mm, a useful word - what really surprised me on my way to double check the etymology was to find a full house of obscurantist listings though: Phrontistery, Luciferous Logolepsy and WWFTD!

The roots are indeed common as you assumed Zed.
ambition comes from: Middle English ambicioun, excessive desire for honor, power, or wealth, from Old French ambition, from Latin ambiti, ambitin-, from ambitus, past participle of ambre, to go around (for votes). ~ http://www.bartleby.com/61/35/A0243500.html

Looking at 'ambi*' gets you more directly to the Latinate origins but also suggests a Greek root (as in amphitheatre of course!):
http://www.bartleby.com/61/roots/IE15.html

A nice concatenation of footfalls in this family of words, isn't there?