Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 páginas |
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Página 175
... PARALLELOPIPEDON is a prism whose bases are parallelograms . 8. A RECTANGULAR PARALLELOPIPE- DON is one whose faces ... parallel to its base , forming a second base , the part lying between the bases , is called a truncated pyramid , or ...
... PARALLELOPIPEDON is a prism whose bases are parallelograms . 8. A RECTANGULAR PARALLELOPIPE- DON is one whose faces ... parallel to its base , forming a second base , the part lying between the bases , is called a truncated pyramid , or ...
Página 181
... parallel . Let ABCD be a parallelopipedon , then will its opposite faces be equal and parallel . For , the bases ABCD , EFGH , are equal parallelograms , and have their planes parallel ( D. 7 ) . It remains only to show , that the same ...
... parallel . Let ABCD be a parallelopipedon , then will its opposite faces be equal and parallel . For , the bases ABCD , EFGH , are equal parallelograms , and have their planes parallel ( D. 7 ) . It remains only to show , that the same ...
Página 182
... parallel , it follows that any face and the one opposite to it , may be assumed as the bases of the parallelopipedon . Cor . 2. The diagonals of a parallelopipedon bisect each other . For , suppose two diagonals BH , DF , to be drawn ...
... parallel , it follows that any face and the one opposite to it , may be assumed as the bases of the parallelopipedon . Cor . 2. The diagonals of a parallelopipedon bisect each other . For , suppose two diagonals BH , DF , to be drawn ...
Página 183
... parallelopipedon ABCD - H be divided by the plane BDHF , passing through the opposite edges BF , DH : then will the ... parallel ( B. VI . , 9 ) : hence , the sections are equal ( P. 2 ) ; and they are par allelograms because Ba , cd ...
... parallelopipedon ABCD - H be divided by the plane BDHF , passing through the opposite edges BF , DH : then will the ... parallel ( B. VI . , 9 ) : hence , the sections are equal ( P. 2 ) ; and they are par allelograms because Ba , cd ...
Página 185
... parallel to FG , the parallelogram EM is equal to the parallelogram FL ( B. I. , P. 28 , c . 2 ) : also , the ... parallelopipedon ABCD - H ; hence , the two parallelopipedons ABCD - M , ABCD - H , are equivalent . PROPOSITION IX ...
... parallel to FG , the parallelogram EM is equal to the parallelogram FL ( B. I. , P. 28 , c . 2 ) : also , the ... parallelopipedon ABCD - H ; hence , the two parallelopipedons ABCD - M , ABCD - H , are equivalent . PROPOSITION IX ...
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Términos y frases comunes
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 323 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.