Schultze and Sevenoak's Plane and Solid Geometry |
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altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 80 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 280 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 196 - In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side.
Page 190 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 175 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 68 - 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.
Page 186 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 407 - 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...
Page 220 - 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.
Page 440 - COR. 2. The volume of any truncated triangular prism is equal to the product of its right section by one third the sum of its lateral edges.