Disciplina postulat ut discipuli in bibliotheca taceant.

Because postulat here introduces a clause of command or requirement. In Latin, verbs like ask, demand, urge, order, and require are often followed by ut + the subjunctive.

So:

• postulat = demands / requires
• ut discipuli ... taceant = that the students be quiet

A very literal structure would be:

• Disciplina postulat ut discipuli in bibliotheca taceant
• Discipline requires that the students be silent in the library

This is a very common Latin pattern.

Because it is inside an ut clause after a verb of demanding or requiring.

Latin normally uses:

• ut
  • subjunctive

after verbs like postulo, rogo, moneo, impero, and similar verbs when they introduce what someone wants, orders, or requires.

So taceant is not simply stating a fact like they are quiet. It expresses what is being required of them:

• tacent = they are quiet / they keep quiet
• taceant = that they be quiet / that they should keep quiet

Taceant is:

• present
• subjunctive
• active
• third person plural

It comes from taceo, tacere, meaning to be silent or to keep quiet.

Third person plural is used because the subject of the subordinate clause is discipuli, which is plural:

• discipuli ... taceant = the students be quiet

The present subjunctive fits well after the present main verb postulat, since Latin usually follows the sequence of tenses here.

Because discipuli is the subject of taceant.

In the clause:

• ut discipuli in bibliotheca taceant

the students are the ones doing the action of keeping quiet, so discipuli is nominative plural.

It is not the direct object of postulat. Instead, postulat takes a whole clause as its object:

• ut discipuli in bibliotheca taceant

So the structure is roughly:

• Disciplina = subject of the main verb
• postulat = main verb
• ut discipuli in bibliotheca taceant = subordinate clause functioning as the thing required

Because in with the ablative usually means in or inside, indicating location.

So:

• in bibliotheca = in the library

If in were followed by the accusative, it would usually show motion into a place:

• in bibliothecam = into the library

Here there is no movement. The students are being told to be quiet while located in the library, so the ablative is correct.

Disciplina can mean several related things depending on context, such as:

• discipline
• training
• instruction
• orderliness

In this sentence, it most naturally means something like discipline or school discipline/order as an abstract idea: discipline requires students to be quiet in the library.

Grammatically, disciplina is:

• nominative singular
• first declension

and it is the subject of postulat.

Yes, in some contexts discipulus can mean disciple, student, pupil, or learner. The core idea is someone who is learning from a teacher.

In this sentence, students or pupils is the most natural translation because of the school setting created by bibliotheca and disciplina.

So although English disciple is related, that would sound too religious or specialized in most classroom contexts.

Because Latin usually does not use a simple infinitive after verbs like require or demand in this kind of construction.

In English, you might say:

• Discipline requires students to be quiet
• Discipline requires that students be quiet

Latin strongly prefers the second type of idea here:

• postulat ut ... taceant

That is, a full subordinate clause with ut and the subjunctive, rather than an infinitive construction.

The word order is flexible, but the given order is perfectly natural.

Latin uses endings, not just position, to show grammatical roles, so the words could be rearranged without changing the basic meaning. For example, these would still mean essentially the same thing:

• Disciplina postulat ut discipuli in bibliotheca taceant
• Ut discipuli in bibliotheca taceant, disciplina postulat
• Disciplina ut discipuli taceant in bibliotheca postulat

That said, word order can affect emphasis. The original sentence is straightforward and easy to follow:

1. main subject: Disciplina
2. main verb: postulat
3. required action: ut discipuli in bibliotheca taceant

If you want to negate the subordinate command clause, Latin normally uses ne instead of ut.

So:

• Disciplina postulat ut discipuli in bibliotheca taceant = discipline requires that the students be quiet in the library

but:

• Disciplina postulat ne discipuli in bibliotheca clament = discipline requires that the students not shout in the library

With verbs of commanding, asking, warning, and similar ideas:

• ut = positive command/resulting requirement
• ne = negative command

Because its subject, disciplina, is singular.

So:

• disciplina = singular noun
• postulat = third person singular present active indicative

If the subject were plural, the verb would also be plural. For example:

• disciplinae postulant ... = disciplines / rules require ...

In the actual sentence, one singular subject is doing the requiring, so postulat must be singular.