angles of u trihedral angle, of which /3 is the greatest....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1894 - 456 pages
...posithat is, the trihedral angles SOLID GEOMETRY. — BOOK VI. PROPOSITION XXIV. THEOREM. 539. Tlie sum of any two face angles of a trihedral angle is greater than the third face angle. 8 In the trihedral angle S-ABC let the angle ASC be greater than ASB or BSC. To prove Z ASB -f ZL 'SC...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...symmetrical solids. The right glove cannot fit the left hand. PROPOSITION XXXIII. 473. Theorem. The sum oj any two face angles of a trihedral angle is greater than the third face angle. A Let AB С D represent a trihedral angle in which each of the face angles DAB and В А С is smaller...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...two straight lines not in the same plane, one common perpendicular can be drawn, and only one. 539. The sum of any two; face angles of a trihedral angle is greater than the third face angle. 540. The sum of the face angles of any convex polyhedral angle is less than four right angles. 541....
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