## The Essentials of Geometry (solid) |

### From inside the book

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Page 266

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**equal**when they can be applied to each other so that their faces shall coincide . Ο ' 455. Two polyedral angles are ...**parts occur**in the A reverse order . Thus , if face AOB , BOC , B and COA are**equal**respectively to face and C ... Page 267

... portions of the same plane , as also are AOC and A'OC " ; in like manner , diedral & OB and OB ' are vertical ; etc ... equal , respectively , to diedral OA ' , OB ' , etc. ( $ 435 ) But the

... portions of the same plane , as also are AOC and A'OC " ; in like manner , diedral & OB and OB ' are vertical ; etc ... equal , respectively , to diedral OA ' , OB ' , etc. ( $ 435 ) But the

**equal parts**of the triedral**occur**in the ... Page 271

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**equal parts occur**in the same order , and in Figs . 1 and 3 in the reverse order . 460. Cor . If two triedral angles have the face angles of one equal respectively to the face angles of the other , 1. They are equal if the equal ... Page 338

... same or equal spheres , have sides AB , BC , and CA equal , respectively , to sides A'B ' , B'C ' , and B ' Α ' B C C'A ' , and △ A , B , and C to △ A ' , B ' , and C ' , and the

... same or equal spheres , have sides AB , BC , and CA equal , respectively , to sides A'B ' , B'C ' , and B ' Α ' B C C'A ' , and △ A , B , and C to △ A ' , B ' , and C ' , and the

**equal parts occur**in the reverse order , the A are ... Page 342

... equal spheres , are mutually equiangular , their polar triangles are mutually equilateral . B Β ' o ' E E ' F Given ABC and DEF mutually equiangular spherical A on the same sphere ...

... equal spheres , are mutually equiangular , their polar triangles are mutually equilateral . B Β ' o ' E E ' F Given ABC and DEF mutually equiangular spherical A on the same sphere ...

**equal parts occur**342 SOLID GEOMETRY . BOOK VIII .### 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