Auspex diem confarreationis probat.

Because auspex is in the nominative singular, which is the case normally used for the subject in Latin.

Here, auspex means an augur / diviner / official observer of omens, and it is the person doing the action of probat.

So grammatically:

• auspex = subject
• probat = verb
• diem = direct object

Probat is:

• present tense
• indicative mood
• active voice
• 3rd person singular

So it means he/she/it approves, finds acceptable, or judges favorable, depending on context.

Because the subject is auspex, the sense is the augur approves or declares favorable.

Diem is the accusative singular of dies, meaning day.

It is accusative because it is the direct object of probat. In other words, it is the thing being approved.

So the structure is:

• auspex = the one approving
• diem = the day being approved
• probat = approves

Confarreationis is genitive singular.

It depends on diem and means of the confarreatio. So diem confarreationis means the day of the confarreatio.

This is a very common Latin pattern:

• noun + genitive
• day of X
• book of X
• fear of X
• and so on

So confarreationis is not the object of the verb; it is modifying diem.

Confarreatio was a specific ancient Roman form of marriage, especially associated with the patrician class and certain religious traditions.

The word is fairly specialized, so a learner might not recognize it immediately. In this sentence, you do not need to know every historical detail to understand the grammar:

• base noun: confarreatio
• form here: confarreationis = of the confarreatio

So grammatically it works just like any other genitive singular noun.

Because the sentence is not saying that the augur approves the confarreatio itself directly.

If it were confarreationem, that would be accusative singular, and it would make confarreatio the direct object of probat.

But here the direct object is diem. The noun confarreationis is only describing which day:

• diem = the day
• confarreationis = of the confarreatio

So the meaning is the day of the confarreatio, not the confarreatio by itself.

They come from different declensions:

• auspex: third declension
  
  • nominative singular: auspex
• dies: fifth declension
  
  • accusative singular: diem
• confarreatio: third declension
  
  • genitive singular: confarreationis

This sentence is a good example of how Latin can mix declensions freely in one clause.

Classical Latin normally has no articles.

So Latin often leaves it to context whether you should understand:

• the augur
• an augur

and likewise:

• the day
• a day

In this sentence, English usually needs an article, but Latin does not.

The word order is meaningful, but not in the same rigid way as in English.

Latin uses endings more than position to show grammatical roles, so the sentence could be rearranged without changing the basic meaning, for example:

• Auspex diem confarreationis probat
• Diem confarreationis auspex probat
• Auspex probat diem confarreationis

All of these still mean roughly the same thing because:

• auspex is nominative
• diem is accusative
• confarreationis is genitive

The given order is perfectly natural and straightforward.

Latin probo, probare can cover several related ideas, including:

• approve
• find good
• judge acceptable
• test
• prove

In this sentence, with diem as the object and auspex as the subject, the sense is most naturally something like:

• approves the day
• declares the day favorable
• judges the day suitable

So the context points toward approval / favorable judgment, not mathematical or logical proof.

Etymologically, yes, the word is connected with observing birds and omens. But in normal translation here, auspex is better rendered as something like:

• augur
• diviner
• omens-observer
• religious official who interprets signs

A literal translation like bird-watcher would miss the religious and official sense.

A classical-style pronunciation would be approximately:

OWS-peks dee-em kon-far-ray-AH-tee-oh-nis PRO-bat

A few helpful points:

• au in auspex sounds like ow in cow
• diem is two syllables: di-em
• ti in confarreatio is usually pronounced like tee, not like English sh
• probat has a clear t at the end

If using an ecclesiastical pronunciation, some sounds may differ, but the grammar remains the same.

It is:

subject + object + genitive modifier + verb

More specifically:

• Auspex = subject, nominative singular
• diem = direct object, accusative singular
• confarreationis = genitive singular modifying diem
• probat = 3rd person singular present active verb

So the sentence is a simple main clause with one noun phrase inside it:

• main clause: Auspex ... probat
• object phrase: diem confarreationis