Magistra addit vocativum ad eum pertinere qui appellatur.

Because magistra is the subject of the main verb addit. It means the female teacher or the mistress/teacher, and the subject of a finite verb normally appears in the nominative.

This is a very common Latin construction.

After a verb of saying, thinking, knowing, and similar ideas, Latin often uses an indirect statement:

• accusative + infinitive

So in:

• Magistra addit vocativum ad eum pertinere...

the clause vocativum ad eum pertinere is an indirect statement. Inside that clause:

• vocativum is the logical subject of pertinere
• but because it is in indirect statement, it appears in the accusative

So Latin says, literally:

• The teacher adds the vocative to pertain to him...

but good English makes it:

• The teacher adds that the vocative pertains to him...

Because it is part of the indirect statement after addit.

Latin often does not use a separate word for that after verbs like say, think, or add. Instead, it uses:

• an accusative subject
• plus an infinitive verb

So:

• vocativum ... pertinere

means:

• that the vocative pertains...

If Latin had used pertinet, that would make it a direct finite clause instead of an indirect statement.

There is no separate word for that here.

English usually says:

• The teacher adds that...

Latin often expresses that idea through the accusative-and-infinitive construction instead of using a conjunction. So the meaning of that is built into:

• vocativum ... pertinere

The verb pertinere often takes ad plus the accusative and means things like:

• to pertain to
• to belong to
• to concern
• to apply to

So ad eum pertinere means:

• to pertain to him
• to apply to him

In this sentence, it means that the vocative case belongs to or applies to the person being addressed.

Because pertinere here is being used with the preposition ad.

So the structure is:

• pertinere ad aliquem

meaning:

• to pertain to someone
• to apply to someone

Since ad governs the accusative, the pronoun becomes eum.

It refers to eum.

So the structure is:

• ad eum
• qui appellatur

That means:

• to him, who is addressed/called
• more naturally, to the person who is addressed

The relative clause qui appellatur describes which him is meant.

Because the case of a relative pronoun is determined by its job inside its own clause, not by the case of its antecedent.

Here:

• eum is accusative because it is governed by ad
• but inside the relative clause, qui is the subject of appellatur

Since it is the subject there, it must be nominative:

• qui appellatur = who is called/addressed

If it were quem, it would be functioning as an object inside the relative clause, which is not the case here.

Appellatur is:

• 3rd person singular
• present tense
• passive voice
• indicative mood

It comes from appello, appellare.

So it means:

• he is called
• he is addressed
• he is named

In this context, because the sentence is about the vocative, is addressed is especially appropriate.

It is best understood as a grammatical term used substantively.

Latin grammar words like nominativus, genitivus, vocativus, and so on are originally adjectives, often with an implied noun such as casus.

So vocativum here means something like:

• the vocative
• more fully, the vocative case

Learners often translate it simply as the vocative.

Because ad needs an expressed object.

The phrase is:

• ad eum = to him and then
• qui appellatur = who is addressed

So together:

• ad eum qui appellatur = to the one who is addressed

This is a very normal Latin pattern:

• pronoun or noun first
• then a relative clause explaining it

Compared with English, yes, but for Latin it is quite normal.

Latin word order is much more flexible because the endings show the grammatical roles. The sentence is arranged like this:

• Magistra addit = main statement first
• vocativum ad eum pertinere = the indirect statement
• qui appellatur = relative clause at the end, explaining eum

English relies more heavily on word order, but Latin can move parts around for emphasis or style without changing the basic meaning.