Mater puerum monet ne temere per viam currat.

Because they are doing different jobs in the sentence.

• mater is the subject: the mother is the one doing the warning.
• puerum is the direct object of monet: the boy is the one being warned.

So:

• mater = nominative singular
• puerum = accusative singular

This is a very common Latin pattern: the subject is in the nominative, and the direct object is in the accusative.

The verb moneō, monēre means warn, advise, or remind. In Latin, the person who is warned is normally put in the accusative.

So in:

• Mater puerum monet

the structure is literally:

• The mother warns the boy

That is why puerum is accusative.

Here ne introduces a clause meaning that ... not or not to ....

After verbs like monet, Latin often uses:

• ut
  • subjunctive = to tell/advice/warn someone to do something
• ne
  • subjunctive = to tell/advice/warn someone not to do something

So:

• monet ne currat = warns him not to run

This is a very common construction in Latin.

Because after ne in this kind of clause, Latin uses the subjunctive, not the ordinary indicative.

So:

• currit = he runs / is running
  
  • this is indicative
• currat = that he run / that he should run
  
  • this is subjunctive

In this sentence, the mother is not simply stating that the boy runs. She is warning him not to run, so Latin uses:

• ne ... currat

Because the main verb is monet, which is present tense. In standard sequence of tenses, a present main verb is usually followed by the present subjunctive in a dependent clause of this type.

So:

• monet ... currat = present main verb + present subjunctive

If the main verb were past, you would often expect the imperfect subjunctive instead:

• Mater puerum monuit ne temere per viam curreret.
• The mother warned the boy not to run rashly along the road.

Temere is an adverb. It means something like:

• rashly
• carelessly
• recklessly
• without thinking

It modifies currat, telling us how he is not supposed to run.

So the idea is not just not to run, but not to run recklessly.

Per is a preposition that takes the accusative case. So:

• per viam = along the road, through the street, or across the road depending on context

That is why via appears as viam.

A learner should remember:

• per
  • accusative

This is one of the standard case patterns with Latin prepositions.

It can vary a little depending on context. Literally, per often means through or along. In natural English, this phrase might be translated as:

• along the road
• in the street
• across the road

The exact English wording depends on the larger situation. The important Latin point is that per viam expresses movement involving the road/street as the path or area of motion.

It is commonly understood as an indirect command or substantive clause of prevention/admonition, depending on the grammar book.

In simpler learner-friendly terms:

• monet = the mother warns the boy
• ne ... currat = what she warns him not to do

So the whole clause functions as the content of the warning.

You can think of it as:

• She warns him: do not run rashly along the road.

But Latin expresses that idea by embedding it in a ne + subjunctive clause.

Latin word order is much more flexible than English word order because the endings show each word’s role.

This sentence is:

• Mater puerum monet ne temere per viam currat.

A more word-for-word English order might be:

• Mother the boy warns not rashly along the road he-may-run.

That sounds strange in English, but it is perfectly normal in Latin.

The order here is quite natural:

• mater first: the subject
• puerum next: the person being warned
• monet: the main verb
• then the ne clause

Latin often places the main verb before a dependent clause like this.

Not in the normal classical construction after moneō when the meaning is warn someone not to do something.

English says:

• The mother warns the boy not to run

and uses an infinitive: not to run.

Latin usually does not copy that structure here. Instead it prefers:

• monet puerum ne currat

So this is a good example of a place where Latin syntax differs from English syntax.

Yes. Moneō can mean:

• warn
• advise
• remind
• instruct

The exact shade depends on context.

In this sentence, because of ne ... currat, warns or advises fits well. The mother is telling the boy to avoid a dangerous or foolish action.

So the core idea is: she is cautioning him.

Yes, in an indirect way.

It is not a direct command like:

• Noli currere! = Do not run!

Instead, it reports or describes a warning:

• Mater puerum monet ne ... currat.
• The mother warns the boy not to run ...

So it contains a negative instruction, but expressed as part of a larger sentence rather than as a direct order to the boy.