Actually, I believe that it was the muslims who destroyed the library, around the middle of the 7th century AD when they conquored Alexndria, while Cyril, Archbishop of Alexandria (later St. Cyril), burned Hyapatia (one of the greatest "librarians" of Alexandria) in the early 5th century.
I could be wrong about this. It's been about 20 years since I looked into this stuff.
Mark
The Arabs did have possession of many ancient texts which were translated from Greek into Arabic, carried across North Africa to the real gem in their empire, Andalusian Spain, and then translated again into Latin. This was the source of Europe's exposure to Plato's and Aristotle's writings during the late Middle Ages and the Renaissance. But the point is that during a time when any manuscript, scroll, or book was priceless the (First?) Library of Alexandria was a genuine treasure house.
I believe you are correct. The Caliph's "reasoning" was that if a book agreed with the Koran, it was superfluous, if it disagreed, it was heretical. You only need 12 billion copies of one book.
Caesar burned it by accident, he set fire to an enemy fleet and the fire spread. Terrible lose, Muslims of 7th century would not have burned it. Todays Muslims might.
(yay! found my photocopy)
The Library originally had two parts: the biblion (main library), for scholars, and the museion (mus-e-um?), which also had a library. And an Annex was built later, called the Serapeion (Serapeum?).
Caracalla sacked Alexandria in the 3rd century AD. The Museum's library was apparently looted/damaged then. The Serapeion's collection was burned or looted in 391 AD, with some involvement of Theophilus (Patriarch of Alexandria) and the Emperor Theodosius I. And the mobs of Alexandria. Apparently, Alexandria was famous for its mobs (who over the years lynched Roman officials, sundry foreigners, and Hypatia, for example).
The Emir Amrou Ibn el-As captured Alexandria in 641 AD and, traditionally, was said to have used what books remained (except for Aristotle's stuff) to the feed stoves at the public baths.