Concameratio alta est, sed hemisphaerium inferius est.

Because adjectives in Latin must agree with the nouns they describe in gender, number, and case.

• concameratio is feminine singular nominative, so its adjective is alta
• hemisphaerium is neuter singular nominative, so its adjective is inferius

Even though both adjectives are linked to their nouns through est, they still have to match the nouns grammatically.

They are all in the nominative singular.

• concameratio — nominative singular
• alta — nominative singular feminine
• hemisphaerium — nominative singular neuter
• inferius — nominative singular neuter
• est — is

This is because both clauses use esse (to be), and with esse, both the subject and the predicate adjective are normally in the nominative.

Because inferius is the neuter nominative singular form of the comparative adjective inferior, inferius.

Comparative adjectives in Latin often have these forms:

• masculine/feminine nominative singular: inferior
• neuter nominative singular: inferius

Since hemisphaerium is neuter, Latin uses inferius.

Yes. Inferius is a comparative form meaning lower.

Latin comparatives do not always need an explicit than phrase. Sometimes the comparison is just understood from the context. So hemisphaerium inferius est can simply mean that the hemisphere is lower or the lower one, without stating exactly what it is lower than.

Because the sentence is not trying to make both adjectives the same type grammatically. It simply states two qualities:

• concameratio alta est — the vaulting is high
• hemisphaerium inferius est — the hemisphere is lower

Latin does not require parallel adjective forms just because two clauses are joined by sed. One adjective can be positive (alta) and the other comparative (inferius) if that matches the intended sense.

Yes, Latin often can omit the second est if it is understood:

• Concameratio alta est, sed hemisphaerium inferius.

That would still make sense. But repeating est is completely normal and often clearer, especially in straightforward prose.

Because classical Latin has no articles.

So a noun like concameratio can mean:

• a vaulting
• the vaulting

and hemisphaerium can mean:

• a hemisphere
• the hemisphere

The exact sense depends on context.

No. Latin word order is much more flexible than English word order because the endings show the grammatical relationships.

This sentence uses a very straightforward order:

• noun + adjective + verb
• conjunction
• noun + adjective + verb

But other orders are possible, for example:

• Alta est concameratio, sed inferius est hemisphaerium.

That would still be grammatical, though it might place different emphasis on the words.

Sed means but. It introduces a contrast between the two clauses.

So the sentence sets up one statement and then contrasts it with another:

• the vaulting is high,
• but the hemisphere is lower.

It is a very common coordinating conjunction in Latin.

• concameratio is a first-declension feminine noun
• hemisphaerium is a second-declension neuter noun

That helps explain the adjective forms:

• first-declension feminine noun → alta
• second-declension neuter noun → inferius as the neuter comparative form

Recognizing declension and gender is one of the main keys to understanding why Latin words take the endings they do.