...2. A spherical angle is the angle of two arcs of great circles of a sphere. 3. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. 5. A diagonal of a spherical polygon is an arc of a great circle dividing...

...touches a sphere when it meets the sphere, but, being produced, does not cut it. 6. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles, each of which is less than a semi-circumference. These arcs are called...

...each arc passes through the pole of the other. SPHERICAL POLYGONS. XII. DEF. 1. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles, each of which is less than a semi-circumference. DEF. 2. A spherical...

...Hence this intersection is MM, which is consequently in the tangent plane. OF SPHERICAL TRIANGLES. 688. A Spherical Triangle is a portion of the surface of a sphere bounded by three arcs of great circles. In the present treatise these arcs will be considered as each less than a semicircumference; and the...

...Hence this intersection is MM, which is consequently in the tangent plane. OF SPHERICAL TRIANGLES. 688. A Spherical Triangle is a portion of the surface of a sphere bounded hy three arcs of great circles. In the present treatise these arcs will be considered as each less...

...arc BB' (§ 200). SPHE1UCAL POLYGONS AND SPHERICAL PYRAMIDS. DEFINITIONS. 649. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles; as ABCD. The bounding arcs are called the sides of the polygon. The...

...perpendicular to its plane (VI., Proposition XIV.). SPHEEICAL POLYGONS. 43, Definition. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles, as A BCD. Since the planes of all great circles pass through the centre...

...TRIGONOMETRY. INTRODUCTION. 85. SPHERICAL TRIGONOMETRY treats of the solution of spherical triangles. A spherical triangle is a portion of the surface of a sphere bounded by three arcs of great circles of the sphere. NOTE. — Before undertaking the study of spherical trigonometry the student should...

...two curves are arcs of great circles the angle is called a spherical angle. 693. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon; the points of intersection...

...perpendicular to its plane (VI., Proposition XIV.). SPHERICAL POLYGONS. 43. Definition. A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles, as A BCD. Since the planes of all great circles pass through the centre...