Personally, I feel that Mages in general could go without Ancient Library (other than Witch, since they can level it higher, along with sharing it). Just saying though, that's just me.
Erh, Memorize sounds REALLY useful, reducing both casting time and maximum charge time.
I don't see many Elementalists use Aerial Fire Bomb, much less Fire Bomb at all, even when they have it for pre-requisite.
Erh, okay, your build in general. I think we had someone suggest this before, and quite frankly, I don't think these all-elements builds are possible. I don't play Elementalist or a class with a choice of variety (other than Battle Mage, and Chasers don't come close enough to Elementalist varieties), BUT because your third/last-tier magic are all level one, I don't believe their damage will help. Even being able to spam your magic with this variety and having Magic Library, your damage per MP cost will MORE THAN LIKELY be lower than someone that focuses on a few skills.
Plus you don't have the skill points to put into Mastery. X: Masteries give such nice bonuses.
In short, I recommend cutting down your elements to at most three, with focuses on two. Less means more.