(1) If we seek to extend the definition of an orthogonant by making the square of each row equal to σ instead of 1, this fixed quantity will naturally be found to appear in the statement of almost all the properties of the determinant in question. It is therefore convenient and appropriate to call it the base of the orthogonant, and to speak of an orthogonant to the base σ or an orthogonant of base σ.

It is a simple matter to ascertain what modifications are necessary in the statement of the known properties of the ordinary orthogonant to make them applicable to the extended definition.