Quo diligentius discipuli lectionem audiunt, eo facilius vocabula novi auctoris memoria tenent.

It is a very common Latin way to express a correlative comparison: the more ... the more or the more ... the easier.

So:

• Quo diligentius discipuli lectionem audiunt = the more carefully the students listen to the reading
• eo facilius vocabula novi auctoris memoria tenent = the more easily they retain the vocabulary of the new author

Literally, quo and eo are ablative forms, and the pattern originally means something like by which amount ... by that amount. In normal English, though, you should usually translate the whole structure as the more X, the more Y.

They are comparative adverbs.

• diligenter = carefully

• diligentius = more carefully

• facile = easily
• facilius = more easily

In the quo ... eo ... construction, Latin normally uses comparatives, because the idea is comparative by nature:

• the more carefully
• the more easily

So these forms are exactly what you would expect here.

Because this is a special idiomatic structure in Latin. English says:

• the more carefully they listen, the more easily they remember

Latin often expresses that with:

• quo
  • comparative
• eo
  • comparative

So instead of building the sentence with separate words meaning more each time, Latin uses this paired construction. It is not just a random choice: quo ... eo ... is the standard pattern for this kind of idea.

Lectionem is accusative singular.

It is the direct object of audiunt:

• discipuli lectionem audiunt = the students listen to the reading / hear the reading

The verb audio normally takes a direct object in the accusative when it means hear or listen to something.

Because it depends on vocabula and shows possession or association:

• vocabula novi auctoris = the vocabulary of the new author

Both words are genitive singular:

• novi = of the new
• auctoris = of the author

So together they describe whose vocabulary is meant.

Grammatically, Latin does not have articles, so it can mean either:

• of the new author
• of a new author

The exact English wording depends on context.

If the passage has already introduced a particular author, you might translate the new author. If not, a new author could also be possible. Latin leaves that to context.

It is an idiomatic expression meaning keep in memory, retain, or remember.

Literally:

• memoria = in memory or by memory in this expression
• tenent = they hold

So:

• vocabula ... memoria tenent = they keep the words in memory = they retain the words = they remember the words

This is a good phrase to learn as a unit: memoria tenere = to remember / retain.

Because it is not the direct object. The direct object is vocabula.

• vocabula = the words / vocabulary items
• tenent = they hold
• memoria works adverbially in the phrase memoria tenere

So the idea is not they hold memory, but rather they hold the words in memory.

This is one of those expressions where Latin uses a noun in a fixed idiom rather than the exact structure English would use.

Yes. The subject of both verbs is discipuli.

The sentence is:

• discipuli ... audiunt
• [discipuli] ... tenent

Latin often omits a repeated subject when it is already clear. So in the second clause, discipuli is understood rather than repeated.

Because vocabulum means a word or a vocabulary item, and here the idea is plural:

• vocabula = words / vocabulary items

In many teaching contexts, English might simply say vocabulary, but Latin often uses the plural noun to refer to individual words.

It is accusative plural neuter.

That matters because neuter plural nominative and accusative look the same, so a learner might hesitate. Here it must be accusative because it is the direct object of tenent:

• vocabula ... tenent = they retain the words

It cannot be nominative, because the subject is already discipuli.

Latin word order is much freer than English word order. The relationships between words are shown mainly by endings, not just by position.

So Latin can arrange the sentence for emphasis and balance. Here the order helps highlight the comparison:

• Quo diligentius ... eo facilius ...

That makes the parallel very clear.

Also, Latin often puts important or closely connected words in positions that feel natural rhetorically, even if they are not next to each other in the way English would prefer.

In form, audiunt simply means they hear or they listen to, depending on context.

Here, because of diligentius (more carefully), the sense is clearly active attention, so English usually prefers:

• listen to the reading more carefully

rather than just

• hear the reading more carefully

So the context pushes the meaning toward listen to.

Yes. The present tense here expresses a general truth or regular pattern:

• The more carefully students listen, the more easily they retain the vocabulary

It is not necessarily about one specific occasion. Latin often uses the present this way, just as English does in statements of general fact.

Possibly, depending on context, but reading is often the safer choice here.

Lectio can refer to a reading, a lesson, or something read aloud. Since the students are audiunt-ing it, something like the reading or the passage being read fits especially well.

If the broader context is a classroom lesson, lesson might also work, but you should choose the English word that best fits the situation.

A useful way to see it is:

• Quo + comparative adverb + clause, eo + comparative adverb + clause

Applied here:

• Quo diligentius = the more carefully
• discipuli lectionem audiunt = the students listen to the reading
• eo facilius = the more easily
• vocabula novi auctoris memoria tenent = they retain the vocabulary of the new author

So the whole sentence is built around a balanced comparison: increased care in listening leads to increased ease in remembering.