Bonsall gave two constructions of the resolution 
of the identity of a selfadjoint operator, 
which are successive approximations by a 
polynomial $x(1-(x-1)^2)$ and a rational 
function $\frac{2x^2}{1+x^2}$.  On the other 
hand, about 300 years ago, Murase gave a 
successive approximation to obtain a root of 
an algebraic equation of order 3.  
In this note, we observe that, under the 
light of Murase's method, two constructions 
due to Bonsall are essentially same.