 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...stated first, the other follows from the relations shown in §§ 242 and 243. 245. Theorem IV. (a) The sum of any two face angles of a trihedral angle is greater than the third face angle. (b) The sum of any two sides of a spherical triangle is greater than the third side. VA FIRST PROOF... | |
 | Fletcher Durell - 1911 - 234 pages
...pair may be made to coincide, and which not. BOOK VI. SOLID GEOMETRY PROPOSITION XXIV. THEOREM 582. The sum of any two face angles of a trihedral angle is greater than the third face angle. S Given the trihedral angle S-ABC, with angle ASC its greatest face angle. To prove /-ASB + /.BSC greater... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...spherical triangle what is the length of each side in terms of degrees ? 227. THEOREM. TJie sum of two face angles of a trihedral angle is greater than the third face angle. p Proof : Connect points A and D on two sides. Suppose not all three face angles are equal and that... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...are the prolongations through the vertex of the edges of the other. PROPOSITION XXI. THEOREM. 593. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given the trihedral £ V, with £ AVC > £ A1TB or £ BVC. To prove % AVB+% SVC > %. AVC. Proof. In £ ^1... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...equal? Are two birectangular trihedral angles equal ? Prove your answers. PROPOSITION XXXI. THEOREM 710. The sum of any two face angles of a, trihedral angle is greater than the third face angle. V C Given trihedral Z V-ABC in which, the greatest faoc Z is AVB. To prove Z BVC + Z CVA > Z AVB. OUTLINE... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...the first are equal respectively to the dihedral angles of the second. PROPOSITION XXXI. THEOREM 710. The sum of any two face angles of a trihedral angle is greater than the third face angleV c Given trihedral Z V-ABC in which the greatest face Z is AVB. To prove Z. BVC + Z. CVA > Z... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...the first are equal respectively to the dihedral angles of the second. PROPOSITION XXXI. THEOREM 710. The sum of any two face angles of a trihedral angle is greater than the third face angleV c Given trihedral Z V-ABC in which the greatest face Z is AVB. To prove ZB VC + Z CVA > ZA VB.... | |
 | George Clinton Shutts - Geometry - 1912 - 392 pages
...from two given parallel planes and at the same time equidistant from two given points? 509. THEOREM. The sum of any two face angles of a trihedral angle is greater than the third. Given the trihedral A — BCD, in which face angle DAC is the greatest. To Prove Z CAB + L BAD > L... | |
 | University of Calcutta - 1912 - 746 pages
...the graph of j/=tan x. Obtain graphically the general solution of the equation tan x=l. GBOUT C. 1. The sum of any two face angles of a trihedral angle is greater than the third. The sum of any three face angles of a tetrahedral angle is greater than the fourth. 2. Prove that any... | |
 | Education - 1912 - 714 pages
...circumference shall pass through two given points and that shall be tangent also to a given line. 6. The sum of any two face angles of a trihedral angle is greater than the third. 7. The locus of all points equidistant from two intersecting planes is a plane bisecting their dehedral... | |
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The sum of any two face angles of a trihedral angle is greater than the third face angle. 
