Hasta publica ante atrium auctionarium est.

Because hasta is a feminine singular noun, and the adjective has to agree with it.

• hasta = feminine
• publica = feminine singular form of publicus, publica, publicum

So hasta publica means public spear, with both words matching in gender, number, and case.

Hasta publica is in the nominative singular, and it is the subject of est.

A simple way to see this:

• est = is
• the thing that is somewhere is the subject
• here, that thing is hasta publica

So the sentence structure is basically:

• Hasta publica = the subject
• ante atrium auctionarium = where it is
• est = is

Because it comes after ante, and ante as a preposition takes the accusative.

So:

• ante = before / in front of
• atrium here is accusative singular
• therefore it means in front of the auction hall

This is a very common pattern in Latin: a preposition controls the case of the noun that follows it.

Because auctionarium is an adjective modifying atrium, so it must agree with it.

Here:

• atrium is neuter singular accusative
• auctionarium is also neuter singular accusative

Since many neuter second-declension nominative and accusative singular forms look the same, atrium and auctionarium both end in -um.

So atrium auctionarium means auction hall or more literally auction-related hall/courtyard.

Because Latin word order is much freer than English word order.

In English, we usually need:

• subject + verb + other elements

But in Latin, the endings show the grammatical roles, so the verb can often come later, especially at the end.

So:

• Hasta publica ante atrium auctionarium est
• literally arranged in English order, this would be something like The public spear is in front of the auction hall

Putting est at the end is very normal Latin style.

Latin does not have definite or indefinite articles like English the or a/an.

So:

• hasta can mean a spear or the spear
• atrium can mean a hall/courtyard or the hall/courtyard

You figure out which is meant from the context or from the translation already provided.

Ante is a preposition meaning before or in front of.

In this sentence, it introduces a prepositional phrase:

• ante atrium auctionarium = in front of the auction hall

So it tells you the location of hasta publica.

In this sentence, it is best understood as an adjective modifying atrium.

So:

• atrium = hall / courtyard
• auctionarium = auction-related

Together they form:

• atrium auctionarium = auction hall or auction courtyard

Latin often uses adjectives this way where English might prefer a noun used attributively, as in auction hall.

It could. Latin allows a lot of flexibility.

For example, Latin could also say:

• Ante atrium auctionarium hasta publica est

That would still mean the same thing.

The original order puts hasta publica first, which gives it a bit of prominence. Latin authors often move words around for emphasis, rhythm, or style.

Yes. Besides its literal meaning, it can have a cultural association in Roman life.

A hasta could serve as a sign connected with a public sale or auction. So hasta publica may refer not just to any spear, but to a spear used as a marker of an official sale.

That is why this phrase can sound more meaningful than just a public spear. For a Roman reader, it could suggest the setting of an auction.

You can do that as a first step, but the result will sound unnatural.

Word-for-word:

• Hasta = spear
• publica = public
• ante = before / in front of
• atrium = hall / courtyard
• auctionarium = auction-related
• est = is

But better English will usually rearrange and smooth things out. A natural translation depends on the meaning already given to you, not just on the order of the Latin words.

In Latin, adjectives usually match their nouns in:

• gender
• number
• case

Here the pairings are:

• hasta
  • publica
• atrium
  • auctionarium

Even if Latin changes the word order, those matching endings help you see which words belong together. That is one of the most important reading skills in Latin.