Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 189
... convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the ...
... convex surface of the prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the ...
Page 190
... convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges , and the lines in which the lateral faces meet the base are called basal edges of the pyramid . 9. Pyramids are named from the ...
... convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges , and the lines in which the lateral faces meet the base are called basal edges of the pyramid . 9. Pyramids are named from the ...
Page 192
... convex surface of a right prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface ...
... convex surface of a right prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface ...
Page 195
... convex surface of a right pyramid is equal to the perimeter of its base multiplied by half the slant height . Let S be the vertex , ABCDE the base , and SF , perpendicular to EA , the slant height of a right pyramid : then is the convex ...
... convex surface of a right pyramid is equal to the perimeter of its base multiplied by half the slant height . Let S be the vertex , ABCDE the base , and SF , perpendicular to EA , the slant height of a right pyramid : then is the convex ...
Page 196
... convex sur- face of the pyramid , is equal to , ( ABBC + CD + DE + EA ) x SF ; which was to be proved . Scholium . The convex surface of a frustum of a right pyramid is equal to half the sum of the perimeters of its upper and lower ...
... convex sur- face of the pyramid , is equal to , ( ABBC + CD + DE + EA ) x SF ; which was to be proved . Scholium . The convex surface of a frustum of a right pyramid is equal to half the sum of the perimeters of its upper and lower ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - 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.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.