Answer:
He was proud of this piece as it was validation of his career. Euclid is depected as being bent over showing something with a compass; he is known as the father of geometry. Euclid's portait is said to be Raphael's friend Bramante. Plato has his finger pointed toward the sky, as if to say the world they are in is not the physical one, but instead ideas and consepts. It is beilved that Plato face is Leonardo da Vinci's, based on similarites.
I hope this helped a bit
