Magistra existimat hanc sententiam illa difficiliorem esse, sed discipula dicit sensum paulatim clariorem fieri.

Because hanc sententiam is the accusative singular, and here it is the subject of an infinitive in an indirect statement.

After verbs like existimat (thinks) and dicit (says), Latin often uses the accusative + infinitive construction instead of a that-clause.

So:

• Magistra existimat = The teacher thinks
• hanc sententiam ... esse = this sentence to be ...

Even though this sentence is the logical subject of esse, Latin puts it in the accusative because it is inside indirect statement.

This is a classic indirect statement in Latin.

Its parts are:

• existimat = she thinks
• hanc sententiam = accusative subject of the infinitive
• difficiliorem = predicate adjective agreeing with hanc sententiam
• esse = infinitive
• illa = than that (one)

So literally it is something like:

• The teacher thinks this sentence to be more difficult than that one.

In smoother English, we usually say:

• The teacher thinks this sentence is more difficult than that one.

Here illa means than that one, with a noun understood.

The full idea is:

• illa sententia = that sentence

But after a comparative, Latin often leaves the noun out when it is obvious. So illa alone can mean:

• than that one
• more literally, than that sentence

Since sententia is feminine, the pronoun is feminine too.

Because this is an ablative of comparison.

With a comparative adjective like difficiliorem (more difficult), Latin has two common ways to express than:

1. comparative + quam
   • hanc sententiam quam illam difficiliorem esse
2. comparative + ablative
   • hanc sententiam illa difficiliorem esse

In your sentence, Latin uses the second pattern, the ablative of comparison.

So illa is ablative singular feminine, meaning:

• than that one

Because it agrees with hanc sententiam, which is accusative.

In the indirect statement:

• hanc sententiam = accusative subject
• difficiliorem = predicate adjective describing it

Since sententiam is:

• feminine
• singular
• accusative

difficiliorem must also be:

• feminine
• singular
• accusative

That is why it ends in -orem here.

It is the comparative form of difficilis (difficult).

The degrees are:

• difficilis = difficult
• difficilior / difficilius = more difficult
• difficillimus, -a, -um = most difficult

Here the form difficiliorem is the accusative singular masculine/feminine form of the comparative.

Because it modifies sententiam (feminine accusative singular), it means:

• more difficult

Because Latin indirect statement normally uses an infinitive.

In English we say:

• The teacher thinks that this sentence is more difficult.

But Latin usually says:

• The teacher thinks this sentence to be more difficult.

That is why you get:

• hanc sententiam ... difficiliorem esse

The infinitive esse is simply the verb to be inside the indirect statement.

Because fieri means to become or to come to be, not just to be.

So there is a contrast:

• difficiliorem esse = to be more difficult
• clariorem fieri = to become clearer

The first clause describes a state. The second clause describes a change.

So sensum paulatim clariorem fieri means:

• the meaning gradually becomes clearer

Fieri is the present infinitive of fio, fieri.

It can mean:

• to become
• to happen
• sometimes it functions as the passive equivalent of facere in certain contexts

Here it clearly means:

• to become

So:

• clariorem fieri = to become clearer

For the same reason that hanc sententiam is accusative: it is the subject of an infinitive in indirect statement.

After dicit:

• discipula dicit = the student says
• sensum ... clariorem fieri = the meaning to become clearer

So sensum is the logical subject of fieri, but grammatically it is in the accusative because Latin indirect statement requires that.

It agrees with sensum.

So:

• sensum = accusative singular masculine
• clariorem = accusative singular masculine comparative

Together they mean:

• the meaning [to become] clearer

Just as difficiliorem describes hanc sententiam, clariorem describes sensum.

Paulatim is an adverb meaning:

• gradually
• little by little

It modifies the idea of becoming clearer:

• sensum paulatim clariorem fieri
• the meaning gradually becoming clearer

Its placement is flexible, as adverbs often are in Latin.

Latin word order is much more flexible because the endings show the grammatical relationships.

English depends heavily on word order:

• The teacher thinks this sentence is more difficult than that one.

Latin can move words around more freely because case endings tell you what each word is doing.

For example:

• Magistra is nominative, so it is the subject.
• hanc sententiam is accusative, so it belongs inside the indirect statement.
• difficiliorem agrees with sententiam.
• illa is ablative of comparison.

The current order is natural Latin, and it also puts a bit of emphasis on the compared ideas.

Because they are the subjects of the main verbs:

• Magistra existimat = The teacher thinks
• discipula dicit = the student says

So both are nominative singular feminine.

They are not inside the indirect statements; they are the people doing the thinking and saying.

Yes.

Latin often has two ways to express comparison:

1. comparative + quam
   • hanc sententiam quam illam difficiliorem esse
2. comparative + ablative
   • hanc sententiam illa difficiliorem esse

Both mean essentially the same thing here:

• this sentence [to be] more difficult than that one

The sentence you were given uses the ablative pattern, which is very common.

It can, depending on context.

Sententia has a range of meanings, including:

• opinion
• judgment
• view
• meaning
• sometimes sentence in the grammatical sense

In this sentence, since the meaning has already been given to the learner, it is clearly being understood as sentence. But it is useful to know that the word is broader than the English word sentence.

Yes: they balance nicely, but they use slightly different structures inside the indirect statements.

First clause:

• hanc sententiam illa difficiliorem esse
• a comparison with esse

Second clause:

• sensum paulatim clariorem fieri
• a change over time with fieri

So the contrast is not only in meaning but also in grammar:

• to be more difficult
• to become clearer

That is a very Latin way of expressing two related but different ideas.