Avia dicit infantem tandem dormire coepisse.

Because this sentence uses indirect statement after dicit (says).

In Latin, after verbs of saying, thinking, knowing, hearing, and so on, the person or thing that would be the subject of the reported statement usually goes into the accusative, and the verb goes into an infinitive.

So:

• direct idea: Infans tandem dormire coepit = The baby finally began to sleep
• reported after dicit: Avia dicit infantem tandem dormire coepisse = Grandmother says that the baby finally began / has begun to sleep

Here infantem is not the direct object of dicit in the normal English sense. It is the subject of the infinitive phrase dormire coepisse.

This construction is often called the accusative-and-infinitive construction.

Because the clause after dicit is not a normal finite clause. It is an infinitive clause.

Latin does not usually say:

• Avia dicit quod infans tandem dormire coepit

in ordinary classical style.

Instead, it prefers:

• Avia dicit infantem tandem dormire coepisse

So the finite verb coepit becomes the infinitive coepisse in indirect statement.

Coepisse is the perfect active infinitive of coepi, coepisse, which means to begin.

So:

• coepit = he/she/it began
• coepisse = to have begun

In this sentence, dormire coepisse literally means to have begun to sleep.

In smoother English, that often becomes:

• says that the baby began to sleep
• says that the baby has finally fallen asleep
  depending on context and how naturally you want to translate it

Because dormire depends on coepisse.

The verb coepi means begin, and Latin normally uses it with a present infinitive to express the action that is beginning:

• dormire coepit = he/she began to sleep
• dormire coepisse = to have begun to sleep

The present infinitive dormire does not mean present time in the same way an English present tense does. Here it simply names the action: sleeping.

So Latin is effectively saying:

• the baby has begun sleeping

not

• the baby has begun to have slept

which would not make sense.

The infinitive tense in indirect statement is usually relative to the main verb.

Here:

• dicit = says (present)
• coepisse = to have begun (perfect infinitive)

That means the beginning of the sleeping is viewed as earlier than the act of saying.

So the sense is:

• Grandmother says that the baby has begun to sleep
• or Grandmother says that the baby began to sleep

In natural English, either may work depending on context.

It can mean infant, baby, or very young child, depending on context.

The basic idea is a young child, especially one not yet speaking. English translations often choose baby because it sounds more natural in many contexts.

Tandem means at last, finally, or eventually.

It often suggests that something took a while, or happened after waiting or frustration.

So in this sentence it adds the idea:

• the baby finally began to sleep
• the baby at last fell asleep

Usually, yes. Avia most commonly means grandmother.

Depending on context, it can occasionally feel more like an old woman, but grandmother is the normal meaning learners should assume unless the context suggests otherwise.

Because Latin usually does not need one in this construction.

English says:

• Grandmother says that the baby...

Latin often uses the accusative-and-infinitive construction instead of a that-clause:

• Avia dicit infantem ... coepisse

So the idea of that is built into the structure, rather than expressed by a separate word.

No. Dormire is intransitive, so it does not take a direct object here.

Instead:

• infantem is the subject of coepisse and dormire within the indirect statement
• dormire means to sleep
• coepisse means to have begun

So infantem tandem dormire coepisse means that the baby finally began to sleep.

Yes. Latin word order is fairly flexible.

This sentence could be rearranged in various ways without changing the basic meaning, for example:

• Avia infantem tandem dormire coepisse dicit
• Infantem avia tandem dormire coepisse dicit

The original order is perfectly normal, though. Latin often places the verb of saying early, and the infinitive clause after it.

Because avia is the subject of dicit.

So:

• avia = grandmother → subject
• dicit = says

Meanwhile:

• infantem is accusative because it is the subject of the infinitive in indirect statement

This contrast is very common in Latin:

• main-clause subject = nominative
• subject of reported statement = accusative

Possibly, depending on context, but that is a more interpretive translation.

The Latin most literally means:

• Grandmother says that the baby finally began to sleep
• or has begun to sleep

If the context is about a baby who would not go to sleep and then finally did, English might naturally say:

• Grandmother says the baby finally fell asleep

That is not a word-for-word translation, but it can be a good idiomatic one.

Because it is one of the standard ways Latin reports speech, thought, perception, and similar ideas.

After verbs like:

• dicit = says
• putat = thinks
• scit = knows
• audit = hears

Latin very often uses:

• accusative subject
  • infinitive verb

So this sentence is a very typical example of an important Latin pattern. Learning to recognize it will help with a huge number of sentences.