The art of cropping or the cropping of art

At the Uffizi in Florence I was captivated by this portrait of Eleonora and her son by Agnolo Bronzino, and while in the book store saw that each of these book covers had cropped it slightly differently; all had removed some of the right side. She was a very powerful woman at the time and the uncropped version makes her arm more prominent and in my mind more powerful and less motherly.

below is a photo of the painting from the web
also interesting that when I was looking for the original that there were many other crops ofs the same picture!