Consider the quadr angle (projective frame) (a,b,c,d)in a project plane, and let a ′be the inter section of〈d,a〉and〈b,c〉,b ′b ethe inter section of〈d,b〉and〈a,c〉,and c′ be the inter section of〈d,c〉and〈a,b〉.Show that the follow in g quad ruples of lines form harmonic divisions: (〈c,a〉,〈b′,a′〉,〈d,b〉,〈b′,c′〉),(〈b,a〉,〈c′,a′〉,〈d,c〉,〈c′,b′〉),and(〈b,c〉,〈a′,b′〉,〈a,d〉,〈a′,c′〉).