Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page viii
... Pyramid , 120 120 Area of the Frustum of a Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , 121 122 122 123 .... Volume of a Prism , 124 Volume of a Pyramid , 124 ...... Volume of the Frustum of a ...
... Pyramid , 120 120 Area of the Frustum of a Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , 121 122 122 123 .... Volume of a Prism , 124 Volume of a Pyramid , 124 ...... Volume of the Frustum of a ...
Page 179
... pyramid . The triangles taken together make up the lateral or convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges of the pyramid . 9. Pyramids are named from the number of sides of ...
... pyramid . The triangles taken together make up the lateral or convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges of the pyramid . 9. Pyramids are named from the number of sides of ...
Page 180
... pyramid . 12 The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which cuts the ...
... pyramid . 12 The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which cuts the ...
Page 182
... pyramid be cut by a plane parallel to the base • 1 ° . The edges and the altitude will be divided proportionally : 2 ° . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , whose altitude is SO , be cut by ...
... pyramid be cut by a plane parallel to the base • 1 ° . The edges and the altitude will be divided proportionally : 2 ° . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , whose altitude is SO , be cut by ...
Page 183
... pyramids S - ABCDE , and having a common vertex S , and their bases in the same plane , be cut by a plane abc , parallel to the plane of their bases , the sections will be to each other as the bases . • For , the polygons abcd and ABCD ...
... pyramids S - ABCDE , and having a common vertex S , and their bases in the same plane , be cut by a plane abc , parallel to the plane of their bases , the sections will be to each other as the bases . • For , the polygons abcd and ABCD ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.