Aequinoctium diem et noctem aequat.

Because diem and noctem are both clearly accusative singular forms, so they function as the object of aequat. That leaves aequinoctium as the nominative singular subject.

A detail that often surprises beginners: aequinoctium ends in -um, but that does not automatically mean it is an object. It is a second-declension neuter noun, and in that declension the nominative singular and accusative singular are both -um.

Because dies and nox are the dictionary forms (nominative singular). In this sentence they are not subjects; they are in the accusative singular, so their forms change:

• dies → diem
• nox → noctem

Latin changes noun endings to show what job each noun is doing in the sentence.

Because diem et noctem means day and night, and both nouns are joined by et. Together they form a coordinated object of aequat.

This is similar to English in a sentence like It balances day and night: both day and night are objects of the verb.

Aequat is the third-person singular present active indicative of aequare.

That means:

• present = happening now / generally true
• active = the subject performs the action
• indicative = a plain statement
• third-person singular = he/she/it makes equal

So the -t ending tells you it does the action.

Because the subject is singular: aequinoctium.

Latin verbs agree with their subject in person and number. Since there is one equinox, the verb is aequat, not a plural form.

Et simply means and.

It links diem and noctem, showing that the verb applies to both nouns together.

They come from different declensions, which is why their forms look so different:

• aequinoctium: second declension, neuter
• dies: fifth declension
• nox: third declension

This is a very normal feature of Latin: words in the same sentence do not have to belong to the same declension.

No. Latin does not have definite or indefinite articles like the, a, or an.

So aequinoctium can mean the equinox or just an equinox, depending on context. English has to add the article when translating.

Yes, it could be different. Latin word order is much freer than English word order because the endings show the grammatical roles.

This order is quite natural:

• Aequinoctium = subject first
• diem et noctem = object next
• aequat = verb last

But Latin could rearrange the words for emphasis without changing the basic meaning, for example:

• Diem et noctem aequinoctium aequat.
• Aequat aequinoctium diem et noctem.

The endings, not the position alone, tell you who is doing what.

Yes. English equinox comes from Latin aequinoctium.

That connection is useful for memory: the Latin word is the source of the familiar English term.

You usually look up nouns by their nominative singular form, and verbs by their first-person singular form or infinitive.

For this sentence, you would look for:

• aequinoctium, aequinoctii — equinox
• dies, diei — day
• nox, noctis — night
• aequo, aequare — make equal, equalize

So if you see diem, you look under dies; if you see noctem, you look under nox; if you see aequat, you look under aequo or aequare.