Elements of GeometryHarper & brothers, 1897 - 354 páginas |
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Página 247
... lateral face . 658. COR . The lateral area of a frustum of a regular pyramid is equal to one - half the product of the sum of the perimeters of its bases and its slant height . Hint . - Apply $ 375 . 659. Def . - The altitude of a ...
... lateral face . 658. COR . The lateral area of a frustum of a regular pyramid is equal to one - half the product of the sum of the perimeters of its bases and its slant height . Hint . - Apply $ 375 . 659. Def . - The altitude of a ...
Página 262
... lateral edges by the area of the base to which those edges are perpendic- ular . 695. Exercise . - The volume of any truncated triangular prism is equal to the product of one- third the sum of its lateral edges by the area of a right ...
... lateral edges by the area of the base to which those edges are perpendic- ular . 695. Exercise . - The volume of any truncated triangular prism is equal to the product of one- third the sum of its lateral edges by the area of a right ...
Página 264
... lateral faces are considered to be planes . The altitude of the pyramid is 488 ft . , its base is 764 ft . square . What was its cost ? ( 5. ) Express the volume of a cube in terms of the length of a diag- onal . ( 6. ) The area of the ...
... lateral faces are considered to be planes . The altitude of the pyramid is 488 ft . , its base is 764 ft . square . What was its cost ? ( 5. ) Express the volume of a cube in terms of the length of a diag- onal . ( 6. ) The area of the ...
Página 304
... lateral edges are elements of the cylinder and its bases are in the planes of the bases of the cylinder . 845. Def ... area of a cylinder is the area of its lateral surface . PROPOSITION I. THEOREM 850. If the number of lateral faces.
... lateral edges are elements of the cylinder and its bases are in the planes of the bases of the cylinder . 845. Def ... area of a cylinder is the area of its lateral surface . PROPOSITION I. THEOREM 850. If the number of lateral faces.
Página 306
... lateral area of the prism is the lateral area of the cylinder . Q. E. D. III . Let B ' , B " be the respective bases of a circumscribed and corresponding inscribed prism , V , V " their respective volumes , and H their common altitude ...
... lateral area of the prism is the lateral area of the cylinder . Q. E. D. III . Let B ' , B " be the respective bases of a circumscribed and corresponding inscribed prism , V , V " their respective volumes , and H their common altitude ...
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Términos y frases comunes
ABCD adjacent angles angles are equal apothem base and altitude bisector bisects centre chord circumference circumscribed coincide cone of revolution conical surface construct Def.-The Defs.-A diagonals diameter diedral angles distance divided draw equivalent Exercise.-The exterior angle figure frustum given line given point given straight line GIVEN TO PROVE Hence Hint.-Apply homologous homologous sides hypotenuse included angle intersection isosceles triangle lateral area lateral edges lateral faces locus middle point number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyedral angles polyedron prismatic surface PROPOSITION XI Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular inscribed regular polygon respectively equal right angles right section right triangle segment similar slant height sphere spherical polygon spherical triangle surface symmetrical tangent THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Pasajes populares
Página 242 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Página 12 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Página 73 - A line perpendicular to a radius at its extremity is tangent to the circle.
Página 253 - The volume of a triangular pyramid is equal to one-third the product of its base and altitude.
Página 238 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Página 177 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Página 287 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Página 126 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Página 61 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Página 256 - 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.