Magister dicit requiem quoque utilem esse, nam nemo sine requie diu studere potest.

Because after dicit Latin uses an indirect statement construction, often called the accusative-and-infinitive construction.

So instead of saying something like The teacher says that rest is useful, Latin says, more literally:

• Magister dicit
• requiem utilem esse

That second part works like rest to be useful, where:

• requiem = the subject of the indirect statement, but in the accusative
• esse = to be

This is very common after verbs of saying, thinking, knowing, hearing, and so on.

It is an indirect statement.

The pattern is:

• a main verb of saying/thinking/etc.
• an accusative noun or pronoun
• an infinitive

Here:

• dicit = says
• requiem = the accusative subject of the indirect statement
• utilem esse = to be useful

So Latin does not need a separate word for that here. English says:

• The teacher says that rest is also useful

Latin says:

• The teacher says rest also to be useful

That sounds strange in English, but it is normal Latin grammar.

Because utilem agrees with requiem.

Requies, requiei is a feminine noun. Here requiem is:

• feminine
• singular
• accusative

So the adjective describing it must also be:

• feminine
• singular
• accusative

That gives utilem.

This is an important point: in an accusative-and-infinitive construction, the predicate adjective agrees with the accusative subject.

So:

• requiem utilem esse = rest to be useful

Because utilem needs a verb: to be.

So:

• utilem esse = to be useful

In English we often translate smoothly as is useful, but in Latin, because this is an indirect statement after dicit, the verb becomes an infinitive:

• direct statement: requies utilis est = rest is useful
• indirect statement: dicit requiem utilem esse = he says that rest is useful

Quoque means also or too.

A useful rule is that quoque usually comes after the word it emphasizes.

So:

• requiem quoque utilem esse

means something like:

• that rest also is useful
• or more naturally, that rest too is useful

It emphasizes requiem.

This is different from etiam, which often comes before the word it emphasizes.

Nam means for, because, or you see. It introduces an explanation or reason.

So here:

• Magister dicit requiem quoque utilem esse
• nam nemo sine requie diu studere potest

means:

• The teacher says that rest is also useful, for no one can study for a long time without rest.

So the second clause explains why the first statement is true.

Nemo means no one or nobody. Here it is nominative singular and is the subject of potest.

So:

• nemo ... potest = no one can ...

It is worth noting that nemo is slightly irregular as a pronoun-like word, so learners often just memorize it as a common vocabulary item rather than expecting it to behave exactly like an ordinary noun.

Because sine takes the ablative case.

So:

• sine
  • ablative = without ...

Here the ablative singular of requies is requie.

Therefore:

• sine requie = without rest

This is a very common preposition-case combination to memorize.

Diu is an adverb meaning for a long time or long.

It modifies the idea of studying:

• diu studere = to study for a long time

So:

• nemo sine requie diu studere potest = no one can study for a long time without rest

Because potest is followed by an infinitive.

• potest = is able / can
• studere = to study

Together:

• studere potest = can study

This is called a complementary infinitive. The infinitive completes the meaning of potest.

Compare:

• discipulus studet = the student studies
• discipulus studere potest = the student can study

Potest is:

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

from possum, posse, potui = to be able

Because the subject is nemo (no one), which is singular, the verb is singular too:

• nemo potest = no one can

Latin word order is more flexible than English word order, because the endings show how the words function.

Still, the order here is natural and meaningful:

• Magister comes first as the topic
• dicit introduces the statement
• requiem quoque utilem esse gives the content of what he says
• nam introduces the reason
• nemo sine requie diu studere potest explains the claim

So although Latin could rearrange many of these words, this order is clear and idiomatic.

Because in this kind of sentence Latin usually does not use a separate word meaning that. Instead, it uses the accusative-and-infinitive construction.

English:

• The teacher says that rest is useful.

Latin:

• Magister dicit requiem utilem esse.

So the idea expressed by English that is built into the grammar of the accusative plus infinitive.