Elements of Solid Geometry
Southern Publishing Company, 1912 - Geometry, Solid - 110 pages
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ABCDE altitude angles are equal approach base called circle circular circumscribed coincide common cone congruent construct corresponding cube cylinder diagonal diameter dihedral angles dimensions distance divided draw drawn element equal equal altitudes equivalent Find the volume foot formed frustum Given greater Hence homologous included inscribed intersecting lateral area lateral edges lateral faces limit lower base lune measure meet oblique parallel parallel planes pass a plane perimeter perpendicular plane MN polar pole polyhedral angle prism Proof proportional PROPOSITION prove pyramid radius ratio rectangular parallelopiped regular pyramid respectively right section segment sides similar Similarly slant height sphere spherical polygon spherical triangle squares straight line surface symmetrical tangent tetrahedrons THEOREM third trihedral unit upper base vertex vertices zone
Page 4 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.
Page 98 - The area of the surface generated by a straight line revolving about an axis in its plane is equal to the product of the projection of the line on the axis by the circumference whose radius is a perpendicular erected at the middle point of the line and terminated by the axis.
Page 58 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 37 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page xi - Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig.
Page ix - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 4 - ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page viii - Two right triangles are equal if the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an acute angle of the other.
Page 59 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Page 35 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...