Neuter e duobus libris alibi inventus est; denique ambo sub sella iacebant.

Here neuter does not mean neuter gender. It is a pronoun/adjective meaning neither (of two).

So neuter e duobus libris means neither of the two books.

Latin uses neuter when exactly two people or things are being considered. If there were more than two, Latin would use a different word, such as nemo or nullus, depending on the construction.

Because the sentence is specifically talking about two books, not an indefinite larger number.

Latin is very precise here:

• neuter = neither of two
• ambo = both of two

That pairing is very natural in this sentence:

• first clause: neither of the two books
• second clause: both

e (or ex) means out of or from among, and it takes the ablative case.

So:

• e duobus libris = out of the two books / of the two books

This is a common way in Latin to express the idea one out of a group. With neuter, it helps clarify that the meaning is neither one out of the two books.

Because it depends on e.

The preposition e/ex always takes the ablative, so:

• duobus = ablative plural of duo
• libris = ablative plural of liber

Together: e duobus libris = from among the two books.

Because neuter is grammatically singular.

Even though the idea comes from a group of two books, neuter means not one of the two taken individually, so the verb agrees with that singular subject:

• neuter ... inventus est = neither ... was found

By contrast, the second clause has ambo, which is plural, so it takes a plural verb:

• ambo ... iacebant = both ... were lying

Because the understood noun is liber, and liber is masculine.

So although neuter means neither, it still agrees in gender and number with the noun it refers to:

• understood noun: liber
• singular masculine form: inventus

If the hidden noun were feminine, you would expect inventa; if neuter, inventum.

Yes. The noun libri is understood.

Latin often omits a noun when it is obvious from context. So the sentence could be understood as:

• Neuter e duobus libris alibi inventus est
• denique ambo libri sub sella iacebant

But repeating libri would be unnecessary, so Latin leaves it out.

alibi means elsewhere or in another place.

It modifies inventus est:

• alibi inventus est = was found elsewhere

So the idea is that neither book turned up in some other location.

denique often means finally, at last, or in the end.

Here it marks the conclusion of the situation:

• nobody found either book elsewhere;
• in the end, both were under the chair.

So denique helps move the sentence toward its final discovery.

ambo means both, specifically both of two.

That matches the earlier neuter very neatly:

• neuter = neither of the two
• ambo = both

Latin prefers ambo when the number is exactly two. It is more precise than a general word like omnes.

The imperfect often describes an ongoing state or situation in the past.

So ambo sub sella iacebant means:

• both were lying under the chair
• or more naturally in English, both were under the chair

The imperfect paints the scene as a state that was already true when they were finally noticed.

With sub, Latin can use either:

• accusative for motion toward a place: to under
• ablative for location: under

Here the books are not moving; they are already lying there, so the meaning is location:

• sub sella = under the chair

So sella is ablative here, even though without macrons it looks the same as the nominative.

The word order is fairly flexible, but each position gives a certain emphasis.

A very literal unpacking would be:

• Neuter e duobus libris alibi inventus est = Neither, out of the two books, was found elsewhere
• denique ambo sub sella iacebant = finally both were lying under the chair

Natural English would usually be:

Neither of the two books was found elsewhere; in the end both were lying under the chair.

It is a nice Latin contrast.

The first clause says that not one of the two books was found anywhere else. The second clause resolves the mystery by saying where both actually were.

So the structure is almost rhetorical:

• neither was found elsewhere
• in fact, both were under the chair

That contrast makes the sentence feel neat and satisfying.