In peristylio parvo impluvium lucidum est, et puella aquam in eo spectat.

Because it follows in in a location phrase: in peristylio = in the peristyle / in the courtyard.

When in means in or on in the sense of location, it usually takes the ablative case.
Peristylium is the nominative/accusative singular form, while peristylio is the ablative singular.

So:

• peristylium = the peristyle/courtyard
• in peristylio = in the peristyle/courtyard

Because parvo is agreeing with peristylio.

Latin adjectives must match the nouns they describe in:

• gender
• number
• case

Here, peristylio is:

• neuter
• singular
• ablative

So parvus, -a, -um becomes parvo to match it:

• in peristylio parvo = in the small peristyle

Because -um does not always mean accusative. In a second-declension neuter noun, -um can be either:

• nominative singular
• accusative singular

Here, impluvium is the subject of est, so it is nominative singular.

A key Latin rule is that neuter nominative singular and neuter accusative singular often look the same.

So in this sentence:

• impluvium lucidum est = the pool/open rain basin is bright/clear

Because lucidum agrees with impluvium.

Impluvium is:

• neuter
• singular
• nominative

So the adjective lucidus, -a, -um must also be:

• neuter
• singular
• nominative

That gives lucidum.

So:

• impluvium lucidum = the bright/clear impluvium

An impluvium is a special feature of a Roman house: a basin or pool designed to collect rainwater, usually below an opening in the roof.

So this is not just any random pool. It is a specifically Roman architectural term. Latin often uses culturally specific words like this, especially in descriptions of Roman homes.

Latin word order is much more flexible than English word order.

English usually depends heavily on word order:

• The pool is bright

Latin depends much more on endings than on position, so several orders are possible.
In this sentence, impluvium lucidum est is a very natural order, with est at the end.

Putting est later can give the sentence a slightly more orderly or descriptive feel:

• In peristylio parvo impluvium lucidum est
  = In the small peristyle there is a bright impluvium / the impluvium is bright

Because puella is in the nominative singular, which is the normal case for the subject.

The second clause is:

• et puella aquam in eo spectat

Here:

• puella = the girl → subject
• aquam = water → direct object
• spectat = looks at / watches

So puella is the one doing the action.

Because spectat takes a direct object, and the direct object in Latin is usually in the accusative case.

Here the girl is looking at the water, so water is the thing being looked at.

Thus:

• aqua = water (nominative)
• aquam = water (accusative)

So:

• puella aquam spectat = the girl looks at the water

In eo means in it.

The word eo is the ablative singular of the pronoun is, ea, id (he/she/it, or more often this/that/it depending on context).

Since in here means location (in), it takes the ablative case again.
So eo is ablative because it follows in.

Most likely, eo refers back to impluvium:

• in eo = in it, that is, in the impluvium

Because the pronoun must match the noun it refers to in gender and number.

Impluvium is neuter singular, so the pronoun must also be neuter singular.

Forms of is, ea, id include:

• masculine ablative singular: eo
• neuter ablative singular: eo
• feminine ablative singular: ea

Since impluvium is neuter, eo is correct.

Usually spectat means looks at, watches, or observes. It suggests more active looking than a simple sees.

So here the idea is probably that the girl is gazing at or watching the water in the impluvium, not merely noticing it.

It comes from specto, spectare.

Spectat is:

• third person singular
• present tense
• active voice
• indicative mood

So it means:

• he/she/it looks at
• here specifically: the girl looks at

The subject puella tells you that it means she looks at.

Classical Latin has no definite article (the) and no indefinite article (a/an) as regular separate words like English does.

So:

• puella can mean girl, a girl, or the girl
• aquam can mean water, the water
• impluvium can mean an impluvium or the impluvium

The exact English translation depends on context.

Latin often puts setting or background information early in the sentence.

So:

• In peristylio parvo sets the scene first
• then impluvium lucidum est tells what is there
• then et puella aquam in eo spectat adds what the girl is doing

This is a very natural Latin way to organize description: place first, then what is in the place, then action.

Yes. Latin word order is flexible, so several arrangements are possible, for example:

• et puella aquam in eo spectat
• et puella in eo aquam spectat
• et aquam puella in eo spectat

These all keep basically the same grammar, though the emphasis may shift slightly.

The given order is straightforward and natural: object first, then the location phrase, then the verb.