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It will be shown later that all invariants, single or simultaneous, are expressible in terms of symbolic products.
Judgment is an assertion of reality, requiring comparison and ideas which render it directly expressible in words (Hobhouse, mainly following Bradley).
It has been shown by Gordan that every symbolic product is expressible as a sum of transvectants.
The area is (b 2 +a 2 /2)7r, and the length is expressible as an elliptic integral.
The simplest invariant is S = (abc) (abd) (acd) (bcd) cf degree 4, which for the canonical form of Hesse is m(1 -m 3); its vanishing indicates that the form is expressible as a sum of three cubes.