Plurimi cives prorsus credunt principem bonum commune quaerere.

Because Latin uses the accusative + infinitive construction after verbs like credunt (they believe).

So in this sentence:

• principem = the subject of the infinitive quaerere
• quaerere = to seek

In English, we say they believe that the leader seeks the common good.
In Latin, instead of a that-clause, you often get:

• credunt
• principem ... quaerere

So principem is accusative not because it is the direct object of credunt, but because it is the subject of the infinitive inside indirect statement.

For the same reason: after credunt, Latin commonly introduces reported thought or belief with an infinitive.

This is called indirect statement.

Compare:

• Direct statement: princeps bonum commune quaerit = the leader seeks the common good
• Indirect statement after credunt: credunt principem bonum commune quaerere = they believe that the leader seeks the common good

So quaerere is the infinitive form used in that construction.

Plurimi is the superlative form of multus.

Depending on context, it can mean:

• very many
• most

Here it agrees with cives, so plurimi cives means something like:

• very many citizens
• or most citizens

Grammatically:

• plurimi = nominative masculine plural
• cives = nominative plural

They go together as the subject of credunt.

Bonum commune is the object of quaerere.

So:

• bonum = good, neuter singular accusative
• commune = common, neuter singular accusative

Together they form the phrase bonum commune, meaning the common good.

Because quaerere takes a direct object, the phrase is in the accusative.

Prorsus is an adverb. It means something like:

• completely
• absolutely
• entirely

Here it modifies credunt, so the sense is:

• they absolutely believe
• they completely believe

Latin adverbs often have flexible placement, so prorsus can sit near the verb without changing the basic grammar.

Because classical Latin usually does not use a finite that-clause after verbs of saying, thinking, knowing, or believing. Instead, it prefers the accusative + infinitive construction.

So English says:

• They believe that the leader seeks the common good

But Latin says, more literally:

• They believe the leader to seek the common good

That is normal and idiomatic Latin.

The sentence has two layers:

1. Main clause

   • Plurimi cives prorsus credunt
   • Very many citizens / most citizens absolutely believe

2. Indirect statement

   • principem bonum commune quaerere
   • that the leader seeks the common good

So the full structure is:

• subject: plurimi cives
• adverb: prorsus
• main verb: credunt
• indirect statement: principem bonum commune quaerere

Not exactly.

Latin princeps originally means something like:

• leader
• chief man
• first man
• ruler

In some contexts it can refer to:

• a political leader
• the emperor
• a foremost citizen

So principem here does not automatically mean a fairy-tale prince. It is a broader political or social title.

Because quaerere can have more than one meaning depending on context.

Common meanings include:

• to seek
• to look for
• to inquire about
• sometimes to ask

Here the object is bonum commune (the common good), so the natural meaning is to seek or to pursue, not to ask.

So the phrase means that the leader is trying to pursue or aim at the common good.

The word order is fairly natural Latin, but Latin is much freer than English because endings show grammatical relationships.

A helpful way to read it is:

• Plurimi cives = subject
• prorsus credunt = main verb phrase
• principem bonum commune quaerere = what they believe

Latin could rearrange many of these words for emphasis, but the cases would still show the grammar.

For example, the important clue is not position alone, but forms like:

• principem = accusative
• cives = nominative plural
• bonum commune = accusative object of quaerere

So word order matters less than endings.