Mater dicit vultum filiae laetum esse, sed nasum eius frigidum esse.

Because after dicit (says), Latin often uses an indirect statement construction instead of a finite clause with that.

In English, we say:

• Mother says that the daughter’s face is happy
• Mother says that her nose is cold

In Latin, those reported clauses become:

• vultum filiae laetum esse
• nasum eius frigidum esse

In this construction, the subject of the reported statement goes into the accusative, and the verb becomes an infinitive.

So:

• vultum = the subject of laetum esse
• nasum = the subject of frigidum esse

Even though they would be nominative in a direct statement, they become accusative in indirect statement.

For the same reason: this is indirect statement.

A direct statement would be:

• Vultus filiae laetus est.
• Nasus eius frigidus est.

But after dicit, Latin normally changes the clause into:

• accusative subject + infinitive verb

So:

• vultus ... laetus est becomes vultum ... laetum esse
• nasus ... frigidus est becomes nasum ... frigidum esse

So esse is not just randomly chosen; it is the normal infinitive form of to be used in reported speech after verbs like say, think, hear, know, and so on.

Here filiae is genitive singular, meaning of the daughter.

So:

• vultum filiae = the daughter’s face or the face of the daughter

It is true that filiae could also be dative singular in another sentence, because first-declension nouns have the same ending for genitive singular and dative singular. But here the sense is clearly possessive:

• vultum filiae laetum esse = that the daughter’s face is happy

A dative meaning such as for the daughter would not fit naturally here.

Because of agreement.

Latin adjectives agree with the nouns they describe in:

• gender
• number
• case

Here:

• vultum is masculine accusative singular
• laetum is masculine accusative singular

So they match.

But filiae is feminine and not accusative, so laetum cannot go with it.

The same thing happens in the second half:

• nasum is masculine accusative singular
• frigidum is masculine accusative singular

So frigidum goes with nasum.

Because they are predicate adjectives inside the indirect statement, and they agree with the accusative subjects.

In English, we say:

• the face is happy
• the nose is cold

In Latin indirect statement, both the subject and its predicate adjective go into the accusative:

• vultum ... laetum esse
• nasum ... frigidum esse

So the adjective follows the case of the noun it belongs to.

Because Latin usually does not use a separate word like English that in this kind of sentence.

English says:

• Mother says that the daughter’s face is happy

Latin usually says:

• Mater dicit vultum filiae laetum esse

So instead of that + finite verb, Latin uses:

• accusative + infinitive

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

eius means his, her, its, or their, depending on context.

Here it most naturally refers to the daughter, so:

• nasum eius = her nose

That gives the sense:

• Mother says the daughter’s face is happy, but her nose is cold.

The context makes it clear that eius refers back to filiae, not to mater.

This is a very common question.

Latin suus, sua, suum is a reflexive possessive adjective. It usually refers back to the subject of the clause it depends on, and in constructions like this it normally points back to the main subject, here mater.

So if Latin said:

• nasum suum

that would most naturally mean:

• her own nose, with her referring to the mother

But the sentence wants to say that the daughter’s nose is cold, not the mother’s. So Latin uses eius, the non-reflexive form:

• nasum eius = her nose = the daughter’s nose

So the choice between suum and eius helps show whose nose it is.

Latin often avoids exact repetition when a pronoun will make the meaning clear.

So instead of saying something like:

• vultum filiae ... sed nasum filiae ...

the sentence uses:

• vultum filiae ... sed nasum eius ...

This is natural Latin style. It keeps the sentence from sounding repetitive while still making the reference clear.

Not as much as it would be in English.

Latin word order is relatively flexible because the endings show the grammatical relationships. This sentence is arranged clearly and naturally, but other orders would still be possible.

The given order groups related words together:

• vultum filiae laetum esse
• nasum eius frigidum esse

That lets you see each indirect statement as a unit:

1. accusative noun
2. possessor
3. adjective
4. infinitive

Also, sed simply links the two reported statements with the meaning but.

The repetition makes the structure very clear:

• vultum filiae laetum esse
• sed nasum eius frigidum esse

Latin can sometimes omit a repeated word if it is easily understood from context, and a second esse might be omitted in some styles. But repeating it is perfectly normal and often clearer for the reader.

So in this sentence, the repeated esse neatly marks that there are two parallel indirect statements after dicit.

The main clause is:

• Mater dicit = Mother says

Then come two indirect statements joined by sed:

1. vultum filiae laetum esse
2. nasum eius frigidum esse

So the pattern is:

• main verb of saying
• reported statement 1
• but
• reported statement 2

That is why the sentence feels longer than a simple English sentence: Latin is packaging both reported ideas under one verb, dicit.