Dux ingentem multitudinem videt.

Because dux is in the nominative singular, which is the case usually used for the subject of a finite verb in Latin.

Here, videt means he/she/it sees, so we look for a nominative singular noun to go with it. Dux fits that role, so it is the subject.

Its basic dictionary form is dux, ducis, meaning leader.

Because multitudinem is in the accusative singular, and the accusative case is commonly used for the direct object in Latin.

The verb videt is a transitive verb, so it can take an object: someone sees something. In this sentence, the thing being seen is multitudinem.

So:

• dux = subject
• multitudinem = direct object

They are both in the accusative singular, but for different reasons:

• multitudinem is accusative singular because it is the direct object
• ingentem is accusative singular because it describes multitudinem, so it must agree with it

In Latin, adjectives agree with the nouns they modify in:

• gender
• number
• case

So if multitudinem is feminine accusative singular, ingentem must also be feminine accusative singular.

Because adjectives and nouns can belong to different declensions.

Here:

• multitudo, multitudinis is a third-declension noun
• ingens, ingentis is a third-declension adjective

They still agree in case, number, and gender, but agreement does not mean they must look identical letter-for-letter. It means they must have the same grammatical function.

So ingentem and multitudinem both represent feminine accusative singular, even though their endings are not identical in every form across the declension.

Videt is:

• third person singular
• present tense
• active voice
• indicative mood

It comes from video, videre, meaning to see.

So videt means:

• he sees
• she sees
• it sees

In this sentence, it goes with dux, so the sense is the leader sees.

Classical Latin does not have articles like English the and a/an.

So:

• dux can mean leader, a leader, or the leader
• multitudinem can mean a multitude or the multitude

Which English article is best depends on context.

That is very normal in Latin, and learners have to get used to supplying the or a naturally when translating.

Yes. Latin word order is much freer than English word order because the endings show the grammatical roles.

So all of these could still mean essentially the same thing:

• Dux ingentem multitudinem videt
• Ingentem multitudinem dux videt
• Multitudinem ingentem videt dux

The endings still show:

• dux = subject
• multitudinem = object
• ingentem modifies multitudinem

However, different word orders can give different emphasis. The given order is straightforward and natural.

Because multitudo is a collective noun. It is grammatically singular even though it refers to a group made up of many individuals.

English does the same thing with words like:

• crowd
• army
• group

So multitudinem is singular in grammar, even though the idea behind it is plural.

They are:

• dux, ducis — leader
• ingens, ingentis — huge, vast, enormous
• multitudo, multitudinis — multitude, crowd
• video, videre, vidi, visus — see

Latin dictionaries usually list nouns with the nominative and genitive, because that helps you identify the declension and the stem.

Dux is a noun of common gender, which means it can refer to either a male leader or a female leader depending on context.

The form dux itself does not tell you male or female here. The verb videt also does not show gender.

So without more context, dux could mean:

• the male leader
• the female leader

Because of agreement.

Ingentem is accusative singular, while dux is nominative singular. Since adjectives must agree with the nouns they modify, ingentem cannot describe dux here.

It matches multitudinem instead:

• ingentem = accusative singular
• multitudinem = accusative singular

So the phrase is ingentem multitudinem = the huge multitude.

Mostly, yes.

Three important words here are third declension:

• dux, ducis
• ingens, ingentis
• multitudo, multitudinis

The verb videt is not part of a declension, because verbs are conjugated rather than declined.

A learner might notice that third-declension words often have less predictable nominative forms, so the genitive form is especially important for identifying them.