Solid GeometryLyons & Carnahan, 1916 - 162 σελίδες |
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Σελίδα 255
... polygons are to each other as the squares of any two homologous sides . 379. If the radii of a regular inscribed polygon are produced , they pass through the vertices of the regular circumscribed polygon whose sides are parallel to the ...
... polygons are to each other as the squares of any two homologous sides . 379. If the radii of a regular inscribed polygon are produced , they pass through the vertices of the regular circumscribed polygon whose sides are parallel to the ...
Σελίδα 295
... polygon . Only convex polyhedrons are considered in this text . TETRAHEDRON HEXAHEDRON OCTAHEDRON DODECAHEDRON ICOSAHEDRON 572. A regular polyhedron is one all of whose faces are equal regular polygons . Only five regular polyhedrons ...
... polygon . Only convex polyhedrons are considered in this text . TETRAHEDRON HEXAHEDRON OCTAHEDRON DODECAHEDRON ICOSAHEDRON 572. A regular polyhedron is one all of whose faces are equal regular polygons . Only five regular polyhedrons ...
Σελίδα 296
... polygons in parallel planes , and the other faces of which are parallelograms . The equal polygons are called the ... regular prism is a right prism whose bases are regular polygons . 575. It follows from the above definitions that : 1 ...
... polygons in parallel planes , and the other faces of which are parallelograms . The equal polygons are called the ... regular prism is a right prism whose bases are regular polygons . 575. It follows from the above definitions that : 1 ...
Σελίδα 315
... polygons to designate corresponding parts . 620. The following properties of similar polyhedrons are evident from ... regular pyramids find the lateral and total areas . the proper formula in each case . 1. Base a square and base edge 5 ...
... polygons to designate corresponding parts . 620. The following properties of similar polyhedrons are evident from ... regular pyramids find the lateral and total areas . the proper formula in each case . 1. Base a square and base edge 5 ...
Σελίδα 340
... regular polygons TETRAHEDRON HEXAHEDRON OCTAHEDRON DODECAHEDRON ICOSAHEDRON It will be proved in § 679 that there only five regular polyhedrons . They have respectively four , six , eight , twelve , and twenty faces . Their actual ...
... regular polygons TETRAHEDRON HEXAHEDRON OCTAHEDRON DODECAHEDRON ICOSAHEDRON It will be proved in § 679 that there only five regular polyhedrons . They have respectively four , six , eight , twelve , and twenty faces . Their actual ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCDE altitude angles are equal axis base edge bisecting plane circle circumference circumscribed cone cube cylinder D-ABC denote dihedral angles dimensions distance drawn equal bases equal parts occur equal spheres equally distant equi-dimension face angles Find the volume formula frustum geometry given plane Hence homologous inches inscribed isosceles lateral and total lateral area lateral edges lateral faces locus lune mutually equiangular mutually equilateral number of sides parallel planes perimeter perpendicular plane angles plane geometry plane MN polar triangle pole polyhedral angle prismatoid Proof prove pyramid whose base radii radius ratio rectangular parallelopiped regular polygons regular polyhedrons regular pyramid respectively right angle slant height sphere whose diameter spherical angle spherical excess spherical polygon spherical triangle straight line surface symmetrical tangent tetrahedron THEOREM total area triangular prism trihedral V-ABC vertex vertices ZABC
Δημοφιλή αποσπάσματα
Σελίδα 253 - Conversely, when two sides of a triangle are equal respectively to two sides of another, but the third side of the first is greater than the third side of the second...
Σελίδα 254 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 301 - Any oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Let ABCDE-A' be the oblique prism. At any point F in the edge AA', pass a plane perpendicular to AA' and forming the right section FGHIK Produce AA...
Σελίδα 253 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Σελίδα 389 - COR. 2. The volume of any truncated triangular prism is equal to the product of its right section by one third the sum of its lateral edges.
Σελίδα 373 - 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...
Σελίδα 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 396 - If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to two sides and the included angle of the other, I.
Σελίδα 254 - In any proportion the terms are in proportion by division; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth.
Σελίδα 254 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.