Societas inter duas vicinas bona est, quia altera alteri in rebus difficilibus auxilio est.

Because inter normally takes the accusative in Latin when it means between or among.

So:

• duae vicinae = two female neighbors as a subject
• inter duas vicinas = between two female neighbors

Both words are accusative plural feminine:

• duas = two
• vicinas = neighbors

They match because duas describes vicinas.

Vicinas is feminine plural accusative, so it means female neighbors.

That fits the rest of the sentence, because later we get:

• altera = the one
• alteri = to the other

Both of those are also feminine singular here, referring back to the two women. If the sentence were about two male neighbors, you would expect masculine forms instead.

Societas can mean things like association, partnership, companionship, or relationship. In this sentence, it most naturally means something like:

• the relationship
• the bond
• the sense of community

So Societas inter duas vicinas bona est means that the relationship or neighborly bond between the two women is good.

Because bona agrees with societas, which is a feminine singular noun.

So:

• societas = feminine singular
• bona = feminine singular adjective meaning good

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

This is a very common Latin pattern meaning one ... the other.

Here:

• altera = the one / one woman
• alteri = to the other / for the other woman

So altera alteri ... est means the one is ... to the other.

Because there are exactly two people in view, Latin uses forms of alter for one of the two / the other of the two.

They have different jobs in the sentence.

• altera is nominative singular feminine, so it is the subject
• alteri is dative singular feminine, so it means to the other or for the other

In other words:

• altera = the one doing the being
• alteri = the person affected or benefited

This fits the pattern someone is a help to someone else.

Yes, in a sense. Latin often leaves out an obvious noun when a pronoun or adjective can stand on its own.

Here, altera and alteri mean something like:

• altera vicina = the one neighbor
• alteri vicinae = to the other neighbor

But Latin does not need to repeat vicina because it is already clear from the context.

It means in difficult situations, in difficult matters, or when things are hard.

Breaking it down:

• in = in
• rebus = ablative plural of res, meaning things, matters, circumstances
• difficilibus = difficult, agreeing with rebus

So the phrase is literally in difficult matters/things, but natural English often prefers in difficult situations.

Because in with the meaning in or within usually takes the ablative.

So:

• in rebus difficilibus = in difficult matters/situations

By contrast, in takes the accusative when it expresses motion into something.

This is one of the most important grammar points in the sentence.

Auxilio est uses the dative case, not the nominative. This is a standard Latin construction often called the double dative.

• auxilio = for help, as a help
• alteri = to the other

So altera alteri auxilio est literally means:

• the one is for help to the other

More natural English:

• the one is a help to the other
• each is helpful to the other is the general idea of the sentence

If you said auxilium est, that would simply mean is a help in a more ordinary predicate-noun way. Latin often prefers auxilio esse alicui for to be a help to someone.

The double dative is when Latin uses:

1. a dative of reference/person: alteri = to the other
2. a dative of purpose: auxilio = for help, as a help

Together:

• alteri auxilio est = is a help to the other

This is a very common idiom with sum. Other similar examples are:

• curae esse = to be a concern to
• praesidio esse = to be a protection to
• usui esse = to be useful to

There are really two separate clauses:

• Societas inter duas vicinas bona est
• quia altera alteri in rebus difficilibus auxilio est

Latin often repeats est because each clause has its own verb. English might also do this:

• The relationship is good because one is a help to the other

So the repetition is completely normal.

Latin word order is much freer than English word order. The verb often comes at or near the end of a clause, especially in more formal or literary Latin.

So:

• altera alteri in rebus difficilibus auxilio est

puts the verb last, which is very natural in Latin.

English usually requires a more fixed order, but Latin does not.

In a sentence like this, yes: quia means because and introduces a reason.

So the second clause explains why the relationship is good:

• quia ... = because ...

There are other Latin words for because as well, such as quod or cum in certain contexts, but quia is straightforward here.

Strictly speaking, the grammar says one is a help to the other. But because the sentence is about the good relationship between two neighbors, the broader idea is mutual helpfulness or neighborly support.

So the Latin expression focuses on the pair as a whole, even though the wording is singular:

• one to the other
• effectively they help each other

In context, English might naturally express the sense as they are there for each other in difficult times.

Yes.

A more literal translation would be:

• The relationship between two female neighbors is good, because one is a help to the other in difficult circumstances.

A more natural English translation might be:

• The relationship between two neighbors is good, because they help each other in difficult times.
• The bond between the two neighbors is good, because each is a help to the other when things are difficult.

The exact English wording can vary, but the Latin grammar stays the same.