## The Essentials of Geometry (solid) |

### From inside the book

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Page 329

... sphere is called the axis of the circle , and its extremities are called the

... sphere is called the axis of the circle , and its extremities are called the

**poles**. P C B 568. Cor . I. The axis of a circle of a sphere passes through the centre of the circle . 569. Cor . II . All great circles of a THE SPHERE . 329. Page 331

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**poles**. B P ' Given P and P ' the**poles**of O ABC of sphere APC . To Prove all points in circumference ABC ...**pole**if they are equally near , to the circumference . Thus , in figure of Prop . X , the polar distance of ABC is ... Page 332

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**pole**. Given P a**pole**of great O ABC of A sphere APC , B any point in circumfer- ence ABC , and PB an arc of a great O. To Prove arc PB a quadrant ( § 146 ) . 0 C B Proof . Let O be the centre of the sphere , and draw radii OB and OP ... Page 335

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**pole**, included between its sides produced if necessary . B B ' Given ABC and AB'C arcs of great on the surface of sphere AC , lines AD and AD ' tangent to ABC and A'BC , respectively , and BB ' an arc of a great O having A as a**pole**... Page 336

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**pole**of a great circle is perpendicular to its 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 ...### 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