Why is determinant called determinant?

Here is some information about the origin of the term determinant. This term was introduced the first time $1801$ by C.F. Gauss in his Disquisitiones arithmeticae, XV, p. 2 in connection with a form of second degree.

• The following is from The Theory of Determinants in the historical order of development (1905) by Thomas Muir.

  [Muir, p. 64]: Gauss writes the form as \begin{align*} axx+2bxy+cyy \end{align*} and for shortness speaks of it as the form $(a,b,c)$.

  The function of the coefficients $a,b,c$, which was found by Lagrange to be of notable importance in the discussion of the form, Gauss calls the determinant of the form, the exact words being

• [Gauss, 1801] Numerum $bb-ac$, a cuius indole preprietates formae $(a,b,c)$ imprimis pendere in sequentibus decebimus, determinantem huius formae uocabimus.

and Muir continues:

• [Muir, p.64] ... Here then we have the first use of the term which with an extended signification has in our day come to be so familiar. It must be carefully noted that the more general functions, to which the name came afterwards to be given, also repeatedly occur in the course of Gauss' work, ...