5.11 The two statements[i] AECF[/i] projective to[i] BDCF[/i] and [i](AD)(BE)(CF)[/i] are equivalent, not only when[i] C[/i] and [i]F[/i] are distinct, but also when they coincide. Since the statement[i] AECF[/i] projective to [i]BDCF[/i] involves[i] C[/i] and[i] F[/i] symmetrically, the statement [i](AD)(BE)(CF) [/i]is equivalent to [i](AD)(BE)(FC)[/i], and similarly to [i](AD)(EB)(FC)[/i] and to[i] (DA)(EB)(FC)[/i]. This is remarkable because, when the quadrangular set is derived from the quadrangle, the two triads [i]ABC[/i] and [i]DEF[/i] arise differently: the first from three sides with a common vertex, and the second from three that form a triangle. It is interesting that, whereas one way of matching two quadrangles (Figure 2.4b) uses only Desargues's theorem, the other needs the fundamental theorem.