Pater putat augurium bonum esse, si augur laetis verbis auspicium interpretatur.

Because Latin often uses an indirect statement after verbs of thinking, saying, knowing, and perceiving.

Here, putat means thinks, and what the father thinks is:

• augurium bonum esse = that the omen is good

In Latin, this pattern is usually:

• accusative subject + infinitive

So instead of using a word like that, Latin uses the infinitive esse.

In an indirect statement, the subject is normally put in the accusative case.
But augurium is a neuter singular noun, and for many neuter nouns:

• nominative singular = accusative singular

So augurium looks the same in both cases.

That means here it is functioning as the accusative subject of esse, even though its form is identical to the nominative.

Because bonum agrees with augurium.

• augurium is neuter singular
• so the adjective must also be neuter singular
• therefore: bonum

If the noun were masculine, you would expect bonus; if feminine, bona.

So:

• augurium bonum = a good omen

These three words are related, which can make them easy to confuse.

• augur = augur, the priest/diviner who interprets signs
• augurium = omen or augury, often the result or meaning of divination
• auspicium = auspice, sign observed, especially a sign from birds or divine indication

So in this sentence:

• the augur is the person
• the auspicium is the sign being interpreted
• the augurium is the omen/judgment that is considered good

The exact distinction can blur somewhat in practice, but that is the basic difference.

Because interpretatur is a deponent verb.

A deponent verb:

• has passive forms
• but active meaning

So:

• interpretatur looks like is interpreted
• but actually means interprets

Its dictionary form is interpretor, interpretari, meaning to interpret.

This is very common in Latin, and learners often have to get used to recognizing deponent verbs.

Laetis verbis is in the ablative plural.

• laetis = ablative plural of laetus
• verbis = ablative plural of verbum

It most naturally expresses means or manner:

• with joyful/favorable words
• in cheerful/favorable language

In context, it probably means that the augur gives the interpretation in favorable terms, not just that he is cheerful.

Si introduces a conditional clause:

• si augur laetis verbis auspicium interpretatur
• if the augur interprets the auspice with favorable words

This is a straightforward present condition:

• putat ... esse = he thinks ... is
• si ... interpretatur = if ... interprets

So the father thinks the omen is good on the condition that the augur interprets the sign favorably.

Latin word order is more flexible than English word order, because endings show how words relate to one another.

This sentence is arranged quite naturally:

• Pater putat = the main statement begins first
• augurium bonum esse = the indirect statement follows
• si ... interpretatur = the condition comes afterward

A few things to notice:

• bonum comes next to augurium, which makes their agreement easy to see
• laetis verbis is placed before auspicium interpretatur, which helps emphasize the way the augur interprets

Latin often uses word order for emphasis and style rather than strict grammatical necessity.

Because Latin usually does not use a separate word equivalent to English that in this kind of construction.

English says:

• The father thinks that the omen is good

Latin says:

• Pater putat augurium bonum esse

The idea of that is built into the accusative + infinitive construction. So the infinitive esse is doing part of the work that that is does in English.

Yes. Although laetus often means happy, joyful, or glad, in this context it can also suggest something like:

• favorable
• auspicious
• encouraging

So laetis verbis may be better understood as in favorable words rather than literally in happy words.

That fits the religious and interpretive setting of the sentence better.

They are closely related, but not exactly identical.

A learner might expect only one of them, but Latin can distinguish between:

• the sign observed: auspicium
• the omen/judgment/resulting interpretation: augurium

So the sentence can be understood roughly like this:

• the augur interprets the sign
• and the father thinks the resulting omen is good

Even if English translations sometimes use similar words for both, Latin can keep a slight distinction between the observed sign and the interpreted omen.