Perspective Graves triads and triads of perspective inscribed triangles

Any Pappus configuration can be regarded (in six ways) as a triad of triangles, each inscribed in the previous one; such a triad of triangles is called aGraves triad. Graves triads in which each pair of triangles is in perspective may be calledperspective Graves triads; such triads occur in connection with various results in both projective and metrical geometry. In this paper we give a synthetic proof of the existence of perspective Graves triads; the proof is of interest because it holds in allharmonic planes and requires neither the axiom of Pappus nor the full axiom of Desargues. The paper also includes synthetic proofs of other related results.(Results involving perspective Graves triads can be found in [l, p.149] and [2]. This paper is the result of recent correspondence with Guinand concerning [2] and [3].)