Linearly Dependent Curves

Two curves $\phi$ and $\psi$ satisfying

$$\phi+\psi=0$$

are said to be linearly dependent. Similarly, $n$ curves $\phi_i$, $i=1$, ..., $n$ are said to be linearly dependent if

$$\sum_{i=1}^n \phi_i=0.$$

See also Bertini's Theorem, Study's Theorem

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 32-34, 1959.