Cyathus prope craterem est.

Because prope is a preposition that takes the accusative when it means near or close to.

So in this sentence:

• prope = near
• craterem = the accusative singular form of crater

That is why Latin says prope craterem, not prope crater.

A useful pattern to remember is:

• prope + accusative

So if you change the noun after prope, it should still be accusative:

• prope mensam = near the table
• prope portam = near the gate

Cyathus is nominative singular, which is the case normally used for the subject of the sentence.

In Cyathus prope craterem est:

• cyathus = the subject, the cup
• est = is
• prope craterem = near the bowl/mixing-bowl

So cyathus is the thing that is somewhere.

A learner can often spot the subject by looking for:

1. a nominative noun, and
2. a verb that agrees with it

Here, est is singular, and cyathus is singular too.

Latin word order is much freer than English word order. The verb often comes at or near the end, especially in simple textbook sentences.

So:

• Cyathus prope craterem est
• literally: The cup near the bowl is
• natural English: The cup is near the bowl

Latin can move words around more easily because the endings show their grammatical role. English depends much more on word order.

This means that in Latin, putting est at the end is normal and does not make the sentence strange.

No. Classical Latin does not have articles like English the and a/an.

So:

• cyathus can mean a cup or the cup
• craterem can mean a bowl, the bowl, a mixing-bowl, or the mixing-bowl

The exact English translation depends on context.

That is why one short Latin sentence can often be translated into English in more than one natural way.

Their dictionary forms are:

• cyathus, -i, m.
• crater, crateris, m.

A few useful things to notice:

• cyathus is a second-declension masculine noun
• crater is a third-declension masculine noun

That explains why their forms look different:

• cyathus stays cyathus in the nominative singular
• crater becomes craterem in the accusative singular

So craterem is not a completely different word; it is just a different case-form of crater.

Usually in beginner sentences like this, yes, it is being used as a preposition meaning near, and it takes the accusative.

However, prope can also be used as an adverb in some contexts, more like nearby or almost, depending on the sentence.

But here it is clearly a preposition because it has an object:

• prope craterem = near the bowl

So for this sentence, the safest thing to learn is:

• prope
  • accusative = near

Because in the third declension, many masculine and feminine nouns form the accusative singular with -em.

So:

• nominative singular: crater
• accusative singular: craterem

This is very common in the third declension. For example:

• rex → regem
• civis → civem
• homo → hominem

So craterem fits a normal third-declension pattern.

In a classroom-style Classical pronunciation, a learner might say it approximately like this:

• Cyathus: KYAH-too(s) or KÜ-ah-too(s)
• prope: PROH-peh
• craterem: KRAH-teh-rem
• est: est

A few pronunciation points:

• c is always hard, like k
• prope has two clear vowels: pro-pe
• craterem has four syllables: cra-te-rem
• est is pronounced with a clear t

If you are in an Ecclesiastical Latin setting, pronunciation may be somewhat different, but the grammar is the same.

Sometimes Latin can omit a form of to be, especially in certain styles or contexts. But in a simple beginner sentence like this, keeping est is completely normal and helps make the structure clear.

So:

• Cyathus prope craterem est = a full, straightforward sentence

A more advanced learner will later notice that Latin sometimes leaves is/are understood, but at this stage it is best to read est simply as is.