Sic et balneum et cena parva, si recte parantur, corpori mentique auxilio esse possunt.

Sic means so, thus, or in this way. In a sentence like this, it often links back to something said earlier, so it can feel like likewise, in the same way, or so too.

So the sentence is not just making an isolated statement; sic suggests a connection with the previous idea.

This is a very common Latin pattern: et ... et ... means both ... and ...

So:

• et balneum et cena parva = both a bath and a small meal

Latin often repeats the conjunction where English would not.

Balneum literally means bath, but depending on context it can mean:

• a bath
• bathing
• sometimes even a bath-house

In this sentence, it most naturally means a bath or bathing as something beneficial.

Cena parva is nominative singular feminine:

• cena = dinner, meal
• parva = small

The adjective parva agrees with cena in gender, number, and case.

As for word order, Latin is much freer than English. An adjective can come before or after the noun. So cena parva and parva cena could both be grammatical. Here the adjective simply follows the noun, which is very normal Latin.

Because recte is an adverb, meaning properly, correctly, or well.

It modifies the verb parantur:

• si recte parantur = if they are prepared properly

An adjective such as recta would need to describe a noun, not a verb.

Because together they form a compound subject:

• balneum
• cena parva

Since the sentence is talking about both of them together, the verb is plural:

• parantur = they are prepared

This is just like English: the bath and the meal are prepared, not is prepared.

Parantur is the present passive indicative of parare, meaning are prepared, are arranged, or are provided.

Latin uses the passive here because the focus is on the bath and the meal as things that are prepared, not on the person doing the preparing.

So:

• si recte parantur = if they are properly prepared

The agent is left unstated, which Latin often does.

Because this is a straightforward condition:

• si recte parantur = if they are prepared properly

Latin normally uses the indicative in ordinary, real, or general conditions like this. There is no special uncertainty or contrary-to-fact idea here that would call for the subjunctive.

Both are dative singular:

• corpori = to the body
• menti = to the mind
• mentique = and to the mind

So the sentence is saying that the bath and small meal can be of help to the body and to the mind.

-que is an enclitic conjunction meaning and. Instead of standing as a separate word, it attaches to the end of a word.

So:

• mentique = and to the mind

Latin very often uses -que to join the second item in a pair. Here it links corpori and menti.

Auxilio is the dative singular of auxilium, meaning help or aid.

In this sentence it is part of a very common Latin construction:

• auxilio esse alicui = to be a help to someone/something

More specifically, many grammars call this a double dative:

• auxilio = dative of purpose, as a help
• corpori mentique = dative of reference, to the body and mind

So:

• corpori mentique auxilio esse = to be a help to the body and mind

Because possum normally takes an infinitive.

Here the infinitive is esse, and it completes the idiom auxilio esse:

• possunt = they are able / they can
• esse = to be

So:

• auxilio esse possunt = they can be a help

If esse were omitted, the construction would be incomplete.

Yes: the word order is very Latin.

A few things to notice:

• Sic comes first to connect with the previous thought.
• et ... et ... neatly frames the two subjects.
• si recte parantur is inserted between the subject and the rest of the statement.
• corpori mentique auxilio esse keeps the idea be a help to body and mind together.
• possunt comes at the end, which is very common in Latin.

So the order is not random, but it is much freer than English. Latin uses word order for emphasis and style more than for basic grammatical structure.