Magistra discipulas in bibliotheca tacere sinit, sed susurrare non sinit.

Because discipulas is the direct object of sinit.

The main verb is sinit = allows / permits. The person being allowed to do something goes into the accusative in Latin. So:

• magistra = the teacher
• discipulas = the female students
• sinit = allows

Latin often uses this pattern:

someone + accusative person + infinitive

So magistra discipulas tacere sinit means the teacher allows the students to be silent.

Because after sinit Latin normally uses an infinitive to express what someone is allowed to do.

So:

• tacere = to be silent / to keep quiet
• susurrare = to whisper

This is very similar to English:

• The teacher allows the students to be silent
• The teacher does not allow them to whisper

In Latin, sinere commonly takes:

• an accusative noun/pronoun for the person
• an infinitive for the action

The understood subject of both infinitives is discipulas.

That is an important Latin pattern: in an accusative-and-infinitive construction, the accusative noun can function as the logical subject of the infinitive.

So here:

• discipulas tacere = the students to be silent
• discipulas susurrare = the students to whisper

Even though discipulas is accusative, it is still the one doing the actions tacere and susurrare.

Because Latin often leaves it understood when it is obvious from context.

In English we might say:

• The teacher allows the students to be silent, but does not allow them to whisper.

In Latin, once discipulas has already been mentioned, it does not have to be repeated. It is understood with the second sinit as well:

• sed susurrare non sinit = but she does not allow [them] to whisper

If Latin wanted to repeat it for extra clarity, it could, but it is not necessary.

Because it expresses location: in the library.

With in, Latin uses:

• accusative for motion into something
• ablative for location in something

So:

• in bibliothecam = into the library
• in bibliotheca = in the library

Here no movement is involved. It tells us where the allowing happens, or where the students are expected to be silent. So the ablative is used.

It can mean either, depending on context.

Tacere is often best understood as:

• to be silent
• to keep quiet
• to say nothing

In this sentence, to be silent or to keep quiet both fit well.

Because Latin, like English, often repeats the main verb for clarity and balance.

The sentence has a neat contrast:

• tacere sinit
• susurrare non sinit

That repetition makes the contrast very clear:

• one thing is permitted
• the other is not

It is stylistically natural and easy to understand.

Yes, it is normal Latin word order.

The sentence is:

Magistra discipulas in bibliotheca tacere sinit, sed susurrare non sinit.

A very literal unpacking is:

• Magistra = the teacher
• discipulas = the students
• in bibliotheca = in the library
• tacere = to be silent
• sinit = allows
• sed = but
• susurrare = to whisper
• non sinit = does not allow

Latin word order is more flexible than English because the endings show the grammatical roles. The verb often comes near the end, and infinitives commonly stand before it.

Because the sentence is referring to a female teacher and female students.

• magistra = female teacher
• discipulas = female students

If they were masculine, you would expect:

• magister = male teacher
• discipulos = male students

Latin often marks gender clearly in nouns.

Sed means but.

It introduces a contrast between two ideas:

• the teacher allows silence
• the teacher does not allow whispering

So sed is connecting two related but opposite statements.

Yes. Latin word order is flexible, so in bibliotheca could appear in other positions without changing the basic meaning.

For example, Latin could also say:

• Magistra discipulas tacere in bibliotheca sinit
• In bibliotheca magistra discipulas tacere sinit

The exact placement can affect emphasis a little, but the case endings keep the grammar clear.

It comes from sinere, meaning to allow, permit.

Sinit is:

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

So sinit means he/she/it allows. Here, since the subject is magistra, it means she allows.

Yes: this is a very common Latin pattern, often called the accusative + infinitive pattern after verbs like sinere.

Structure:

• magistra = subject of the main verb
• discipulas = accusative person affected
• tacere / susurrare = infinitives describing the action

So a good model to remember is:

X Y-accusative infinitive verb

Here:

Magistra discipulas tacere sinit
= The teacher allows the students to be silent

This is a very useful pattern in Latin and appears with several verbs, not just sinere.