Amicitia inter duas discipulas paulatim nascitur, dum cotidie simul in bibliotheca sedent.

Because amicitia is the subject of nascitur.

In this sentence, the thing that is arising / is developing is the friendship, so Latin puts amicitia in the nominative singular.

• amicitia = nominative singular
• subject of nascitur

Even though English often says friendship develops, Latin here says friendship is born / arises, using amicitia as the subject.

Because nascitur comes from a deponent verb: nascor, nasci, natus sum.

Deponent verbs use passive-looking forms but have active meanings. So:

• nascitur looks like he/she/it is being born
• but in normal usage it means he/she/it is born, arises, or comes into being

Here, amicitia ... nascitur means that friendship arises or develops.

Nascitur is:

• 3rd person singular
• present tense
• indicative mood
• from the deponent verb nascor

It is singular because the subject is amicitia, which is singular.

Because inter takes the accusative case.

So after inter, Latin uses accusative forms:

• duas = accusative feminine plural of duae
• discipulas = accusative feminine plural of discipula

So inter duas discipulas means between two female students.

Because duas is an adjective/number word agreeing with discipulas.

In Latin, modifiers agree with the noun they describe in:

• gender
• number
• case

Here:

• discipulas is feminine plural accusative
• so duas must also be feminine plural accusative

If the students were male, you would have inter duos discipulos.

Because discipulas specifically means female students.

• discipula = female student
• discipulus = male student

So the Latin sentence tells you that the friendship is developing between two girls / two female students, not just two students of unspecified sex.

Because its subject is understood to be the two students.

Latin often leaves subject pronouns unstated when the verb ending already makes the number clear. Sedent is:

• 3rd person plural
• present indicative
• from sedeo, sedere

So sedent means they are sitting.

The implied they refers to duae discipulae, understood from inter duas discipulas.

Dum here means while.

It introduces a clause describing what is happening at the same time:

• Amicitia ... nascitur
• dum ... sedent

So the sense is that the friendship develops while they are sitting together every day in the library.

Because Latin commonly uses dum with the present indicative to describe an action going on at the same time as another action.

So:

• nascitur = is developing / arises
• dum ... sedent = while they are sitting

This is a very normal construction for simultaneous action.

Because this sentence expresses location, not motion toward a place.

With in:

• in + ablative = in / on a place, indicating location
• in + accusative = into / onto, indicating motion toward

So:

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

Since they are already sitting there, Latin uses the ablative: bibliotheca.

Cotidie is an adverb meaning daily or every day.

It modifies sedent, telling you how often they sit together in the library.

Because it is an adverb, it does not change form.

Simul is also an adverb. It means together or at the same time.

Here it modifies sedent:

• simul sedent = they sit together

It helps show why the friendship is developing: they are regularly spending time together.

Paulatim is an adverb meaning gradually, little by little, or slowly.

It modifies nascitur and shows that the friendship is not appearing all at once, but is developing step by step.

It is perfectly normal for Latin.

Latin word order is much freer than English word order because the endings show the grammatical relationships. This lets Latin place words for emphasis or style.

Here the order does a nice job of presenting the main idea first:

• Amicitia — the important topic
• inter duas discipulas — where the friendship exists
• paulatim nascitur — what is happening
• dum ... sedent — the accompanying circumstance

An English speaker may expect a stricter order, but this Latin arrangement is natural.

Yes. Latin often uses nascor for things that come into being or arise, not just literal birth.

So amicitia nascitur is an idiomatic and elegant way to say that friendship:

• begins
• springs up
• develops

It is a very Latin way of expressing the idea.

Because duas discipulas is accusative, not nominative.

The subject of a finite verb like sedent is normally in the nominative. But here we have:

• duas discipulas = accusative, governed by inter
• therefore it cannot be the grammatical subject as written

Instead, the subject of sedent is understood: they, referring to those two students. If Latin wanted to state that subject explicitly, it would use nominative forms such as duae discipulae.