Magistra postea quaerit cur unus liber a bibliopola carius vendi videretur quam alter.

The sentence has a main clause and an indirect question.

• Main clause: Magistra postea quaerit
  = The teacher then asks
• Indirect question: cur unus liber a bibliopola carius vendi videretur quam alter
  = why one book seemed to be sold more expensively than the other

So after quaerit, everything introduced by cur depends on that verb.

Because cur here introduces an indirect question.

In Latin, indirect questions normally use the subjunctive, not the indicative. So after quaerit and cur, you expect a subjunctive verb such as videretur.

This is a very common pattern:

• rogat quid faciat = he asks what she is doing
• quaerit cur veniat = he asks why she is coming

So in your sentence, videretur is subjunctive because it belongs to an indirect question.

The basic reason is still indirect question, but the imperfect needs a little more explanation.

Videretur is often understood here as following secondary sequence, probably because quaerit is being used as a historical present in a narrative context. In other words, Latin sometimes uses a present form like quaerit while still telling a past story, and then the subordinate clause behaves as if it were after a past tense.

So:

• quaerit = historical present, used in narration
• videretur = imperfect subjunctive in the dependent clause

If the sentence were purely present-time with no historical coloring, a learner might expect videatur instead.

Not here.

Although videor, videri is formally the passive of video, it very often means seem.

So:

• videtur = he/she/it seems
• videretur = he/she/it seemed

That is why vendi videretur means seemed to be sold, not was seen to be sold in a literal visual sense.

Because Latin often uses videor + infinitive to express seem to ...

So:

• vendi = to be sold
• videretur = seemed
• vendi videretur = seemed to be sold

This is very normal Latin syntax. The infinitive tells you what seemed to be happening.

Vendi is the present passive infinitive of vendo, vendere, vendidi, venditum.

So:

• vendo = I sell
• vendi = to be sold

Because it is passive, the book is not doing the selling; the book is the thing being sold.

It is the subject.

That can feel strange to an English speaker, because with active sell we think of the book as the object:

• The bookseller sells the book

But here Latin uses the passive infinitive vendi:

• the book is sold

So unus liber is nominative singular and functions as the subject of videretur, and also as the logical subject of vendi.

Because carius is an adverb, and it modifies the verbal idea vendi.

It means more dearly, or more naturally in English, at a higher price.

Compare:

• carior = dearer / more expensive as an adjective
• carius = more dearly / more expensively as an adverb

Here the sentence is talking about how the book seemed to be sold, so the adverb is the right form.

The sentence compares one book with the other book in respect to the price at which it seemed to be sold.

So the idea is:

• one book seemed to be sold more expensively than the other

After quam, Latin often leaves out words that are easy to understand from the context. So alter stands for alter liber.

You can mentally expand it as something like:

• quam alter liber
• or even more fully, quam alter liber vendi videretur

Latin does not need to repeat everything.

Because unus ... alter is a common pair meaning one ... the other.

So:

• unus liber = one book
• alter = the other one, the other book

This pair is especially natural when there are two things being contrasted.

It marks the personal agent with a passive verb.

Since the book is being sold, Latin uses a/ab + ablative to show by whom it is sold:

• a bibliopola = by the bookseller

That is the normal construction for the agent of a passive verb.

Bibliopola is in the ablative singular because it follows a in an agent phrase:

• a bibliopola = by the bookseller

Even though the form looks like a nominative -a noun, first-declension ablative singular also ends in -a, so the phrase is ablative because of the preposition a.

Because not all first-declension nouns are feminine.

Bibliopola is a first-declension masculine noun, a type that often appears with occupations or words of Greek origin.

So even though it looks like a typical first-declension feminine noun, it can still refer to a man and take masculine agreement when needed.

Because this is an indirect question, not an indirect statement.

Latin uses:

• accusative + infinitive for indirect statement
• subjunctive clause for indirect question

Since the sentence asks why, introduced by cur, Latin uses an indirect question with videretur in the subjunctive, not an accusative-and-infinitive construction.