 This procedure is relatively elementary (readers not familiar with the relevant Euclidean constructions are encouraged to consult Euclid’s  Elements III.36  [1908: [2] 73–75]). The method employed is clear. The problem is algebraically expressed by means of letters for known and unknown magnitudes, and an equation is produced in which the unknown magnitude is expressed exclusively in terms of known magnitudes. The unknown magnitude is then constructed by the addition of a line that satisfies the equation. The construction is such that the solution to the problem can be intuited or directly seen in spatial intuition by the intellect aided by the imagination (or on paper, which embodies the operations of the intellect on line segments in the imagination). Geometrical construction is, therefore, the foundation of intuition in Cartesian geometry, and it constitutes the final step in the solution to any problem.