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ABCD altitude approaches axis base bisector called centre chord circle circumference circumscribed coincide common cone construct contains corresponding curve cylinder describe diagonals diameter diedral angles difference distance divided draw drawn edges equal equilateral equivalent Exercise extremities faces figure Find formed four geometry given given point GIVEN—the greater half Hence included inscribed intersection length less limit line joining locus mean measured meet method middle points parallel parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron polygon prism PROBLEMS projection proportional PROPOSITION PROVE pyramid quadrilateral radii radius ratio rectangle respectively right angles right triangle segment sides similar sphere spherical square straight line surface symmetrical tangent tetraedron THEOREM third triangle triangle ABC triedral unit vertex vertices volume
Side 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Side 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Side 393 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 185 - To construct a square equivalent to the sum of any number of given squares.
Side 390 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 67 - 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.
Side 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Side 476 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.