You have the ability to turn back time. Tchaikovsky and Petipa are about to launch their careers.

If you had a chance to give them each a copy of "Ballet 101", would you give it to them?

Being boring, I would most definately not give it to them, as it would change the future and throw in a few paradoxes to boot. Can you imagine what would happen? You give them Ballet 101, they see the ballets that are about to choreograph. WOuld they still do them? They might decide, 'Oh this ballet by this Balanchine bloke has some nicer and better ideas'. Then they incorporate that into their 'new ballets' and disaster..there would be no Balanchine, or there would , but he would have been something else as his 'choreography would have already been copied'. But then if Balanchine wasn't a choreographer, then his ballets wouldn't have been in 'Ballet 101' in the first place, so Tchaikovsky and Petipa couldn't have used them...hence a paradox.
So no I wouldn't give the copy to them. I would watch in wonder at how they developed their ballets and take extensive notes, so that when I got back to the present, I could write a wonderful book about it.