Servus linteum invenit et rogat: “Cuius est hoc linteum?”

Servus is nominative singular (2nd declension), because it’s the subject of the verbs invenit and rogat: the slave/servant is the one doing the finding and asking.

Invenit can be either:

• Present: he finds
• Perfect: he found / has found

In many story contexts, invenit is commonly read as perfect (he found). Latin often uses the perfect to move a narrative forward. The surrounding context usually makes the intended time clear.

Rogat is present tense (he asks). If invenit is taken as perfect (he found), then rogat can be understood as a historical present: Latin (and English sometimes) uses the present tense to make narration more vivid: He found it and (now) asks...

If you instead read invenit as present (he finds), then rogat matches naturally.

Linteum is a neuter noun of the 2nd declension (linteum, linteī). It means something like linen cloth, and in many contexts a towel / cloth. Here it’s the object being found, and then the thing being asked about.

It could change case in other sentences, but here it makes sense that it stays nominative/accusative singular neuter, which look the same in the 2nd declension.

• In Servus linteum invenit, linteum is accusative (direct object of finds).
• In Cuius est hoc linteum?, hoc linteum is nominative (the subject of is).

Because neuter nominative and accusative singular are identical, you don’t see a form change.

Cuius is genitive singular of quis/quī (who?). It means whose?

With esse (to be), Latin often uses a genitive of possession:

• Cuius est hoc linteum? = Whose (person’s) is this towel? → more naturally: Whose towel is this?

So cuius is a predicate genitive expressing the owner.

Because linteum is neuter singular, the demonstrative must match it:

• hic = masculine nominative singular
• haec = feminine nominative singular
• hoc = neuter nominative/accusative singular

So hoc linteum = this towel/cloth (neuter + neuter).

Yes, Latin word order is flexible. Cuius est hoc linteum? is very normal, but you could also see:

• Cuius hoc linteum est?
• Hoc linteum cuius est? (often with extra emphasis on this towel)

The meaning stays basically the same; changes mainly affect emphasis and rhythm.

In modern edited Latin texts, punctuation like a colon often introduces direct speech: rogat: ...

Classical Latin manuscripts originally had little or no punctuation; modern editors add it to help readers. So the colon is an editorial/modern convention signaling: “what follows are his words.”

Yes, et simply means and: He finds a towel and asks...

Latin also often uses:

• -que (attached to the second word): invenit rogatque = finds and asks
• ac/atque (often “and also,” sometimes with a closer connection)

But et is the most straightforward and common.