Aqua in fonte frigidior est quam aqua in amphora.

Yes, Latin could often omit the second aqua if the meaning is clear:

Aqua in fonte frigidior est quam in amphora.

That would still mean The water in the spring/fountain is colder than the water in the amphora.

The full version repeats aqua for clarity and balance:

• aqua in fonte
• aqua in amphora

Latin often repeats a noun where English might not.

Here in means in or inside, and it is followed by the ablative case because it shows location rather than motion.

So:

• fonte = ablative singular of fons (spring, fountain)
• amphora = ablative singular of amphora (amphora, jar)

A useful rule is:

• in + ablative = in/on somewhere, with no movement
• in + accusative = into/onto somewhere, with movement

So:

• aqua in fonte = water in the spring
• aqua in amphora = water in the amphora

Frigidior is the normal Latin comparative form of frigidus, frigida, frigidum (cold).

Latin usually forms comparisons with a special comparative adjective rather than with a separate word like English more.

So:

• frigidus = cold
• frigidior = colder

Latin does sometimes use magis (more) with some adjectives, especially where a regular comparative is awkward, but with frigidus the simple comparative frigidior is the standard form.

Because frigidior agrees with aqua, and aqua is feminine singular.

Comparative adjectives in Latin use these nominative singular forms:

• masculine/feminine: -ior
• neuter: -ius

So:

• masculine/feminine nominative singular: frigidior
• neuter nominative singular: frigidius

Since aqua is feminine, Latin uses frigidior.

Quam means than in a comparison.

So the structure is:

frigidior est quam ... = is colder than ...

In this sentence:

• Aqua in fonte frigidior est quam aqua in amphora.
• The water in the spring is colder than the water in the amphora.

This is one of the most common uses of quam.

Sometimes Latin can omit est (is) when the meaning is obvious, especially in poetry or very compact style. But in normal prose, including a teaching sentence like this one, est is very natural.

So:

• Aqua in fonte frigidior est quam aqua in amphora. = fully expressed
• Aqua in fonte frigidior quam aqua in amphora. = possible in some contexts, but less basic and less straightforward for beginners

Latin word order is more flexible than English because Latin uses endings to show grammatical relationships.

English depends heavily on word order:

• The water in the spring is colder than the water in the amphora.

Latin can move parts around more freely:

• Aqua in fonte frigidior est quam aqua in amphora.
• Frigidior est aqua in fonte quam aqua in amphora.
• Aqua frigidior est in fonte quam in amphora.

These can all mean roughly the same thing, though the emphasis may change.

The given order is clear and natural:

• subject first: Aqua in fonte
• comparison adjective: frigidior
• verb: est
• comparison phrase: quam aqua in amphora

Their dictionary forms are:

• fons, fontis (masculine) = spring, fountain
• amphora, amphorae (feminine) = amphora, jar

In the sentence:

• fonte is the ablative singular of fons
• amphora is the ablative singular of amphora

A beginner might notice that amphora looks the same in the nominative and ablative singular. That is normal for many first-declension nouns.

Latin has no articles like English the and a/an.

So aqua can mean:

• water
• the water
• some water

The context tells you which is best in translation. In this sentence, English naturally uses the:

• The water in the spring is colder than the water in the amphora.

But Latin itself does not include a separate word for the.

The subject is aqua, because:

• it is in the nominative singular
• the verb est is singular
• the adjective frigidior agrees with it

The phrase in fonte is just a prepositional phrase modifying aqua:

• aqua = water
• in fonte = in the spring

So the subject is not just aqua, but more fully the water in the spring.

It can mean either, depending on context.

Fons commonly means:

• spring in the sense of a natural source of water
• fountain in some contexts

If the meaning shown to the learner is already given, then that tells you which sense is intended here. Grammatically, either works the same way:

• in fonte = in the spring or in the fountain

With quam, Latin often compares two things in the same construction.

Here:

• aqua in fonte is one thing being compared
• aqua in amphora is the other thing being compared

So both use aqua in the nominative:

• Aqua ... frigidior est quam aqua ...

Latin also has another way to make comparisons, using the ablative of comparison without quam, but that is not what is happening here.

This sentence uses the very common beginner pattern:

• comparative adjective + quam

The pattern is:

[subject] + [prepositional phrase] + [comparative adjective] + [verb] + quam + [noun phrase for comparison]

More specifically:

• Aqua in fonte = subject phrase
• frigidior = comparative adjective
• est = verb
• quam aqua in amphora = comparison phrase

So the sentence means: Water in the spring is colder than water in the amphora.

This is a very useful model for making your own Latin comparisons.