Pater domi adest, et mater iam placidior est.

Pater is in the nominative singular, which is the case used for the subject of the sentence. Here, pater is the one who is present.

Similarly, mater is also nominative singular because she is the subject of est in the second part of the sentence.

Domi means at home. It is a special locative form, used with a few words—especially names of towns and small islands, and also certain common words like domus.

So:

• domi = at home
• in domo = in the house/home

The difference is subtle:

• domi focuses on the idea of being at home
• in domo is more literally inside the house

In this sentence, domi is the natural choice.

Adest means is present, is here, or is nearby.

It comes from:

• ad- = to, near
• est = is

So literally it is something like is at hand or is present.

It is the 3rd person singular present active indicative of adesse.

Because the two verbs express slightly different ideas:

• pater domi adest = the father is present at home
• mater iam placidior est = the mother is now calmer

In the first clause, the point is the father’s presence. In the second clause, the point is the mother’s state or condition.

So Latin uses:

• adesse for being present
• esse with an adjective for being X

Iam means now, already, or sometimes by now, depending on context.

Here it modifies the second clause:

• mater iam placidior est = the mother is now/already calmer

It suggests a change from an earlier state: she was less calm before, but now she is calmer.

Placidior is the comparative form of placidus, placida, placidum, meaning calm or quiet.

So:

• placida = calm
• placidior = calmer

The sentence is not just saying that the mother is calm; it is saying that she is calmer than before or than someone else implied by the context.

Adjectives in Latin agree with the nouns they describe in:

• gender
• number
• case

Here, mater is:

• feminine
• singular
• nominative

And placidior is also:

• feminine
• singular
• nominative

The reason it does not end in -a is that comparative adjectives often use a different pattern. In the nominative singular:

• masculine: placidior
• feminine: placidior
• neuter: placidius

So the feminine comparative does not have to end in -a.

Yes. A comparative adjective like placidior normally implies than before, than someone else, or than expected, even if Latin does not state the comparison explicitly.

Here, the most natural sense is:

• the mother is now calmer = calmer than she was before

Latin often leaves that standard of comparison unstated when it is obvious from context.

Et means and, joining the two clauses:

• Pater domi adest
• mater iam placidior est

Latin often does use conjunctions clearly, just as English does. In some contexts, Latin can omit a conjunction and simply place clauses next to each other, but et is perfectly normal and straightforward here.

Yes, Latin word order is more flexible than English word order because the endings show the grammatical roles.

This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Domi pater adest
• Mater iam est placidior
• Iam mater placidior est

That said, the given order is natural and clear:

• pater first introduces the subject
• domi adds the setting
• adest completes the idea
• then et introduces the second clause

Latin word order often reflects emphasis and style, not just grammar.

Both are 3rd person singular present indicative active forms.

More specifically:

• adest = from adesse, he/she/it is present
• est = from esse, he/she/it is

They are singular because their subjects are singular:

• pater
• mater

Classical Latin has no definite article equivalent to English the, and no indefinite article equivalent to a/an.

So:

• pater can mean father, the father, or sometimes a father
• mater can mean mother, the mother, or sometimes a mother

The context tells you which English translation makes the most sense.

A good classroom pronunciation would be something like:

PAH-ter DOH-mee AH-dest, et MAH-ter yahm plah-kih-dee-or est

A few notes:

• c in placidior is always hard, like k
• vowel lengths matter in careful pronunciation, though many beginners are not expected to master them immediately
• iam is often pronounced roughly like yahm

If you want a more classical-style breakdown:

• Pater = PA-ter
• domi = DO-mi
• adest = a-DEST
• mater = MA-ter
• iam = yam
• placidior = pla-ci-di-or
• est = est

Yes. This is a standard Latin pattern:

• esse
  • adjective

So:

• placidior est = is calmer

Here est is a linking verb, connecting the subject mater with the predicate adjective placidior.

Yes. Latin can express an explicit comparison in two common ways:

• with quam = than
• with the ablative of comparison

For example:

• mater placidior quam pater est = the mother is calmer than the father
• mater patre placidior est = the mother is calmer than the father

But in your sentence, no explicit than phrase is needed, because the comparison is understood from context.