???? latin common italian language in 1513?

I'm not in the field but I know for sure latin was not a spoken language anymore by that time. it already evolved in what became the regional languages. only in liturgical and academic occasions it would be still used (in fact the real name of "the prince" is " De Principatibus" and all the chapters'title is still in latin.

but if you want your book to be read by someone NOT academic, it's a really bad idea to write it in the academic language.