 This is the method of analysis, which will also find some application in metaphysics (see  Section 9).  To apply the method to problems in geometry, one must first “consider [the problem] solved”, using letters to name both known and unknown lines. One must then produce as many equations as there are unknown lines, and each equation must express the unknown line in terms of the known lines. (Equations define unknown magnitudes in terms of known magnitudes. For example, the equation \(x^2=ax+b^2\) defines the unknown magnitude “x” in relation to the known magnitudes “a” and “b”, thereby expressing one quantity in two ways.) Finally, one must employ these equations in order to geometrically construct the required line(s).