Years ago, I had read a book that had sparked an interest in these mathematical principals. In this book, it was speculated that Da Vinci most likely was not familiar with these principals previous to his work with the mathematician Luca Pacioli. Together, Da Vinci and Pacioli had published the very first book on this subject of geometry appropriately named De Divina Proportione (published 1509). 

For this piece;

The aspect ratio of the composition: h : Φ²  or where h = 1, l = Φ²

The golden spiral is based on h with its width subsequently equaling the above  l / Φ

Utilizing the above rules and further applying them,  one will discover a triangle with sides relative to  1 :  Φ  :  √ ( Φ² + 1 ) , which further develops the central composition.

This is a pretty impressive feat for someone who had yet to meet Pacioli – what do you think?

As the original composition requires the piece to be completed as Da Vinci originally intended in order for these these principles to be fully realized, the original piece can be found here  if one chooses to do their own analysis.