What is the symbolism behind depicting Kaga Ryosuke as a centaur when he uses his invisible dictionary? In the Boku-H anime, whenever Ryosuke uses his invisible dictionary, he is shown as a centaur.

What is the symbolism behind that figure?
The Centaur, in Greek mythology, is a creature related to both basal instincts and wisdom (lust, or in the context, perverseness). They are connected to the god Dionisius, god of carnal desires (sexual drive) and carousing.

From Monstruous.com:


  The wicked centaurs are the antithesis of the knight and the horseman. Instead of mastering or taming their instincts, these centaurs are ruled by them. They symbolize violent lust, adultery (...)


From Wikipedia article on Centaurs:


  Like the satyrs, centaurs were notorious for being wild and lusty, overly indulgent drinkers and carousers, given to violence when intoxicated, and generally uncultured delinquents.


So the first symbolism of the centaur relates to the fact that Ryosuke is unleashing his perverted spirit energy.

The most famous centaur is Chiron, and according to Wikipedia again:


  Chiron, by contrast, was intelligent, civilized and kind (...) A great healer, astrologer, and respected oracle, Chiron was said to be the first among centaurs and highly revered as a teacher and tutor.  


This could be connected to the fact that Ryosuke is displaying his great knowledge or wisdom, by assimilating the content of the dictionary.