Pax quidem melior est quam bellum.

Because pax is the subject of the sentence. The sentence is saying something about peace, so pax is in the nominative singular.

• pax = peace
• nominative singular
• 3rd-declension noun
• gender: feminine

So pax ... est means peace ... is.

In Latin, when you compare two things with quam after a comparative adjective, the second thing is usually put in the same case as the first.

Here:

• pax is nominative
• so bellum is also nominative after quam

So:

• Pax ... melior est quam bellum = Peace is better than war

Latin also has another comparison pattern:

• pax melior est bello

There, bello is ablative, and quam is not used. Both patterns are correct, but this sentence uses the quam + same case pattern.

Because melior agrees with pax, and pax is feminine singular.

Melior is the comparative form of bonus (good), and it means better.

Comparative forms look like this:

• masculine/feminine: melior
• neuter: melius

Since pax is feminine, Latin uses melior, not melius.

Yes. It comes from bonus (good), but the comparative is not formed in a simple predictable way from bonus itself.

The main forms are:

• positive: bonus = good
• comparative: melior, melius = better
• superlative: optimus = best

So this is something learners usually just memorize.

Quidem adds emphasis. In this sentence it means something like:

• indeed
• certainly
• to be sure

So Pax quidem melior est quam bellum has the sense of:

• Peace is indeed better than war
• Peace certainly is better than war

It does not change the basic grammar of the sentence; it adds tone and emphasis.

Because quidem is usually postpositive, which means it tends to come after the word it is connected with or after the first word in its part of the sentence.

So Latin prefers:

• Pax quidem ...

rather than:

• quidem pax ...

This is a very common behavior for quidem.

Quam means than when used with a comparative.

Here it connects the two things being compared:

• pax = peace
• bellum = war

and the comparative word is:

• melior = better

So the structure is:

• X melior est quam Y
• X is better than Y

In this sentence:

• Pax melior est quam bellum
• Peace is better than war

Because Latin has no articles. It does not have words that exactly match English the, a, or an.

So:

• pax can mean peace, the peace, or sometimes a peace
• bellum can mean war, the war, or sometimes a war

The context tells you what sounds best in English. In a general statement like this, English usually just says:

• Peace is better than war

The word order is fairly natural, but Latin word order is more flexible than English word order.

This sentence is:

• Pax quidem melior est quam bellum

A learner can think of it as:

• Peace indeed better is than war

But in normal English we say:

• Peace is indeed better than war

Latin can move words around for emphasis more easily because the endings show their roles. For example, pax is clearly the subject because of its form, and bellum is clearly the second term of comparison because of quam.

Sometimes Latin does omit forms of esse (to be), especially in poetry, informal expression, or certain compressed styles. But in a straightforward prose sentence like this, est is perfectly normal and expected.

So:

• Pax quidem melior est quam bellum

is the standard full form.

If est were omitted, a reader could still understand it, but that is not the basic form a beginner should expect first.

A common reconstructed classical pronunciation would be approximately:

• paks kwi-dem meh-lee-or est kwahm bel-lum

A few helpful points:

• x sounds like ks
• qu sounds like kw
• c is always hard, though there is no c here
• v in Classical Latin sounded like w, but there is no v here either

So:

• pax = paks
• quidem = kwi-dem
• melior = meh-lee-or
• quam = kwahm
• bellum = bel-lum