so that it's easy to rec­og­nize the line from half the base to the ver­tex E as √5 (Py­­tha­g­o­ras docet); then to rotate it to join the base­line, de­fin­ing the long side of a gold­en rec­tan­gle ABDF.


The ratio is implicit in, as of the base AB: (1+√5) to the height BD: 2, same as that of 2 to ED: (√5-1).
Of course, the diagonal BF of the first rec­tan­gle cuts the square's side, ie. the base of the se­cond rec­tan­gle, at the same distance from E as the side ED, defining the next square as c-D-E, and the same phi ratio for the rec­tan­gle in E-D-B. This recurrent criterion may define any new inner rec­tan­gle, as well as the outer ones, since the Phi perfection is virtually re­solved in its infinity.