MORE ON WHY EUROPEANS RULED
As far as European dominance goes, you’re best off reading Guns, Germs, and Steel by Jared Diamond. [Paul M.] Kennedy’s points on the subject [in The Rise and Fall of the Great Powers, which Cecil cited] are rather weak:
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As for Diamond’s book, I’ll confess I hadn’t read it. Sounds like none of the folks who urged it on me read it either. Diamond and Kennedy address two related but distinct questions. Diamond asks why Eurasia and North Africa dominated the world; he mainly considers developments from prehistory through 1500 AD. Kennedy asks why Europeans specifically, out of all the Eurasian societies, dominated; he mostly looks at things from 1500 on. The answers they come up with are similar–they both blame environmental factors–and insofar as they address European dominance, their answers are pretty much the same.
(2) Whatever may be said for Islamic culture prior to 1500 AD, few would dispute that Europe was more open intellectually than other Eurasian societies after that date.