Where does the "inertia" term come from? Where does the "inertia" term in regard to quadratic forms (e.g. Sylvester's law of inertia) come from? Thank you!

Inertia in latin means not changing, inert. If you reduce a quadratic form to a canonic form, the number of terms at positive coefficient and the number of terms at negative coefficients don't change changing the canonic form.