Italian author Lucio Russo in his book "Forgotten revolution" argues that a large part of the scientific knowledge of Hellenistic world has been lost. I find his arguments very convincing.
Exact sciences in the modern sense of this word originated in Ptolemaic Egypt and
other Hellenistic states, and reached very high degree of development. Few first class works
survived, like Euclid, Apollonius and Archimedes, but there is a lot of evidence that this
is just the tip of the iceberg. For example, almost all writings of Hipparchus, "the father of astronomy" are lost. We know about them from the account of C. Ptolemy who lived 3 centuries later. Or look at the "Antikythera mechanism" on Wikipedia and elsewhere, to get some evidence of what was lost.
L. Russo is a mathematician, and on his opinion, the level of development in some areas of mathematics in
Hellenistic time was not really surpassed until XIX century. I am also a mathematician,
and I confirm this.
This does not only apply to exact sciences. Critical scientific study of ancient texts, as we understand it now, also apparently originated in these Hellenistic states.
A legend says that one of the Ptolemy rulers tried to buy (from Athens) original texts
of Aeschylus, Sophocles and Euripides. Athenians refused. Then he asked to borrow them to copy. Athenians agreed, but required an enormous security deposit. He payed the deposit,
and did not return the original manuscripts:-) I suppose they were kept in Alexandrian Library (where else?).
The same Ptolemy issued the order that all ships arriving to Alexandria must be inspected
and searched for books. All books found must be confiscated, and copies made and given to the owners:-)
So we really lost a lot with the Alexandrian library.
When exactly it disappeared and how, is also subject to discussion. Some blame Julius Caesar who started a fire during a battle that destroyed a large part of the library. Other people say that it still existed at the time of the Arab conquest, and was destroyed by the conquerors. And many events in between are also mentioned.
The fact is that Claudius Ptolemy (astronomer, who probably worked in Alexandria in 2 century AD) could read Hipparchus. And we cannot. In fact almost all work in astronomy before Ptolemy is lost. And all work in mathematics before Euclid is lost.
We recently learned from secondary sources that there was highly developed combinatorics in the Hellenistic times (Habsieger, L.; Kazarian, M.; and Lando, S. "On the Second Number of Plutarch." Amer. Math. Monthly 105, 446, 1998). None of the original work survived.
We know the name of the great polymath
Posidonius (135-51 BC) whose scientific output is comparable with that of Aristoteles. He wrote on all sciences. All his works are lost. Philosopher (logician)
Chrysippus (279-206 BC) was regarded by contemporaries higher than Aristoteles. None of his works survived. None of the works of the founder of scientific medicine, Herophilos (335-280), survived. The great engineer (mechanic, hydraulic, pneumatic)
Ctesibius (3d century BC) is credited for many inventions. All his work is lost.
Several sources frequently mention enormous warships of Hellenistic era
Leontophoros are the largest mentioned) whose crew could exceed the crew of a modern aircraft carrier. Historians speculate for the last 2000 years how these ships looked and
how could they be constructed. No clear description survives.
REMARK for a mathematician. What we know of mathematics before 300 BC mostly comes from Euclid. Imagine that from our contemporary period only Bourbaki books survive...
REMARK 2. There is a consensus among modern scientists that Democritus of Abdera was one of the greatest scientists who ever lived.
Here is the list of all of the works of Democritus, with their titles as given by
Diogenes Laertius: Great Cosmology; Little Cosmology; Cosmography; On the
Planets; On Nature; On Human Nature; On Intelligence; On the Senses; On the
Soul; On Flavors; On Color; On Diverse Movements of the Atoms; Of
Changes in Shape; The Causes of Celestial Phenomena; The Causes of
Atmospheric Phenomena; On Fire and On Things in Fire; The Causes of
Acoustic Phenomena; Concerning the Magnet; The Causes of Seeds, Plants and
Fruits; On Animals; A Description of the Sky; Geography; A Description of the
Pole; On Geometry; Geometrical Reality; On the Tangents of the Circle and the
Sphere; Numbers; On Irrational Lines and Solids; Projections; Astronomy;
Astronomical Table; On Rays of Light; On Reflected Images; On Rhythm and
Harmony; On Poetry; On the Beauty of Song; On Euphony and Cacophony;
Concerning Homer, or on Correct Epic Diction; The Science of Medicine; On
Agriculture; On Words; On Names; On Values, or On Virtue; On the Disposition
which Characterizes the Wise; On Painting; A Treatise on Tactics;
Circumnavigation of the Ocean; On History; The Thought of Chaldea; The
Thought of the Phrygians; On the Sacred Writings of Babylon; On the Sacred
Writings of Meroe; On Fevers and the Coughs Deriving from Illness; On
Aporiae; Legal Questions; Pythagoras; On Logic, or Criterion of Thought;
Confirmations; Points of Ethics; On Well-being. All lost …
This is an incomplete list (just samples) of the items that WE KNOW and which are lost. What things were there which we do not know, (because all references to them are also lost) is open to speculation.