Imagine.....

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The Bibliotheca Alexandrina was located in at least three buildings: (1) the original Muesum in the royal district of the city, (2) the additional building mostly for book storage, located on the harbor, and (3) the "daughter Library" located in the Serapeum, the temple to Serapis, cult god of Alexandria. The Serapeum was located in the southwest part of the city, the popular quarter.
The Library disappeared slowly, suffering a slow decline from the time of Caesar and Cleopatra. Indeed, the first disaster was in 48 B.C., when the part of the library located at the harbor was accidentally set afire during the Alexandrian war of Julius Caesar. However, Marc Anthony gave Cleopatra the 200,000 scrolls of Pergamon, to make up for the losses. Yet, subsequent upheavals within the Roman Empire resulted in the gradual neglect and ultimate destruction of the library. Roman armies came to Alexandria to "restore order several times between 200 and 300 AD, and it was on one of those occasions, (probably the campaign of Aurelius in 272 AD) that the entire royal quarter and the original Museum were destroyed. Christianity was brought to Africa through Alexandria by St. Marc in the first century AD, and it was followed by merciless and brutal persecution of the Christians by the Romans in the first three centuries. Persecution ceased with the conversion of Constantine the Great, but schisms erupted in the church. Tensions were running high and tolerant church fathers such Clement of Alexandria had to leave the city and his disciple Origen suffered much for his views. In 391 AD Emperor Theodosius issued a decree banning all religions other than Christianity and Christian Groups under Bishop Theophilus burnt the Serapeum in 391 AD. This was the end of the ancient library as a public institution.
Thus by 400 A.D. the Library had vanished, and the era of Alexandrian scholarship came to an end a few years later. It had thus disappeared over two centuries before the arrival of the Muslim Arab armies in 641 AD.
Needless to say, the library's collection was vast, but the knowledge of exactly how many scrolls the library contained at any given point has been lost. Estimations range from 40,000 scrolls to 600,000. We do know that the collection spurred the need for a system of library organization. A precursor to today's library catalogue was developed called Pinakes, or "tablets." The tablets were divided into genre and sorted by the author's name. It's likely that this served as a record of the contents of the library rather than a precise system for finding the scrolls. Scrolls could not stand up on shelves but lay in heaps, meaning a precise method of organization would be nearly impossible to achieve. Unfortunately, the tablets along with the rest of the library have been lost to fire or time, meaning we have little record of the library's exact contents.Partially because of the library, Alexandria became a seat of scholarship and learning. Scholars from all over the Hellenistic world were allowed to browse the library. They researched, discovered, and taught.
Aristarchus was the first person to state that the earth revolves around the sun, a full 1800 years before Copernicus;
Eratosthenes proved that the earth was spherical and calculated its circumference with amazing accuracy, 1700 years before Columbus sailed on his epic voyage
Hipparchus established the first atlas of the stars and calculated the length of the solar year accurately to within 6.5 minutes
Callimachus the poet described the texts in the library organized by subject and author, becoming the father of library science,
Euclid wrote his elements of geometry, the basic text studied in schools all over the world even now
Herophylus identified the brain as the controlling organ of the body and launched a new era of medicine
Manetho chronicled the pharaohs and organized our history into the dynasties we use to this day
Zenodotus and the grammarians established the basics of literary scholarship with their meticulous definition of the Homerian text for the Iliad and the Odyssey
And the list of great names and great achievements goes on and on… Diophantes, Appolonius of Perga, Heron and visiting scholars such as Archimedes… They and many others were all members of that amazing community of scholars, which mapped the heavens, organized the calendar, established the foundations of science and pushed the boundaries of our knowledge. They opened up the cultures of the world, established a true dialogue of civilizations. Indeed, it was at the ancient Library of Alexandria that 72 specialists first translated The Old Testament from Hebrew into Greek (the famous Septuagint). Together these scholars promoted rationality, tolerance and understanding and organized universal knowledge. For over six centuries the ancient Library of Alexandria epitomized the zenith of learning, as later scholars, such Claudius Ptolemy and Dioscoredes built on that explosion of knowledge and added their contributions.
 
The idea that the loss of the Library's collection somehow led to the loss of unique advanced information found nowhere else in the world is pure fantasy. It assumes a very modern and recent connection between speculation/science and technology that didn't exist in the ancient world. With a couple of notable exceptions, Greek and Roman philosophers who did "natural philosophy" (what we call science) rarely made any connection between it and something as practical as technology. Philosophy was for the learned elite, who were usually aristocrats or associated with them. Technology, on the other hand, was a matter for builders, architects, artisans and armourers and other lower class people who got their hands dirty and was not the kind of thing to interest a lofty student of science. Most Greek and Roman era science was done in the form of thought experiments and contemplation of ideas rather than practical empiricism. It was not until the later Medieval Period that we see the first glimmering of practical, experimental science and not until the Sixteenth Century that genuine empirical science made the connection between science and technology fully possible. So the idea that this (supposed) lost unique knowledge in the Great Library would have led to much earlier advances in technology doesn't fit the evidence - ancient science didn't work that way.
For example, every Chemistry student hears about Democritus and his ATOMIC (from the Greek atomos (uncutable) theory
The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible; have always been, and always will be, in motion; that there are an infinite number of atoms, and kinds of atoms, which differ in shape, and size. Sounds pretty darn modern for 440BC when we had to wait for John Dalton in 1808 to essentially propose the exact same thing BUT Democritus' IDEA was a philosophical one only. To actually DO anything with it or TEST it for validity would have been a totally repugnant thought to him and/or any other philosopher. Democritus was largely ignored in ancient Athens, and Plato is said to have disliked him so much that he wished all his books burned.
 
