## The Essentials of Geometry (solid) |

### From inside the book

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Page 336

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**SPHERICAL POLYGONS**AND SPHERICAL PYRAMIDS . DEFINITIONS . 587. 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 spherical ... Page 337

... polygon form a polyedral angle , O - ABCD , whose face AOB , BOC , etc. , are measured by arcs AB , BC , etc. , respectively . A

... polygon form a polyedral angle , O - ABCD , whose face AOB , BOC , etc. , are measured by arcs AB , BC , etc. , respectively . A

**spherical polygon**is called convex when the ...**spherical polygons**, on the same or equal THE SPHERE . 337. Page 340

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**spherical polygon**ABCD . To Prove AB + BC + CD + DA < 360 ° . ( By 458 , sum of AOB , BOC , COD , and DOA is << 360 ° . ) PROP . XX . THEOREM . 596. The sum of the angles of a spherical triangle is greater than two , and less than six ... Page 351

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**spherical**△ PAB and P'A'B ' are symmetrical . But**spherical**△ PAB is isosceles . In like manner , .. △ PAB = △ P ...**polygon**of n sides is greater than 2 n − 4 , and less than 2 n , right angles . - 6. The arc of a great circle drawn ... Page 356

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**spherical polygon**is equal to the sum of its angles , diminished by as many times two right angles as the figure has sides less two , multiplied by the area of a tri- rectangular triangle . Given K the area of any**spherical polygon**...### Other editions - View all

### Common terms and phrases

ABCD Algebra altitude approaches the limit area ABC axis bisecting centre cents circle circular cone circular cylinder circumference circumscribed cone of revolution conical surface convex polyedron cube cylinder of revolution diameter diedral angle distance Draw lines entire surface equal parts occur equal spheres equally distant Find the area Find the volume frustum Geometry Given line given point homologous inscribed intersection lateral area lateral edges lateral faces lateral surface line drawn lune O-ABC parallel planes perimeter perpendicular plane determined Plane Geometry plane MN pole polyedral angle proof is left PROP Prove pupil radii radius rectangular parallelopiped regular polygon respectively sector sides slant height solid Solid Geometry spherical angle spherical polygon spherical pyramid spherical triangle straight line tangent tetraedron THEOREM total surface tri-rectangular triangular prism triedral vertex vertices Wells's Whence