La théorie des invariants des formes quadratiques ternaires revisitée

The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan algebra structure of the space of ternary quadratic forms, we give these invariants explicitely.