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A B C D ABCD adjacent altitude angle formed base bounding centre chord circle circumference coincident common composed cone considered construction contained Corollary corresponding cubes curve surface cylinder described determined diagonal diameter difference dihedral angles diverging divided draw drawn edges equal angles evidently Example expressed exterior angle extremities faces feet figure formed four given greater inscribed interior intersecting isosceles join less mean meet oblique opposite parallel parallelogram passing perpendicular plane angles polygon position preceding PROBLEM proportional quadrilateral radii radius ratio regular relatively remaining Remark respectively equal right angles right line segment sides sides A B similar solid sphere spherical triangle square subtended tangent termed THEOREM third triangle A B C triangular prisms triangular pyramids trihedral twice units vertex vertices volume wherefore
Page 33 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 20 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 213 - The surface of a sphere is equal to four times the area of a circle...
Page 10 - If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles.
Page 99 - THE square of the side of a regular pentagon inscribed in a circle, is equal to the squares of the sides of a regular hexagon and regular decagon, inscribed in the same circle.
Page 26 - To describe a square that shall be equal to a given rectilineal figure. To describe an isosceles triangle having each of the angles at the base double of the third angle. To inscribe a regular pentagon in a given circle. The squares on two sides of a triangle are together equal to twice the square on half the third side and twice the square on the median to that side. If...
Page 73 - THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD.
Page 76 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.