An example of ternary group defined on the points of an ellipse

Let g be the points set of an ellipse and et.° – I! a ternary operation defines’ on follows: – it m,.14,0M, then (X„M„M,I, ie the point in which the parallol of my, for or tne tangent to I in X, if N. – through K, intersects again the respectively Fig.1c): – Tr the tangent to g in M, is parallel to X,X„ then (M„K„1.1,),-M, !rig.lb); – If M, – M, then (M,,X„X,), – X, (alco for ref,< la an semacommutative ternary group isomorphic, to the 3-
group (U,*) where LT-lzCC; r -7.1 and •;rri-ir; (z„ a2, z,) ‘1th