Mike I have to disagree, look how many single examples of ancient technology that has so far been discovered such as the Antikythera Mechanism or the medical kit salvaged from a 2,000-year-old shipwreck off the coast of Tuscany that contained preserved medicines they were able to analyze. Or an ancient medicinal elixir that has proven to kill 99.9 % of modern anti-biotic resistant MRSA bacteria. There are numerous things from the ancient world we know/think existed but none of the details such as what makes up Greek Fire or was Archimedes' Death Ray real and if so how was it built. There are theories but nobody knows for sure. I think claiming we today know any and all technology/knowledge the ancients ever devised is ludicrous.
 
Again, we look at these things with modern eyes and totally forget to put them in their proper context. Heron's or Hero's steam turbine was never developed any farther than a novelty. In 1st century Greece, slaves were an important element of the economy, salves outnumbering freemen by more than two to one and they provided all the work anyone needed. The slave-based economy would have been rocked by the introduction of laborsaving devices and displaced slaves might have caused unrest or even revolution. And, so, the steam engine played a role in entertainment, but not business. It is reported that in Rome, at about the same time, that the emperor Vespasian purchased and destroyed the model of a mechanical device that would have made construction work more efficient, saying, "You must let me feed my poor commons" Preserving political stability motivated government to suppress technology.
And once again "context of the times" the Greeks made a distinction between science and Engineering or technology. Engineers teached their skills to their sons or apprentices who learned more from practice and experience than by reading books. Their skills were generally kept sometimes as "trade secrets" within the artisan group or groups, much as the medieval guilds kept their secrets in later centuries. They did no controlled experiments to understand the nature of the material they used except probably trial and error methods for developing better, cheaper products. The Scientists and Philosophers, were skilled in argument, debate and formal reasoning. The classical logic of hypothesis and syllogism and the logical beauty of Euclidean plane geometry are examples of this turn of mind and culture. The idea of resolving a dispute between theories by experiment rather than by debate would not have occurred to them. Even if it had, the technological ability to do the experiments was often absent; more important, perhaps, was the conceptual problem, because the concepts of their science were not clearly enough defined to suggest experiments that they could have carried out.
Plato: Mechanics is the corrupter and destroyer of the pure excellence of geometry.
Aristotle: To dwell on utility is bad taste.
Plutarch: Archimedes regarded the work of an engineer and every art that ministers to needs of life as ignoble and vulgar?
 
Viking, that is not at all what I intended to convey. Without a doubt valuable knowledge was lost but in many cases, like Greek Fire, these were closely held Guild secrets. Much the same with the medicines you mention, recipes held secret because they were worth money. You mention the Antikythera mechanism, an extremely complex navigational device that was supposedly built sometime between 150-100 BC. The Library of Alexandria is said to have burned AFTER it was in use, around 48 BC. Since there are a few obscure references to this device it must have been made and utilized during this time period. It was an incredibly complex machine - something that later civilizations could neither build nor understand. In fact it was so complex the 20th century people who discovered it felt it must be a modern device that somehow fell into an ancient shipwreck. Would the Bruchreon have contained detailed plans? Again in my view very doubtful as it was worth money. Do Coke and Pepsi publish their formulas?
While a vast amount of ancient knowledge has been lost and while copies of many of those lost works would have been held in the Great Library's collection, what has come down to us gives no indication that the Greeks and Romans were on the verge of some kind of scientific revolution. On the contrary, by the time Aurelian was burning the Bruchreion and (probably) the Library, science and learning generally had already been stagnant for some time and the following centuries of civil war in the Roman Empire, economic decline and barbarian invasions led to a further decline. When these pressures led to the collapse of the Western Roman Empire, virtually all intellectual pursuits were abandoned apart from what was preserved by the Church and huge amounts of knowledge was lost.

In the Eastern Empire and in the parts of the east converted to Nestorian Christianity, a great deal of ancient science and knowledge was preserved. These Christian scholars passed it to the Arabs and it then eventually made its way back to back to Europe via Muslim Sicily and Spain where it sparked the great revival of learning in Medieval Europe in the Twelfth Century. So while a great deal was lost, what survived came back into western Europe at the time that saw the rise of the first universities and laid the intellectual foundations of the later Scientific Revolution and its application in technology.

