## The Essentials of Geometry (solid) |

### From inside the book

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Page 249

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**circumference**of a given circle ? 3. A line parallel to a plane is everywhere equally distant from it . ( Fig . of Prop . IX . Draw lines AC and BD1 MN . To prove AC = BD . ) PROP . XVI . THEOREM . 423. A straight line LINES AND PLANES ... Page 330

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**circumference**, can be drawn , and but one . For the two points , with the centre of the sphere , deter- mine a plane which intersects the surface of the sphere in the required arc . Note . If the points are the extremities of a ... Page 331

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**circumference**ABC . Therefore , all points in**circumference**ABC are equally I distant from P. In like manner , all points in**circumference**ABC are equally distant from P ' . 576. Def . The polar distance of a circle of a sphere is the ... Page 336

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**circumference**. 586. Cor . II . The angle between two arcs of great circles is the plane angle of the diedral angle between their planes . ( § 429 ) SPHERICAL POLYGONS AND SPHERICAL PYRAMIDS . DEFINITIONS . 587. A spherical polygon is a ... Page 337

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**circumferences**of great circles be drawn with the vertices of a spherical triangle as poles , they divide the ...**circumference**A'C " A " with B as a pole , and circum- ference A'B " A " B ' with C as a pole , the surface of the ...### 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