Magistra dicit neminem contemnendum esse propter paupertatem.

Because after dicit Latin is using an indirect statement. In an indirect statement, the subject of the reported idea goes into the accusative, and the verb goes into the infinitive.

So the direct statement would be:

Nemo contemnendus est propter paupertatem.
= No one should be despised because of poverty.

After dicit, that becomes:

Magistra dicit neminem contemnendum esse propter paupertatem.
= The teacher says that no one should be despised because of poverty.

So:

• nemo = nominative, used in a direct statement
• neminem = accusative, used as the subject of the infinitive in indirect statement

Neminem means no one or nobody, and it is the accusative singular form of nemo.

In this sentence it is not the direct object of dicit. Instead, it is the subject of the infinitive clause:

neminem contemnendum esse
= that no one is to be despised / should be despised

This is a very common Latin construction, even though it feels strange in English.

Because Latin normally uses accusative + infinitive after verbs of saying, thinking, knowing, hearing, and similar verbs.

So after dicit (says), Latin does not usually say quod... the way English says that.... Instead it says:

• accusative subject
• infinitive verb

Here:

• neminem = accusative subject
• esse = infinitive

So dicit neminem ... esse literally means something like:

she says no one to be...

but in natural English:

she says that no one should be despised...

Contemnendum is a gerundive from contemnere (to despise).

Here it agrees with neminem:

• neminem = accusative singular
• contemnendum = accusative singular masculine

The gerundive often expresses the idea of necessity, duty, or what ought to be done.

So:

contemnendum esse
means roughly
to be despised, but more specifically
to deserve being despised / to be one who should be despised

With the negative neminem, the whole phrase means:

that no one should be despised

Yes. It is the infinitive form of the passive periphrastic.

The ordinary finite version would be:

contemnendus est
= must be despised / should be despised

In indirect statement, est becomes esse:

• direct: Nemo contemnendus est
• indirect: neminem contemnendum esse

So yes, this is a passive periphrastic inside an indirect statement.

Because it agrees with neminem, which is accusative singular.

The gerundive behaves like an adjective, so its ending changes to match the noun it goes with.

Here the matching is:

• neminem = accusative singular masculine
• contemnendum = accusative singular masculine

If the noun were feminine singular, the gerundive would be feminine too. If plural, it would be plural.

Latin wants to say not just that no one despises, but that no one should be despised.

That idea is naturally expressed with the gerundive + esse construction, which gives a sense of obligation or propriety.

Compare:

• neminem contemnere = for no one to despise or that no one despises
• neminem contemnendum esse = that no one should be despised

So the passive form is important because it expresses the correct meaning.

Paupertatem is accusative singular because it follows propter.

Propter is a preposition that takes the accusative and usually means:

• because of
• on account of

So:

propter paupertatem
= because of poverty

Here it means because of poverty or on account of poverty.

It tells us the reason for the contempt:

no one should be despised because of poverty

English sometimes uses for in similar contexts, but because of is the clearest meaning here.

The sentence breaks down like this:

• Magistra = the teacher
• dicit = says
• neminem contemnendum esse = that no one should be despised
• propter paupertatem = because of poverty

So the main clause is:

Magistra dicit
= The teacher says

And everything after that is the indirect statement:

neminem contemnendum esse propter paupertatem
= that no one should be despised because of poverty

Yes, very helpful. The direct version is:

Nemo contemnendus est propter paupertatem.

Then after dicit, Latin changes it like this:

• nemo → neminem
• contemnendus est → contemnendum esse

So:

Magistra dicit neminem contemnendum esse propter paupertatem.

Seeing the direct statement first is often the easiest way to understand the grammar.

That is a normal Latin word order. In infinitive phrases, especially with a gerundive or participle, Latin often puts the descriptive word before esse.

So:

contemnendum esse

is more natural in Latin than constantly placing esse first.

But the exact word order is flexible. Latin relies more on endings than on position.

Yes. Latin word order is flexible, so you could move it for emphasis.

For example, Latin could also say:

Magistra dicit propter paupertatem neminem contemnendum esse.

That would still mean the same thing. The original order is simply a natural, straightforward one.

It can mean either, depending on context.

Dicit is present tense, so it may be translated as:

• says
• is saying

In many textbook sentences, says is the most natural translation.

No agent is expressed here.

The sentence does not say who would be doing the despising. It gives a general principle:

no one should be despised because of poverty

If Latin wanted to name the agent in a passive periphrastic, it could use a dative of agent in some contexts, but here the statement is general and no agent is needed.

Because classical Latin usually does not need a separate word for that in this kind of sentence. Instead, it uses the accusative-and-infinitive construction.

English says:

The teacher says that no one should be despised...

Latin says:

Magistra dicit neminem contemnendum esse...

So the idea of that is built into the construction rather than expressed by a separate word.

Yes. A more literal translation would be:

The teacher says no one to be despised because of poverty.

That is not good English, but it helps show the Latin structure.

A better natural English translation is:

The teacher says that no one should be despised because of poverty.

Or even:

The teacher says that nobody ought to be despised because of poverty.