Parcimonia familiae usui est, luxuria autem saepe patrimonium laedit.

Because the subject of the first clause is parcimonia.

• parcimonia = frugality / thrift
• familiae = to/for the family

So familiae is not nominative; it is dative singular here. The clause means something like Frugality is useful to the family.

Familiae is dative singular.

It is used with the expression usui est, which means is useful to or more literally is for a use to. In this construction, the person or thing benefited is often put in the dative. So:

• familiae = to the family
• usui est = is useful

Together: parcimonia familiae usui est = frugality is useful to the family.

Usui est is a very common Latin way to say is useful or is of use.

Literally:

• usus, usūs = use
• usui = dative singular, for use / for benefit
• est = is

So usui est literally means is for use, but in natural English we usually translate it as is useful.

This is a standard idiom in Latin, and English learners often need a little time to get used to it because Latin often expresses ideas with noun + esse where English prefers an adjective.

Because usus is a fourth-declension noun.

Its dative singular is usuī (usually written usui). Fourth-declension nouns can have endings that look unusual if you are more familiar with first- and second-declension forms.

So here:

• nominative: usus
• dative: usui

That dative form is what appears in familiae usui est.

Yes. It is often explained as the double dative construction.

There are two datives here:

• familiae = dative of reference/advantage: for the family / to the family
• usui = dative of purpose: for use / as a benefit

So the whole idea is:

• parcimonia familiae usui est
  = frugality is useful to the family
  = more literally, frugality is for a benefit to the family

You do not need to translate it literally, but recognizing the pattern is very helpful.

Both are nominative singular, because both are subjects:

• parcimonia = frugality / thrift
• luxuria = luxury / extravagance

They are both first-declension feminine nouns.

So the sentence contrasts two subjects:

• parcimonia ... usui est
• luxuria ... laedit

Autem means however, but, or moreover, depending on context. Here it is contrastive, so however/but fits best.

Latin autem is usually postpositive, which means it tends to come second in its clause rather than first. So Latin says:

• luxuria autem...

not usually:

• autem luxuria...

That is a normal Latin word order pattern.

Because English and Latin do not always use connecting words in exactly the same way.

In this sentence, autem marks a contrast between parcimonia and luxuria:

• frugality is useful
• extravagance, however, often harms...

In natural English, that often becomes but extravagance often harms... Even though autem literally leans more toward however, but is often the best smooth translation.

Saepe is an adverb meaning often, and it modifies the verb laedit.

So:

• luxuria autem saepe patrimonium laedit
• extravagance, however, often harms the patrimony/estate

It tells us how often the action happens.

Laedit is the third person singular present active indicative of laedere, meaning to hurt, injure, damage, harm.

So luxuria ... laedit means:

• extravagance harms
• extravagance damages

Because the subject is singular (luxuria), the verb is singular too: laedit = she/it harms.

They refer to different things:

• familia = family, household
• patrimonium = patrimony, inheritance, family property, estate

So the sentence is saying:

• frugality benefits the family
• extravagance harms the family’s property/estate

The contrast is meaningful: one noun refers to the people/household, the other to the wealth or inherited property.

Because it is the direct object of laedit.

The verb laedere takes a direct object: you harm something. So:

• subject: luxuria
• verb: laedit
• direct object: patrimonium

Since patrimonium is a second-declension neuter noun, its accusative singular is the same as its nominative singular: patrimonium.

Because Classical Latin has no articles.

So Latin simply says:

• parcimonia
• familiae
• patrimonium

Depending on context, English may need to add the, a, or no article at all:

• Frugality is useful to the family
• Extravagance often harms the family estate

The article is supplied by the translator, not by a Latin word in the sentence.

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

So in the first clause:

• Parcimonia familiae usui est

the verb est comes at the end, which is very common in Latin. The order helps emphasize the key ideas and keeps the idiomatic phrase usui est together.

In English we must rely more on position, but in Latin the endings carry much of the work.

Yes. More literally it is:

• is for a benefit to the family
• or is for use to the family

But those are not natural English. So the best normal translation is:

• is useful to the family

A literal translation can help you understand the grammar, but an idiomatic translation is usually better for meaning.

Yes. The sentence sets up a balanced contrast between two abstract nouns:

• parcimonia = a good quality
• luxuria = a bad quality

And it contrasts their effects:

• usui est = benefits
• laedit = harms

So the sentence is neatly structured to show a moral lesson: thrift helps the household, while extravagance damages inherited wealth.