## Solid Geometry Developed by the Syllabus Method |

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Solid Geometry Developed by the Syllabus Method Eugene Randolph Smith,William H. B. 1863 Metzler No preview available - 2016 |

### Common terms and phrases

altitude angles are equal axis b₁ b₂ base bisector bisects called circle arcs circumference circumscribed conical surface construct coplanar cube cubic determine a plane diagonal diameter dihedral angle draw drawn equivalent face angles figure Find the area Find the locus Find the ratio Find the volume frustum given plane given point inscribed intersecting lines lateral area lateral edges locus of points lune non-coplanar lines number of faces oblique opposite pair parallel planes parallel sections parallelogram perimeter plane angles plane geometry plane parallel plane perpendicular planes are parallel points equidistant polar triangle pole polyhedral angle prismatic Prismatoid proof radians radii rectangular parallelepiped regular polyhedrons regular pyramid regular tetrahedron right circular cone right circular cylinder sides slant height solid geometry space sphere of radius spherical angle spherical cone spherical polygon spherical surface spherical triangle square straight line tangent Theorem three planes trihedral vertex vertices zone

### Popular passages

Page 343 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 251 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.

Page 329 - The sum of the sides of any spherical polygon is less than the circumference of a great circle.

Page 288 - Two rectangular parallelepipeds are to each other as the products of their three dimensions.

Page 297 - Every section of a circular cone made by a plane parallel to the base is a circle.

Page 298 - The lateral area of a frustum of a right circular cone is one half the product of the slant height and the sum of the circumferences of the bases.

Page 398 - Bh where B is the area of the base and h is the height.

Page 260 - The acute angle which a straight line makes with its own projection upon a plane is the least angle it makes with any line of that plane.

Page 389 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 267 - Find the locus of a point such that the difference of the squares of its distances from two given points is equal to a given constant k-.