Post tepidarium puella in caldarium it, ubi balneatrix aquam in piscinam fundit.

Because post is a preposition that takes the accusative case.

So:

• tepidarium = accusative singular
• not tepidario

Here post tepidarium means after the tepidarium or after leaving the warm room.

A useful rule:

• post + accusative = after

Since tepidarium is a neuter noun, its nominative and accusative singular look the same, so tepidarium could be either nominative or accusative depending on its job in the sentence. Here it is accusative because it follows post.

Puella is nominative singular, so it is the subject of it.

That means puella is the one doing the action of going.

Latin often shows the job of a word by its ending, not mainly by word order. Even though English usually depends on order, Latin does not need to put the subject first every time. Here, though, puella is also placed in a very natural position near the beginning.

So:

• puella = nominative = subject
• it = she goes

In Latin, it is a verb, not a pronoun.

It is the 3rd person singular present active indicative of ire, meaning to go.

So:

• eo = I go
• is = you go
• it = he/she/it goes

In this sentence, because the subject is puella, it means she goes.

This is a very common point of confusion for English speakers, because Latin it looks exactly like English it, but they are completely unrelated.

Because in with the accusative usually shows movement into a place.

So:

• in caldarium it = she goes into the caldarium

Compare:

• in + accusative = into / onto (motion)
• in + ablative = in / on (location)

For example:

• in caldarium it = she goes into the hot room
• in caldario est = she is in the hot room

This is one of the most important uses of Latin cases with prepositions.

For the same reason: in is showing movement toward the inside of something.

• aquam in piscinam fundit = she pours water into the pool

The water is moving into the pool, so Latin uses:

• in + accusative

If the sentence were describing water already located in the pool, Latin would normally use in + ablative instead.

Aquam is accusative singular, and it is the direct object of fundit.

That means aquam is the thing being poured.

So in:

• balneatrix aquam in piscinam fundit

we have:

• balneatrix = subject, the person doing the pouring
• fundit = pours
• aquam = direct object, the thing poured
• in piscinam = where it is poured

This is very similar to English structure, even though the word order is not exactly the same.

Balneatrix is nominative singular, and it is the subject of fundit.

It means something like bath attendant or female bath worker.

So in the clause:

• ubi balneatrix aquam in piscinam fundit

the balneatrix is the one who pours the water.

A learner might briefly wonder whether puella is still the subject here, but the new nominative noun balneatrix shows that the subject of this clause is now different.

Ubi here means where.

It introduces a clause that tells us what happens in that place:

• ubi balneatrix aquam in piscinam fundit
• where the bath attendant pours water into the pool

So the structure is:

• main clause: Post tepidarium puella in caldarium it
• subordinate clause: ubi balneatrix aquam in piscinam fundit

You can think of ubi as connecting the caldarium with the action happening there.

Because Latin has no articles.

So a word like puella can mean:

• the girl
• a girl

and caldarium can mean:

• the hot room
• a hot room

The exact sense depends on context.

English speakers often want to know why the Latin sentence does not show the before tepidarium, caldarium, balneatrix, or piscinam. The answer is simply that Latin normally leaves that idea unstated.

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

English relies heavily on order:

• The girl sees the servant
• The servant sees the girl

Latin can often rearrange words without changing the basic meaning, because the endings still mark subject, object, and so on.

In this sentence, the order is quite natural, but it is still more flexible than English:

• Post tepidarium puella in caldarium it
• literally something like After the tepidarium the girl into the caldarium goes

Latin places words partly for clarity, style, and emphasis, not just strict grammatical necessity.

Yes. Both are neuter second-declension nouns.

Their basic forms are:

• tepidarium, tepidarii = warm room
• caldarium, caldarii = hot room

Because they are neuter, an important rule applies:

• nominative singular = accusative singular

So tepidarium and caldarium look the same whether they are nominative or accusative. You have to tell their case from context:

• after post or in with motion, they are accusative
• as a subject, they could be nominative

Fundit means pours.

It is the 3rd person singular present active indicative of fundere.

So:

• fundo = I pour
• fundis = you pour
• fundit = he/she/it pours

In the sentence:

• balneatrix aquam in piscinam fundit

it means the bath attendant pours water into the pool.

This verb is a good example of how Latin often puts the verb near the end of the clause, though it does not have to.

It can be understood as a kind of sequence, and in context it usually means something like after the tepidarium or after leaving the tepidarium.

In a bath-house description, that often implies movement from one room to the next:

• first the tepidarium
• then the caldarium

So although post literally means after, the idea is tied to moving through spaces in order.

This is a nice example of Latin letting a short phrase express something that English might spell out more fully, such as after passing through the tepidarium.