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ABCD adjacent altitude angles are equal base bisects Book called centre chord circle circumference circumscribed coincide common cone consequently construct contained Corollary cylinder Definition describe diagonal diameter diedral angle difference distance divided draw drawn equal equally distant equivalent Exercise extremities faces fall figure follows formed four frustum given line given point given straight line greater half Hence included angle increased indefinitely inscribed intersection isosceles joining length less limit locus mean measure meet middle point number of sides one-half opposite parallel parallelogram parallelopiped pass perimeter perpendicular placed plane pole polyedron polygon prism problem proportional Proposition VII prove pyramid radii radius ratio rectangle regular polygon right angles Scholium segment sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC unit vertex vertices volume
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - 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 245 - 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 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.