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ABCD altitude angle angles are equal base bisect bisector called chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divide draw drawn equal equidistant equivalent exterior angle faces figure Find formed four frustum geometrical given circle given line given point greater Hence homologous hypotenuse inches included inscribed intersecting isosceles triangle lateral edges length less limit line joining measured median meet midpoints opposite sides parallel parallel lines parallelogram passing perimeter perpendicular plane polyedron polygon prism PROBLEM Proof PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle segments sides similar sphere spherical triangle square straight line student surface tangent THEOREM third transform triangle triangle are equal vertex vertices
Σελίδα 144 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 41 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 301 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 176 - Two triangles having 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.
Σελίδα 27 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 149 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 333 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 123 - If a line parallel to one side of a triangle intersects the other two sides, either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE : EC.
Σελίδα 308 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...