## The Essentials of Geometry (solid) |

### From inside the book

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Page 335

... spherical surface can be passed through A , B , C , and D. 583. Defs . The angle between two intersecting curves is the angle between tangents to the curves at their point of intersection . A

... spherical surface can be passed through A , B , C , and D. 583. Defs . The angle between two intersecting curves is the angle between tangents to the curves at their point of intersection . A

**spherical angle**is the angle between two ... Page 336

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**angle**between their planes . ( § 429 )**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 ... Page 337

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**spherical**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 polyedral**angle**formed by the planes of its sides is ... Page 339

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**spherical**triangles , each of which is the polar triangle of the other , are called polar triangles . PROP . XVII . THEOREM . 593. In two polar triangles , each**angle**of one is measured by the supplement of that side of the other of ... Page 342

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**spherical**tri-**angles**on the same sphere , or equal spheres , are mutually equilateral , their polar triangles are mutually equiangular . ( The proof is left to the pupil ; compare § 600. ) PROP . XXII . THEOREM . 602. If two**spherical**...### 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