  For a given triangle $T$ and a real number $\rho$ we define Ceva's triangle
$\CT_\rho(T)$ to be the triangle formed by three cevians each joining a vertex
of $T$ to the point which divides the opposite side in the ratio
$\rho:(1-\rho)$. We identify the smallest interval $\nM_T \subset \nR$ such
that the family $\CT_\rho(T), \rho\in \nM_T$, contains all Ceva's triangles up
to similarity. We prove that the composition of operators $\CT_\rho, \rho \in
\nR$, acting on triangles is governed by a certain group structure on $\nR$. We
use this structure to prove that two triangles have the same Brocard angle if
and only if a congruent copy of one of them can be recovered by sufficiently
many iterations of two operators $\CT_\rho$ and $\CT_\xi$ acting on the other
triangle.
