5.32 [i]An involution is determined by any two of its pairs.[/i] Following from theorem 5.31, it is convenient to denote the involution[i] AA1B[/i] projective to [i]A1AB1[/i] by [i](AA1)(BB1)[/i] or[i] (A1A)(BB1)[/i], or[i] (BB1)(AA1)[/i], and so forth. This notation reminas valid when[i] B1[/i] coincides with [i]B[/i]; in other words, the involution[i] AA1B[/i] projective to[i] A1AB[/i], for which [i]B[/i] is invariant, may be denoted by [i](AA1)(BB)[/i]. If [i](AD)(BE)(CF)[/i], as in Figure 2.4A (reproduced and provided), we can combine the projectivity[i] AECF[/i] projective to[i] BDCF[/i] of 5.11 with the involution[i] (BD)(CF)[/i] to obtain [i]AECF[/i] projective to[i] BDCF[/i] which is projective to [i]DBFC[/i] which shows there there is a projectivity in which [i]AECF[/i] projective to [i]DBFC[/i]. Since this interchanges [i]C[/i] and [i]F[/i], it is an involution, namely [i](BE)(CF)[/i] or[i] (CF)(AD)[/i] or[i] (AD)(BE)[/i]; all equivalent statements. Thus the quadrangular relation [i](AD)(BE)(CF) [/i]is eqquivalent to the statement that the projectivity[i] ABC[/i] projective to [i]DEF[/i] is an involution, or that [i]ABCDEF[/i] projective to [i]DEFABC[/i].