The idea that the loss of the Great Library set back science and technology by centuries is a nice fable, but not a viable historical idea. The Greeks and Romans were not on the verge of a scientific and technological revolution such as the one seen in the early Modern era - that required a number of unique circumstances which were simply not present in the Roman Era.
The world did lose works by many classical authors, but we only know of some because of mentions in other sources. But, many of those works may exist elsewhere yet to be found, or have been found already. Archaeology is making surprising discoveries all the time. Regardless, life may have been more enriched, but little different than it is now, whether or not they were available today.

Growing up, I was always told that if the Library had not been destroyed and the Dark Ages had never occurred, we may have gotten to space two or three centuries earlier than we did. But recent research has suggested that this is just not so. Space travel would have still waited until the 20th century, as well as nuclear power and weapons, the electronic computer and on and on. It is possible that these advancements may have happened a few decades earlier, but it is just as likely they would have happened later. Hero's inventions were curiosities, and within the Library, they may have remained oddities for quite some time (coin operated and noise making diversions). James Watt (or some contemporary) likely would have still rediscovered the concept and become the first to put it to serious use.

Even with the knowledge available at the time, materials required to make usable devices (like steel) were not available in practical quantities until the middle ages and frequent warfare accelerated the development of processes to increase the production of those materials.
 
The simple fact that we had absolutely no idea what was in the library so it is not unreasonable to theorize that loss of knowledge could have had a significant impact. However if it was like the major libraries today, there is a good chance that it possessed a number of one off items.
 
At it's peak, the library possessed nearly a half million scrolls and here's something interesting to know: when any ship came into harbor, the authorities seized any books aboard ship for immediate duplication. The book's owner was given a copy and the library retained the original - per orders of the Pharaoh.

So it can be easily assumed that the Library contained an incredible wealth of information of contemporary and older information that we can only speculate at, today.
 
Going to make a persnickety point here. The Library did not contain "books" but rather Papyrus scrolls. I think that this is important point because what we call a book nowadays would have covered several papyrus scrolls thus the number of scrolls does not equate to "number of books"
IMHO 500,000 scrolls (I've even read a million) is high. I suspect 400,000 is more like it so perhaps 100,000 books.
Viking also makes the very valid point that we really have no exact idea of what the Library contained.
What we do know that the collection was so large it required a system of library organization. A precursor to today's library catalogue was developed called Pinakes, or "tablets." The tablets were divided into genre and sorted by the author's name. It's likely that this served as a record of the contents of the library rather than a precise system for finding the scrolls. Because scrolls could not "stand-up" on shelves a precise method of organization would be nearly impossible to achieve. Unfortunately, the tablets along with the rest of the library have been lost to fire or time, thus we have little record of the library's exact contents.
ASSUMING they were in the Library, IMHO the worst losses are:
Berossus' Babylonaica (written circa 281 BC): Berossus was an incredibly bright historian whose masterpiece Babylonaica covered the history of the world in three volumes. The first volume describes everything between the creation of the world and the Great Flood, a period Berossus astonishingly estimated as being about 432,000 years! Sadly, as only fragments of the history survived.
The works of Sappho (written circa 612-570 BC): Hardly a scrap of the 9 volumes of Sappho's poetry kept at the Library survived its destruction. But that tiny sliver of her immense genius was still enough to earn her the artistic immortality about which she often wrote: "Although they are/ Only breath, words/ which I command/ are immortal". More than a poet, Sappho was perhaps the finest musician of antiquity: her talent was frequently considered proof she was either a tenth muse or a goddess. Stobaeus's Florilegium describes Solon of Athens hearing one of Sappho's songs and asking that it be taught to him. When asked why, he said, "so that I may learn it, then die."
The works of Hero of Alexandria (written circa 10-70 AD): Hero was the greatest experimenter of Greek antiquity. Endowed with mind-boggling mechanical genius, he invented steam engines, wind turbines and hydrostatic fountains millennia before these systems became commonly used. He even created automated machinery, which scholars today see as the groundwork for cybernetics! In mathematics he discovered imaginary numbers and probably knew the laws of refraction. Thankfully, Arab scholars saved a portion of his works, we do not know the bulk of wonders discovered by this brilliant man.
The works of Aristarchus of Samos (circa 310 BC-230 BC): Sometime in the 3rd Century BC, Aristarchus of Samos figured out that the Earth orbits the Sun, and not the other way around. He also correctly deduced the order of the planets, and he knew that the solar system was many, many times bigger than his contemporaries' estimates.
The Epic Cycle (compiled 100BC) Homer's Iliad and Odyssey (48 books) are only part of the story of the Trojan War. There are fragments of 29 other books written by various authors which tell of events before, between and after Homer's two epic poems.
Works of Archimedes Unlike Euclid the works of Archimedes were not well known at the time though he is often quoted in the works of well-known Alexandrian mathematicians such as Heron, Pappus, and Theon. Twelve of his works survive (only a fragment of the Stomachion) and there are references to seven others which are lost.
 
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