Elements of GeometryAmerican Book Company, 1896 - 540 σελίδες |
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Αποτελέσματα 1 - 5 από τα 44.
Σελίδα vi
... PYRAMIDS 308 SIMILAR POLYEDRONS . 326 REGULAR POLYEDRONS 335 GENERAL THEOREMS ON POLYEDRONS 345 PROBLEMS OF DEMONSTRATION 348 PROBLEMS OF CONSTRUCTION . 350 PROBLEMS FOR COMPUTATION 351 BOOK VIII THE CYLINDER 353 THE CONE 360 THE SPHERE ...
... PYRAMIDS 308 SIMILAR POLYEDRONS . 326 REGULAR POLYEDRONS 335 GENERAL THEOREMS ON POLYEDRONS 345 PROBLEMS OF DEMONSTRATION 348 PROBLEMS OF CONSTRUCTION . 350 PROBLEMS FOR COMPUTATION 351 BOOK VIII THE CYLINDER 353 THE CONE 360 THE SPHERE ...
Σελίδα 306
... TO PROVE Construct the parallelopiped ABCD - F having BA , BC , and BF as edges . 8672 Then the volume of the parallelopiped is the product of. vol . ABC - F = ABC X EZ . the regular pyramid O - ABCDE . OA OB OC. 306 GEOMETRY OF SPACE.
... TO PROVE Construct the parallelopiped ABCD - F having BA , BC , and BF as edges . 8672 Then the volume of the parallelopiped is the product of. vol . ABC - F = ABC X EZ . the regular pyramid O - ABCDE . OA OB OC. 306 GEOMETRY OF SPACE.
Σελίδα 308
... is the base ; O is the vertex ; OA , OB , etc. , are the lateral edges ; and OAB , OBC , etc. , are the lateral faces of the pyramid O - ABCDE . 682. Defs . - A regular pyramid is a pyramid. 308 GEOMETRY OF SPACE PYRAMIDS.
... is the base ; O is the vertex ; OA , OB , etc. , are the lateral edges ; and OAB , OBC , etc. , are the lateral faces of the pyramid O - ABCDE . 682. Defs . - A regular pyramid is a pyramid. 308 GEOMETRY OF SPACE PYRAMIDS.
Σελίδα 309
... pyramid . PROPOSITION XV . THEOREM 683. The lateral edges of a regular pyramid are equal . E E Z C A B GIVEN TO PROVE = = Let OZ be the axis of the regular pyramid . Then Therefore ZA ZB = ZC = etc . OA = OB = OC = etc. $ 461 III $ 539 ...
... pyramid . PROPOSITION XV . THEOREM 683. The lateral edges of a regular pyramid are equal . E E Z C A B GIVEN TO PROVE = = Let OZ be the axis of the regular pyramid . Then Therefore ZA ZB = ZC = etc . OA = OB = OC = etc. $ 461 III $ 539 ...
Σελίδα 310
... pyramid is the sum of the areas of its lateral faces . PROPOSITION XVI . THEOREM 688. The lateral area of a regular pyramid is equal to one- half the product of the perimeter of its base and its slant height . D E C A H B GIVEN the ...
... pyramid is the sum of the areas of its lateral faces . PROPOSITION XVI . THEOREM 688. The lateral area of a regular pyramid is equal to one- half the product of the perimeter of its base and its slant height . D E C A H B GIVEN the ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles allel altitude angles are equal apothem axis bisecting bisector centre chord circumference circumscribed coincide construct Def.-The Defs Defs.-A diagonals diameter diedral angles distance divided draw equally distant equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum geometry given circle given line given point given straight line GIVEN TO PROVE given triangle Hence hypotenuse lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane geometry plane MN polyedral angle polyedron prism prismatic surface pyramid Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon spherical triangle square straight line joining surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 30 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Σελίδα 466 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 315 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Σελίδα 205 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Σελίδα 36 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 379 - 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...
Σελίδα 138 - ... twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 57 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 137 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Σελίδα 147 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.