Domina dicit servam fidelem sibi magno auxilio esse.

Because after dicit Latin uses an indirect statement construction.

With verbs like dico, puto, audio, scio, and similar verbs of saying, thinking, or knowing, Latin often says:

• accusative subject + infinitive verb

So in Domina dicit servam fidelem sibi magno auxilio esse, the main statement is:

• Domina dicit = The mistress says

What she says is expressed as an indirect statement:

• servam ... esse = that the slave ... is

In that indirect statement, the subject is servam, so it goes into the accusative.

Because fidelem describes servam, and it must agree with it.

Since servam is:

• feminine
• singular
• accusative

the adjective must also be:

• feminine
• singular
• accusative

So:

• servam fidelem = the faithful slave in the accusative

This is a predicate adjective inside the indirect statement: it tells us something about servam.

It is an accusative-and-infinitive clause, the normal Latin way to express indirect statement.

You can break it up like this:

• servam = subject of the indirect statement, in the accusative
• fidelem = adjective describing servam
• sibi = to herself / to her, dative
• magno auxilio = for great help / as great help, dative phrase
• esse = infinitive verb, to be

So the core pattern is:

• servam ... esse = that the slave is ...

Because the verb in an indirect statement is usually put in the infinitive.

If this were a direct statement, it would be something like:

• Serva fidelis sibi magno auxilio est.

But after dicit, Latin changes the clause into indirect statement:

• servam fidelem sibi magno auxilio esse

So esse is the infinitive form corresponding to est.

Because sibi is the reflexive form, and it refers back to the subject of the main clause, domina.

So:

• Domina dicit ... sibi ... esse
  = The mistress says ... to herself / to her

In smoother English, this is usually just to her, but Latin uses sibi to show that the person benefited is the same as the subject of dicit, namely domina.

If Latin used ei, that would normally mean to her referring to some other woman, not back to domina.

Sibi is dative.

It is in the dative because it marks the person affected or benefited:

• to her
• for her

In this sentence, the faithful slave is said to be a great help to the mistress, so sibi is the dative of the person concerned.

This is a very common Latin construction called the double dative.

The pattern is:

• alicui auxilio esse = to be a help to someone
• more literally, to be for help to someone

Here:

• sibi = dative of the person
• magno auxilio = dative of purpose or result

So magno auxilio esse means:

• to be a great help
• more literally, to be for great help

This is a standard idiomatic Latin expression.

Formally, auxilio and magno could look like either dative or ablative singular. You tell from the construction.

Here the clue is the idiom:

• alicui auxilio esse

That expression takes:

• a dative of the person: sibi
• a dative of purpose: auxilio

So in this sentence, magno auxilio is understood as dative, not ablative.

In other words, grammar and idiom tell you the case function, even when the form itself could be ambiguous.

Because Latin is not saying the slave is a great help with a simple nominative or accusative noun here. Instead, it uses the idiomatic construction:

• magno auxilio esse alicui

So auxilio is not a direct object or a normal predicate nominative. It is part of the double dative construction.

That is why you get:

• magno auxilio = for great help / as a great help

rather than magnum auxilium.

Because it belongs with servam and agrees with it.

Latin word order is flexible, but words that belong together are often placed near each other for clarity. So:

• servam fidelem naturally goes together

This helps you see immediately that the faithful one is the slave, not something else in the sentence.

Not in the same way as in English.

Latin relies much more on case endings than on fixed word order. So the relationships are shown mainly by the endings:

• domina = nominative subject
• servam = accusative subject of the infinitive
• fidelem = adjective agreeing with servam
• sibi = dative
• magno auxilio = dative phrase
• esse = infinitive

That means Latin can move words around for emphasis or style without changing the basic meaning.

Still, this order is quite natural and readable.

Yes. That is exactly the right idea.

Inside the indirect statement, servam is the logical subject of esse:

• the faithful slave is ...

But because Latin indirect statement requires an accusative subject, the form is servam, not serva.

So it is:

• subject in function
• accusative in form

That is one of the most important features of Latin indirect statement.

Probably two things at once:

1. Indirect statement

   • dicit + accusative + infinitive
   • servam ... esse

2. Double dative

   • sibi magno auxilio esse
   • to be a great help to her

So the sentence is a good example of how Latin can pack a lot of grammar into a short clause.