Puella dicit operculum parvum non inveniri, sed lagenam ipsam in mensa manere.

Because Latin commonly uses the accusative-and-infinitive construction for reported statements after verbs of saying, thinking, knowing, hearing, and so on.

So instead of saying:

• The girl says that the small lid is not found, but that the bottle itself remains on the table

Latin says literally:

• The girl says the small lid not to be found, but the bottle itself to remain on the table

That sounds strange in English, but it is normal Latin.

In this kind of indirect statement, the subject of the infinitive goes into the accusative case.

So:

• operculum parvum non inveniri = that the small lid is not being found
• lagenam ipsam in mensa manere = that the bottle itself remains/is staying on the table

Even though operculum and lagena are the logical subjects of inveniri and manere, they appear in the accusative because they are inside indirect statement constructions.

If these were direct statements instead, you would expect nominatives:

• operculum parvum non invenitur
• lagena ipsa in mensa manet

Inveniri is the present passive infinitive of invenire.

• invenire = to find
• inveniri = to be found

So operculum parvum non inveniri means that the small lid is not being found or more naturally that the small lid cannot be found / isn’t found.

Because non negates the verbal idea of that infinitive clause.

So:

• operculum parvum non inveniri = that the small lid is not being found

Latin often puts non directly before the word or phrase it negates. Here it naturally goes before inveniri.

Because Latin usually does not use a separate word like English that in this construction.

English says:

• The girl says that ...

Latin typically says:

• Puella dicit
  • accusative + infinitive

So the idea of English that is built into the grammar of the accusative-and-infinitive construction.

Ipsam is a form of ipse, ipsa, ipsum, which is an intensive pronoun/adjective. Here it means something like:

• the bottle itself
• the very bottle

It adds emphasis. The point is that although the lid cannot be found, the bottle itself is still on the table.

It agrees with lagenam in:

• gender: feminine
• number: singular
• case: accusative

So lagenam ipsam means the bottle itself.

Because it modifies lagenam, and modifiers must agree with the nouns they describe.

Since lagenam is:

• feminine
• singular
• accusative

ipsam must also be:

• feminine
• singular
• accusative

So lagenam ipsam is one unit: the bottle itself.

Because it follows in used for location.

• in + ablative = in/on a place
• in + accusative = into/onto a place

Here the bottle is not moving onto the table; it is already there. So Latin uses:

• in mensa = on the table

with mensa in the ablative.

Latin in with the ablative can cover both in and on, depending on context.

With something like a table, English naturally says on the table, but Latin can still use in mensa for that location.

So you should not force Latin prepositions into one exact English equivalent every time. The main idea is location, and English chooses the most natural wording.

Because it agrees with operculum.

Operculum is a neuter singular noun, so its adjective must also be neuter singular:

• operculum = neuter singular accusative
• parvum = neuter singular accusative

Together they mean the small lid.

Latin adjective placement is more flexible than English word order.

Both of these are possible Latin patterns:

• noun + adjective
• adjective + noun

So operculum parvum simply means small lid or the small lid. The adjective comes after the noun here, which is very normal Latin.

Because the same dicit governs both infinitive clauses.

So the structure is:

• Puella dicit
  • operculum parvum non inveniri
  • sed lagenam ipsam in mensa manere

In English we often repeat the idea with that, but Latin does not need to repeat dicit. The second clause is just linked with sed: but.

Sed connects the two reported statements:

• operculum parvum non inveniri
• lagenam ipsam in mensa manere

So the contrast is:

• the lid cannot be found,
• but the bottle itself remains on the table.

It marks a clear opposition between the missing lid and the still-present bottle.

Both are present infinitives. In indirect statement, the present infinitive usually shows action happening at the same time as the main verb.

So:

• dicit ... inveniri ... manere suggests:
  • she says the lid is not being found
  • and the bottle is remaining on the table

In more natural English, we often simplify that to:

• She says the small lid cannot be found, but the bottle itself is on the table.

A direct version would normally be:

• Operculum parvum non invenitur, sed lagena ipsa in mensa manet.

Then, when Latin reports that after dicit, it changes to indirect statement:

• Puella dicit operculum parvum non inveniri, sed lagenam ipsam in mensa manere.

So the main changes are:

• nominative subjects become accusative
• finite verbs become infinitives

That is one of the most important patterns in Latin syntax.