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adjacent altitude applied arranged base bisect called chord circle circumference coincide common cone construct Corollary Corollary.-The corresponding curve demonstration described diagonals diameter diedral difference direction distance divided draw edges ends equal equally distant equivalent EXERCISES extend extreme faces figure formed four geometry given line given point gles greater half Hence homologous hypothesis included inscribed intercepted intersection isosceles Join length less limit means measured meet method oblique opposite sides parallel parallel lines parallelogram pass perimeter perpendicular plane position principle prism problem produced proportional proved pyramid quadrilateral radii radius ratio reason regular polygon respectively equal right angles secant sides similar similarly sphere spherical square straight line student Suppose surface tangent tetraedrons theorem Theorem.-The third triangle triedral vertex vertices volume whole
Page 94 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 137 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 259 - The area of the surface of a sphere is equal to the area of the...
Page 254 - 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...
Page 133 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Page 223 - ... the two planes are equal polygons. Each side of one of the sections is parallel to the corresponding side of the other section, since they are the intersections of two parallel planes by a third. Hence, that portion of each side of the prism which is between the secant planes, is a parallelogram. Since the sections have their sides respectively equal and parallel, their angles are respectively equal. Therefore, the polygons are equal. 674. Corollary — The section of a prism made by a plane...
Page 233 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 187 - Theorem. — The intersections of two parallel planes by a third plane are parallel lines. Let AB and CD be the intersections of the two parallel planes M and N, with the plane P.