Lucia codicem fratris capit et menda diligenter corrigit.

Because codicem is the accusative singular, and it is the direct object of capit.

The dictionary form is codex meaning book / manuscript / codex, but third-declension nouns often change their form in other cases:

• nominative singular: codex
• accusative singular: codicem

So Lucia codicem capit means Lucia takes the book.

Fratris is the genitive singular of frater, and the genitive often shows possession.

So:

• frater = brother
• fratris = of the brother / the brother’s

That means codicem fratris means the brother’s book.

Not by grammar alone.

Fratris literally means of a brother or of the brother. Latin does not automatically mark it as her brother. We understand her brother’s from the context, since Lucia is the subject and that is the most natural interpretation.

So the Latin form itself gives possession, but context tells you whose brother is meant.

Lucia is in the nominative case, which is the normal case for the subject.

Also, both verbs are third-person singular:

• capit = she/he takes
• corrigit = she/he corrects

Since Lucia is a singular nominative noun, it matches those verb forms and is understood as the subject of both verbs.

Both are present indicative active, third-person singular.

So:

• capit = she takes / is taking
• corrigit = she corrects / is correcting

In a simple sentence like this, English usually translates them with the simple present: takes and corrects.

Because menda is the accusative plural of mendum, a neuter second-declension noun meaning mistake / error.

Its forms are:

• singular: mendum
• plural: menda

For neuter nouns, the nominative plural and accusative plural are often the same and usually end in -a.

So menda corrigit means she corrects mistakes.

Because Classical Latin has no articles.

Latin does not have separate words for the, a, or an. Whether a noun should be understood as definite or indefinite is usually decided by context.

So:

• codicem could mean a book or the book
• fratris could mean of a brother or of the brother
• menda could mean mistakes or the mistakes

English has to choose one wording, but Latin leaves that unstated.

Diligenter is an adverb meaning carefully, diligently, or with care.

It modifies the verb corrigit:

• menda diligenter corrigit = she carefully corrects the mistakes

Adverbs in Latin often stand near the word they modify, but word order is fairly flexible.

Because Latin does not need to repeat the subject when the same subject continues.

The sentence has one subject, Lucia, and two verbs joined by et:

• capit
• et corrigit

So the sense is:

Lucia takes her brother’s book and carefully corrects the mistakes.

English can do this too: Lucia takes the book and corrects the mistakes.

Latin word order is more flexible than English word order, because the case endings show the grammatical relationships.

In this sentence:

• Lucia is the subject
• codicem is the object of capit
• fratris depends on codicem
• menda is the object of corrigit

So Latin could rearrange parts of the sentence and still keep the same basic meaning, though the emphasis might change.

This order is quite natural:

• subject first: Lucia
• object phrase: codicem fratris
• verb: capit
• then the second clause: et menda diligenter corrigit

Yes. It is a noun phrase made of:

• codicem = book in the accusative
• fratris = of the brother in the genitive

Together they mean the brother’s book.

A helpful way to see it is:

• main noun: codicem
• dependent noun showing possession: fratris

So fratris is not a separate object; it belongs with codicem.

Capit basically means takes, seizes, gets hold of, or sometimes takes up depending on context.

Here, with codicem, the natural meaning is something like:

• takes the book
• picks up the book

So it probably suggests that Lucia takes her brother’s book and then begins correcting the mistakes in it.