I am reading an Italian encyclopedia on the history of Invariant Theory. This was an early branch of abstract algebra that was big in the middle of the nineteenth century.
Here is a line that I don't understand which I hope that some of you people might answer:
$u= ae- 4bd+3c^2$ is an invariant of $A=ax^4 + 4bx^{3}y + 6cx^{2}y^{2}+ 4dxy^{3}+ey^{4}$
Why is $u$ an invariant for this particular homogenous form?