Dux magnam virtutem praestat.

Because dux is in the nominative singular, which is the case typically used for the subject of a finite verb.

A learner might expect a subject to look like a first- or second-declension nominative, but dux is a third-declension noun. Its dictionary form is dux, ducis.

So here:

• dux = the leader as subject
• praestat = shows / displays / exhibits
• therefore dux is the one doing the action

Magnam virtutem is accusative singular feminine.

It is in the accusative because it is the direct object of praestat—it receives the action of the verb.

Breaking it down:

• virtutem = accusative singular of virtus
• magnam = accusative singular feminine of magnus, magna, magnum

So the phrase means great virtue or great courage as the thing the leader displays.

Because adjectives in Latin must agree with the nouns they modify in:

• gender
• number
• case

Here, virtutem is:

• feminine
• singular
• accusative

So the adjective has to match it:

• magnam virtutem

If you used magna, that would be nominative or ablative singular feminine, so it would not match the object form virtutem.

Praestat is:

• third person singular
• present tense
• active voice
• indicative mood

It comes from praesto, praestare.

The ending -t tells you it is he/she/it in the present tense:

• praesto = I show / provide / excel
• praestas = you show
• praestat = he/she/it shows

Since the subject is dux, the verb is singular: the leader shows.

Because Latin has no articles.

So dux can mean:

• the leader
• a leader

and magnam virtutem can mean:

• great virtue
• a great virtue

Which one is best in English depends on context. Latin usually leaves that unstated.

Latin word order is more flexible than English word order because the endings show the grammatical roles.

In this sentence:

• dux = subject
• magnam virtutem = object
• praestat = verb

So even if you changed the order, the core meaning would stay the same, for example:

• Magnam virtutem dux praestat
• Praestat dux magnam virtutem

However, word order can change emphasis. The given order is perfectly normal, with the verb placed at the end, which is very common in Latin.

Virtus is one of those Latin words with a wider range of meaning than any single English word.

Depending on context, it can mean:

• virtue
• courage
• valor
• excellence
• manly quality in an older Roman sense

In a sentence like this, magnam virtutem praestat, it often suggests something like great courage or great excellence, not just moral goodness in the modern English sense of virtue.

Not always. Praestare has several related meanings, such as:

• to provide
• to show
• to display
• to offer
• to surpass / excel

In this sentence, with virtutem as its object, it most naturally means something like displays or shows.

So the grammar is straightforward: praestare takes a direct object here, and that object is magnam virtutem.

The ending -em is the accusative singular ending for many third-declension nouns, including virtus.

Its forms include:

• nominative singular: virtus
• accusative singular: virtutem

If it were plural accusative, it would be virtutes.

So magnam virtutem means one great virtue / courage, not great virtues.

Because grammatical gender and noun declension are not the same thing.

A masculine noun in Latin does not have to end in -us. That is only common in the second declension.

Dux is:

• masculine in meaning here
• but third declension in form

Its nominative singular is simply dux, and that is completely normal for third-declension nouns.

Yes. Latin often omits subject pronouns, and sometimes even an explicit subject noun if context makes it clear.

Since praestat already means he/she/it shows, the sentence magnam virtutem praestat could mean:

• he shows great courage
• she displays great virtue
• it exhibits great excellence

Adding dux makes the subject explicit: the leader is the one doing it.

In a reconstructed classical pronunciation, approximately:

duks mag-nam wir-too-tem prae-stat

A few helpful points:

• x = ks
• v is pronounced like w in classical Latin, so virtutem sounds roughly like wirtutem
• ae in praestat is like the ai in aisle or a similar diphthong

So a rough guide is:

duks MAG-nam WIR-too-tem PRAI-stat

That said, pronunciation systems vary depending on whether you are learning classical, ecclesiastical, or another style of Latin.