Cothurnus scaenicus in tragoedia geritur.

Because cothurnus is the subject of the sentence.

The verb geritur means is worn or more literally is carried/worn in the passive, so the thing being worn is what the sentence is about:

• cothurnus = the buskin / tragic boot
• geritur = is worn

So cothurnus is nominative singular: the boot is worn.

Because scaenicus is an adjective modifying cothurnus, and Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

Here:

• cothurnus is masculine singular nominative
• so scaenicus must also be masculine singular nominative

That is why you get cothurnus scaenicus = the theatrical/stage buskin.

Geritur is:

• 3rd person singular
• present tense
• passive voice

from the verb gero, gerere.

A very literal sense of gero is carry or bear, but Latin often uses it in wider ways, including wear for clothing or footwear.

So geritur here means is worn.

Latin often uses the passive when the agent is unimportant, obvious, or left unstated.

So instead of saying:

• someone wears the tragic boot

Latin says:

• the tragic boot is worn

This keeps the focus on the object itself, not on the person wearing it.

Tragoedia is in the ablative singular because it follows in in the sense of in or within the sphere of.

A useful rule is:

• in + ablative = in, on, within
• in + accusative = into, onto

So here in tragoedia means something like:

• in tragedy
• in tragic drama
• on the tragic stage

It is not motion into tragedy, so the ablative is used.

Because tragoedia is a first-declension noun.

In the first declension:

• nominative singular = -a
• ablative singular = -ā

If macrons are not written, both appear simply as -a.

So:

• nominative: tragoedia
• ablative: tragoediā

In ordinary printed Latin without macrons, they look the same.

The word order is perfectly normal Latin.

Latin word order is much freer than English word order because case endings show how words function. So all of these are possible in Latin, with slightly different emphasis:

• Cothurnus scaenicus in tragoedia geritur.
• Scaenicus cothurnus in tragoedia geritur.
• In tragoedia cothurnus scaenicus geritur.

The version you have is straightforward:

• noun + adjective
• phrase with in
• verb at the end

Putting the verb at the end is especially common in Latin prose.

Correct: Latin has no word for the or a/an.

So cothurnus can mean:

• a buskin
• the buskin
• buskin in a general sense

You decide from context which English article fits best.

In a sentence like this, English usually wants the or sometimes a generalizing translation such as the tragic boot is worn in tragedy.

Latin often uses the singular to refer to a type of thing in a general way.

So cothurnus here means the tragic boot as a characteristic item of costume, not necessarily one single physical shoe being discussed in isolation.

English can do something similar:

• The lion is a dangerous animal
• meaning lions in general

Likewise, cothurnus can stand for the costume item as a class or symbol.

Yes. Scaenicus means of the stage, theatrical, or stage-related.

So cothurnus scaenicus is not just any boot. It is specifically the boot associated with the stage, especially tragic drama.

A Roman reader would likely understand this as the buskin, the high boot traditionally linked with tragic actors.

It is more naturally understood as in tragedy in the sense of:

• in tragic drama
• in the genre of tragedy
• on the tragic stage

Latin often uses in with an abstract noun this way, to indicate a setting, field, or sphere rather than strict physical location.

So here the idea is not mainly physical containment, but dramatic context.