...case the above construction will produce but two triangles, whose sum is equal to AB C. 674. A lime is a portion of the surface of a sphere included between two semi-circumferences of great circles, as ABC D. 675. The angle of a lune is the angle of ° the two semi-circumferences which bound the lune,...

...sphere. SOLID GEOMETRY — BOOK VIII MENSURATION OF THE SPHERE SPHERICAL SURFACES DEFINITIONS 815 A zone is a portion of the surface of a sphere included between two parallel planes. The bases of a zone are the circumferences of the sections formed by the parallel...

...Show that a trirectangular spherical triangle and its polar triangle are congruent. 691. Definition. A lune is a portion of the surface of a sphere included between the halves of two great circles. Thus, ACBDA is a lune. 692. The angle of a lune is the spherical angle...

...2 TTCH .'. AB X 2 TTCE = DF X 2 TrCH. .'. area AB = DF X 2 TTCH. BOOK VIII 706 Definitions. A zone is a portion of the surface of a sphere included between two parallel planes which cut the sphere. The circumferences of the sections of the sphere are the bases...

...respectively; the volume of the sphere being 180. MEASUREMENT OF THE SPHERE DEFINITIONS 583. A zone is a portion of the surface of a sphere included between two parallel planes. The circumferences of the circles which bound the zone are called the bases, and the...

...The angle of a lune is the spherical angle between the semicircles that bound it. 786. DEF. A zone is a portion of the surface of a sphere included between two parallel planes. 787. DEF. The common sections of the sphere and the planes are the bases of the zone,...

...is a birectangular spherical triangle whose third angle is an angle of one degree. 423. Definition. A lune is a portion of the surface of a sphere included between two semicircumferences of great circles. 424. COROLLARY. The two angles of a lune are equal. 425. COROLLARY. Two lunes on the same sphere or...

...Angle at the Center of a Regular Polygon is an angle formed by radii to the extremities of any side. The Angle of a Lune is the angle between the semicircumferences which form its boundaries. See definition, " The angle of two curves." An Angle Measured by its Intercepted Arc is...

...rectangular parallelepiped (a unit of volume), each of whose dimensions is one linear unit. A Zone is a portion of the surface of a sphere included between two parallel planes which cut the sphere. A Zone of One Base is a zone having one of its bounding planes...

...squares of their diameters. 675. A Lune is the portion of a spherical surface bounded by two semicircles of great circles ; as ACBD. The Angle of a Lune is the angle between its bounding arcs. It is evident that two lunes on the same sphere or equal spheres are congruent if...