Dum magister tacet, discipuli paulatim intellegunt cur haec verba inter se similia sint.

Here dum means while, so dum magister tacet is a temporal clause: while the teacher is silent / while the teacher says nothing.

A learner should know that dum can mean different things in different contexts, especially:

• while
• sometimes until

In this sentence, the sense is clearly while.

Also, with dum meaning while, Latin very often uses the present indicative, as it does here with tacet.

Tacet is the 3rd person singular present active indicative of tacere, meaning to be silent or to say nothing.

It is present because the sentence is describing an action happening at the same time as the main action:

• dum magister tacet = while the teacher is silent
• discipuli ... intellegunt = the students understand

So both actions are presented as happening simultaneously.

The subject is discipuli.

You can tell because:

• discipuli is nominative plural
• intellegunt is 3rd person plural

So they match: the students understand.

Paulatim is an adverb, and it means gradually, little by little, or step by step.

It modifies intellegunt, so the sense is:

• the students gradually understand
• the students come to understand little by little

This is a very natural Latin way to express gradual progress.

Yes. Intellegunt and intelligunt are spelling variants of the same verb, from intellegere / intelligere.

Both mean to understand.

Many textbooks and dictionaries prefer one spelling over the other, but they refer to the same word. In this sentence, intellegunt is simply they understand.

Cur means why.

Here it introduces an indirect question:

• cur haec verba inter se similia sint
• why these words are similar to one another

After verbs like ask, know, see, understand, and similar verbs, Latin often uses an indirect question introduced by words like:

• cur = why
• quid = what
• quis = who
• ubi = where
• quomodo = how

So after intellegunt, the cur clause gives what the students are understanding.

Because the clause introduced by cur is an indirect question, Latin uses the subjunctive.

So:

• direct question: Cur haec verba inter se similia sunt?
  = Why are these words similar to one another?
• indirect question: discipuli intellegunt cur haec verba inter se similia sint
  = the students understand why these words are similar to one another

So sint is the present subjunctive of esse.

This is one of the most important rules to learn: indirect questions in Latin normally take the subjunctive.

Because the main verb intellegunt is present, and the indirect question expresses something understood at the same time.

So the tense sequence is natural:

• main verb: intellegunt = present
• subordinate verb: sint = present subjunctive

This fits the normal Latin sequence of tenses for an indirect question referring to time contemporary with the main verb.

Haec verba means these words.

Here:

• verba is neuter plural
• so the demonstrative must also be neuter plural
• that gives haec

This is a very common point for English speakers, because verbum means word, but it is a neuter noun in Latin.

So:

• singular: hoc verbum = this word
• plural: haec verba = these words

Because similia agrees with verba.

• verba = neuter plural
• similia = neuter plural of similis

So haec verba ... similia sint means these words are similar.

Here similia is a predicate adjective, describing the subject verba after a form of esse.

Inter se is an idiomatic expression meaning:

• among themselves
• with one another
• to each other
• in relation to one another

In this sentence, it means the words are similar to one another.

The se is reflexive, and it refers back to the plural noun verba. So the idea is not that the words are similar to something else, but that they resemble each other.

Because Latin and English express this idea differently.

English usually says:

• similar to each other
• similar to one another

Latin can express the same idea with:

• similis + dative
• or, as here, inter se to show reciprocity

So inter se similia is a compact Latin way to mean similar to one another.

The sentence has two main parts:

1. dum magister tacet
   = a temporal clause: while the teacher is silent

2. discipuli paulatim intellegunt cur haec verba inter se similia sint
   = the main clause plus an indirect question:

   • discipuli = subject
   • paulatim intellegunt = main verb
   • cur haec verba inter se similia sint = indirect question, functioning as the object of intellegunt

So the structure is:

• While X happens, Y understand why Z is the case.

Latin word order is fairly flexible, so the sentence could be arranged differently without changing the basic meaning.

For example, Latin often places the verb at the end of a clause, but it does not have to. In this sentence:

• tacet ends its clause
• intellegunt comes before the indirect question
• sint comes at the end of the indirect question

That is all very natural Latin style.

The current order is clear and elegant:

• first the time setting: dum magister tacet
• then the main action: discipuli paulatim intellegunt
• then what they understand: cur haec verba inter se similia sint

It can mean either, depending on context.

So dum magister tacet could be understood as:

• while the teacher is silent
• while the teacher says nothing

Both fit well. Often tacere has the sense of keeping quiet rather than merely making no sound.

Because the idea here is not just they understand something, but they understand why something is true.

That requires a full clause, and Latin uses an indirect question for that:

• intellegunt cur ... sint

If the sentence only had a simple object, Latin could use a noun or pronoun. But when the object is a question like why these words are similar, Latin normally uses an interrogative word plus a subjunctive clause.