the main library was gone long before then, burned accidentally when Rome’s Julius Caesar attacked Egypt in 47 - 48 BC.
THEODOTUS (on the steps, with uplifted arms). Horror unspeakable! Woe, alas! Help!
RUFIO. What now?
CAESAR (frowning). Who is slain?
THEODOTUS. Slain! Oh, worse than the death of ten thousand men! Loss irreparable to mankind!
RUFIO. What has happened, man?
THEODOTUS (rushing down the hall between them). The fire has spread from your ships. The first of the seven wonders of the world perishes. The library of Alexandria is in flames.
RUFIO. Psha! (Quite relieved, he goes up to the loggia and watches the preparations of the troops on the beach.)
CAESAR. Is that all?
THEODOTUS (unable to believe his senses). All! Caesar: will you go down to posterity as a barbarous soldier too ignorant to know the value of books?
CAESAR. Theodotus: I am an author myself; and I tell you it is better that the Egyptians should live their lives than dream them away with the help of books.
THEODOTUS (kneeling, with genuine literary emotion: the passion of the pedant). Caesar: once in ten generations of men, the world gains an immortal book.
CAESAR (inflexible). If it did not flatter mankind, the common executioner would burn it.
THEODOTUS. Without history, death would lay you beside your meanest soldier.
CAESAR. Death will do that in any case. I ask no better grave.
THEODOTUS. What is burning there is the memory of mankind.
CAESAR. A shameful memory. Let it burn.
THEODOTUS (wildly). Will you destroy the past?
CAESAR. Ay, and build the future with its ruins. (Theodotus, in despair, strikes himself on the temples with his fists.) But harken, Theodotus, teacher of kings: you who valued Pompey’s head no more than a shepherd values an onion, and who now kneel to me, with tears in your old eyes, to plead for a few sheepskins scrawled with errors. I cannot spare you a man or a bucket of water just now; but you shall pass freely out of the palace. Now, away with you to Achillas; and borrow his legions to put out the fire. (He hurries him to the steps.)
POTHINUS (significantly). You understand, Theodotus: I remain a prisoner.
THEODOTUS. A prisoner!
CAESAR. Will you stay to talk whilst the memory of mankind is burning? (Calling through the loggia) Ho there! Pass Theodotus out. (To Theodotus) Away with you.
THEODOTUS (to Pothinus). I must go to save the library. (He hurries out.)
The Great Library was burned in the 7th century by order of the Caliph when the muzzies conquered Egypt. The drunk has-been Elizabeth Taylor helped stoke the myth. The myth that Caesar burned it is largely modern in origin, and of course absolves the muzzies, which is what it is designed to do. Caesar noted that the fires he had set among the ships of his enemy spread to a warehouse and consumed "some books which chanced to be there" -- the Alexandrian library was also known as The Ships' Library, because the collection came from copying the originals found on board ships at the busy port, returning the copies, and archiving the originals -- and he was himself was holding the citadel, which is where the library was located.