On minor forms of Desargues and Pappus
In this paper, the projective plane \(\pi\) coordinatized by a ternary ring \((R,F)\) and with operations +, . and \(*\) defined by \(a+b=F(a,1,b)\), \(a,b=F(a,b,0)\) and \(a*b=F(1,a,b)\) for \(a,b\in R\) is considered. Several minor forms of propositions of Desargues and Pappus are introduced in \(\pi\) and their geometrical properties are developed. Some algebraic identities in \((R,F)\) are proved to be equivalent to some of these.
scientific article; zbMATH DE number 58799