Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 94
... lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE , is its numerical value ...
... lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE , is its numerical value ...
Page 95
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal ... lower base A BA of the parallelogram ; B then , because they have equal altitudes , the vertex of the triangle will lie in ...
... base and an equal altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal ... lower base A BA of the parallelogram ; B then , because they have equal altitudes , the vertex of the triangle will lie in ...
Page 178
... bases of the prism ; one the upper , and the other the lower base ; the parallelograms taken together make up the lateral or convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges of the prism ...
... bases of the prism ; one the upper , and the other the lower base ; the parallelograms taken together make up the lateral or convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges of the prism ...
Page 180
... base is a regular polygon , and in which the perpendicular drawn from the vertex to the plane of the base , passes ... lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the ...
... base is a regular polygon , and in which the perpendicular drawn from the vertex to the plane of the base , passes ... lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the ...
Page 185
... base ( D. 11 ) : hence , the lateral edges , SA , SB , & c . , are all equal ( B. VI . , P. V. ) ; but the sides of ... lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then ...
... base ( D. 11 ) : hence , the lateral edges , SA , SB , & c . , are all equal ( B. VI . , P. V. ) ; but the sides of ... lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then ...
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Common terms and phrases
ABĀ² ABCD adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed cone consequently convex surface cosec Cosine Cosine D Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area following RULE Formula frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log cot log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar slant height solution sphere spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prism triedral angle upper base vertex volume whence write the following