...equations.

The notion of a property (i.e., quantifiers can only range over the elements of the domain) was introduced, in Volume III of Schröder's Algebra of Logic, as part of his study of the Calculus of Relations. Schröder was more interested in quantifying over the relations than over the domain elements, and he did little with the first-order statements.

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...form.

This procedure is described in Schröder's third volume. By avoiding the digression through what appears to be an infinitary language - yielding a result which depends on the domain - Skolem introduced his presentation of this normal form in 1928. The process of creating this normal form is now called Skolemizing

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