Pulsus in vena celer est, sed post quietem tardior fiet.

Because pulsus is in the nominative singular, which is the case normally used for the subject of a sentence.

Here, pulsus ... celer est means the pulse is fast.
Later, the same subject is still understood in tardior fiet: it will become slower.

So the basic structure is:

• Pulsus = subject
• celer / tardior = adjectives describing the subject
• est / fiet = verbs

Celer is the nominative singular masculine form of the adjective, and it has to agree with pulsus, which is also nominative singular masculine.

So:

• pulsus = masculine, singular, nominative
• celer = masculine, singular, nominative

This is a normal example of adjective agreement in Latin: the adjective matches the noun in gender, number, and case.

Because in with the ablative usually means in or on in the sense of location.

So in vena means in the vein.

Compare:

• in vena = in the vein / location
• in venam = into the vein / motion toward

Since the sentence describes where the pulse is being considered, not movement into the vein, Latin uses the ablative.

Because the preposition post takes the accusative case.

So:

• post
  • accusative = after
• quietem is the accusative singular of quies, quietis

Therefore post quietem means after rest.

This is something you often just have to memorize with prepositions: each Latin preposition regularly governs a particular case.

Tardior is the comparative form of tardus, meaning slower.

So:

• tardus = slow
• tardior = slower

It agrees with pulsus, just like celer does. Since pulsus is masculine nominative singular, tardior is also masculine nominative singular.

The comparison is understood from the context: the pulse is fast now, but after rest it will be slower than it is now.

Because Latin does not always need an explicit than phrase with a comparative.

In English, we might say:

• it will become slower
• or it will become slower than before

Latin can do the same thing. Tardior fiet already makes sense by itself, because the thing being compared is understood from the context: the pulse will be slower than it is now.

So quam is only needed when the second part of the comparison has to be stated clearly.

Fiet is the future tense of fio, which here means become.

So:

• est = is
• fiet = will become

That is why the sentence means a change of state:

• now the pulse is fast
• later it will become slower

If Latin used erit, that would simply mean will be, not so clearly will become.
So fiet is a good choice when the idea is changing into a different condition.

Latin word order is more flexible than English word order, because the endings show how the words function.

This sentence is:

• Pulsus in vena celer est, sed post quietem tardior fiet.

A more English-like order might be:

• Pulsus celer est in vena, sed tardior fiet post quietem.

Both would still be understandable, though the original order is more natural and stylistically balanced.

The important thing is not position alone, but the forms:

• pulsus = subject
• vena = ablative after in
• quietem = accusative after post
• celer, tardior = adjectives agreeing with pulsus

Because Latin has no articles.

So pulsus can mean:

• the pulse
• a pulse

and vena can mean:

• the vein
• a vein

Which one is best in English depends on the context. In a sentence like this, English usually wants the pulse and the vein, but Latin does not need separate words for that.

Here sed is just the normal conjunction meaning but.

It links two contrasting ideas:

• Pulsus in vena celer est = the pulse in the vein is fast
• sed post quietem tardior fiet = but after rest it will become slower

So sed marks the contrast between the pulse’s present condition and its later condition.