Cum pater ē tablinō exit, puella eī librum amissum ostendit.

Here cum means when, not with.

Latin cum can be:

• a preposition meaning with when followed by the ablative
• a conjunction meaning when, since, or although

In this sentence, cum pater ē tablinō exit is a clause, so cum is a conjunction: when father comes out of the tablinum/study.

Because this is a straightforward time clause, the verb is in the indicative: exit.

Exit is present indicative, from exeō (go out, come out, leave).

So the sentence is using present tense in both clauses:

• exit = comes out
• ostendit = shows

This can describe:

• something happening now
• something that happens regularly
• a simple narrative style often used in Latin teaching texts

So the sense is something like: When father comes out..., the girl shows...

Ē means out of or from.

It takes the ablative case, so tablinō is ablative singular of tablinum.

So:

• ē tablinō = out of the tablinum / from the study

A tablinum was a room in a Roman house, often used as a kind of study, office, or reception room.

Ē and ex mean the same thing here: out of / from.

Latin commonly uses:

• ex before vowels or sometimes before consonants
• ē especially before consonants

In practice, both forms are very close in meaning, and authors may vary. Here ē tablinō is completely normal.

Eī is the dative singular of is, ea, id, and here it means to him.

The verb ostendit (shows) can take:

• a direct object: the thing shown
• an indirect object: the person shown to

So:

• librum amissum = the thing being shown
• eī = the person to whom it is shown

If Latin used eum, that would be accusative, meaning him as a direct object, which would not fit here.

So:

• eī ostendit = she shows to him
• natural English: she shows him

Yes, eī can mean:

• to him
• to her
• sometimes to it

The form itself does not show gender clearly in the dative singular.

But in this sentence, the context makes it clear that eī refers to pater, so it means to him.

Librum is accusative singular of liber (book).

It is the direct object of ostendit:

• puella eī librum amissum ostendit
• the girl shows him the lost book

So librum is the thing being shown.

Because amissum describes librum, it must agree with it in:

• gender
• number
• case

So:

• librum = masculine, singular, accusative
• amissum = masculine, singular, accusative

This is basic Latin adjective agreement.

So librum amissum means the lost book or the misplaced book.

It is a perfect passive participle of amittō (lose).

Literally, amissus means something like:

• having been lost
• lost
• mislaid

In this sentence, it is being used adjectivally, simply to describe the book:

• librum amissum = the lost book

So although it comes from a verb, here it functions like an adjective.

Latin word order is much more flexible than English word order because the endings show what each word is doing.

Here:

• pater is the subject of exit
• puella is the subject of ostendit
• eī is the indirect object
• librum amissum is the direct object

So Latin does not need to rely on position as much as English does.

The order here is quite natural:

• first the time/background clause: Cum pater ē tablinō exit
• then the main action: puella eī librum amissum ostendit

A very literal order would be: When father comes out of the study, the girl to him the lost book shows.

English has to rearrange that, but Latin can leave it this way because the endings make the roles clear.

Because Latin has no articles.

So:

• pater can mean father, the father, or sometimes a father
• puella can mean girl, the girl, or a girl
• librum amissum can mean a lost book or the lost book

English has to choose an article, but Latin usually leaves that to context.

In this sentence, context would normally make us translate naturally as something like the father, the girl, and the lost book.