Cum librum e scrinio evolvit, discipula prooemium primum legit et deinde ad argumentum redit.

Because cum can be either:

• a preposition meaning with, followed by the ablative
• a conjunction meaning when, since, or although, introducing a clause

Here it is followed by a whole clause, librum e scrinio evolvit, so it must be the conjunction. That is why it means when here.

Not every cum clause uses the subjunctive.

A cum clause often takes the indicative when it simply gives the time of an action, especially in a straightforward temporal sense: when X happens.

So here cum ... evolvit is just a normal time clause: when she opens/unrolls the book from the bookcase.

If Latin wanted a more circumstantial, causal, or concessive sense, the subjunctive would be more likely.

Librum is accusative singular.

It is the direct object of evolvit, because it is the thing being opened/unrolled. The dictionary form is liber, and its accusative singular is librum.

So:

• liber = book, nominative
• librum = book, as object of the verb

Because e or ex means out of or from, and it takes the ablative case.

So:

• scrinium = writing case, book box, chest, cabinet
• scrinio = ablative singular

That is why Latin says e scrinio: out of the bookcase/chest/case.

It comes from evolvo, which literally means roll out or unroll.

With books or scrolls, it can mean things like:

• unroll
• open
• turn over
• look through

So with librum, the basic image is physical: she takes the book out and opens or unrolls it.

Because evolvit can be either:

• present: he/she opens, unrolls
• perfect: he/she opened, unrolled

Those two forms look exactly the same in many third-conjugation verbs.

So you have to use context. In this sentence, since legit and redit are also present-looking forms, a learner will usually understand evolvit as present as well, unless the larger context shows a past narrative.

Because discipula is nominative singular, and it is the only explicit nominative noun in the sentence.

Latin word order is flexible, so the subject does not have to come first. A sentence can begin with a subordinate clause, and the main subject can appear afterward.

Here discipula is naturally understood as the subject of the main clause, and also as the understood subject of evolvit, unless the context indicates otherwise.

Because Latin adjective order is much freer than English adjective order.

Both of these can work:

• primum prooemium
• prooemium primum

The important thing is agreement:

• prooemium is neuter accusative singular
• primum is also neuter accusative singular

So primum clearly goes with prooemium, regardless of position.

Here it is best taken as an adjective modifying prooemium: the first proem/preface.

Why?

Because it sits right next to prooemium and agrees with it in form. The neuter accusative singular form primum can also be an adverb meaning first, which is why the form may look tricky at first. But in this sentence the noun-adjective reading is the natural one.

Prooemium is a Greek loanword in Latin. It means something like:

• preface
• introduction
• proem
• opening section

It is a second-declension neuter noun, so forms like prooemium can be either nominative or accusative singular. Here it is accusative singular, because it is the object of legit.

Because ad takes the accusative and shows movement or direction toward something.

With redit = returns, Latin often uses ad + accusative, whether the return is literal or metaphorical.

So:

• ad argumentum = back to the subject/theme/argument

This is a metaphorical use of movement: she returns not to a place, but to the main topic.

Deinde by itself already means then or next.
Et simply links this action to the previous one.

So et deinde means something like:

• and then
• and next

It is not wrong or strange. Latin often uses both a connector and a sequencing word together.

Latin often puts background information first and the main action after it.

So the structure is:

1. Cum librum e scrinio evolvit = the time/background
2. discipula prooemium primum legit
3. et deinde ad argumentum redit

This is a very normal Latin pattern. English can do the same thing, but Latin uses flexible word order much more freely, so learners often need to focus on case endings and verb forms more than on position.