Medica novam medicinam puellae dat, quia vetus remedium non iam iuvat.

Latin has no articles. It does not have separate words for the, a, or an. Whether a noun is definite or indefinite is understood from context.

So:

• medica can mean the female doctor or a female doctor
• puellae can mean to the girl or to a girl
• remedium can mean the remedy or a remedy

English has to choose; Latin usually does not.

Medica is the feminine form of medicus, -a, -um. It can be an adjective, but here it is being used as a noun, meaning female doctor or physician.

It is in the nominative singular, because it is the subject of dat: the doctor is the one doing the action.

Medicinam is the direct object of dat, so it is in the accusative singular.

Novam is the adjective novus, -a, -um meaning new, and it agrees with medicinam in:

• gender: feminine
• number: singular
• case: accusative

So novam medicinam means new medicine as the thing being given.

Because puellae is the indirect object: it means to the girl or for the girl.

With dare (to give), Latin often uses:

• nominative for the giver
• accusative for the thing given
• dative for the person receiving it

So in this sentence:

• medica = the giver
• novam medicinam = the thing given
• puellae = the receiver

Mostly from the case endings, not from word order.

Here the endings tell you the roles:

• medica = nominative singular, so it is the subject
• medicinam = accusative singular, so it is the direct object
• puellae = dative singular, so it is the indirect object

That is why Latin can use a freer word order than English.

Yes. Latin word order is much more flexible than English word order because the endings already show each word’s job in the sentence.

For example, the main clause could be rearranged in several ways and still mean essentially the same thing, as long as the forms stay the same:

• Medica novam medicinam puellae dat
• Puellae medica novam medicinam dat
• Novam medicinam medica puellae dat

The exact order can affect emphasis, but the grammar stays clear because of the endings.

Dat is from dare, meaning to give.

Its ending -t tells you it is:

• third person
• singular
• present tense

So dat means he/she/it gives. Here it matches the singular subject medica, so the meaning is the female doctor gives.

Quia means because. It introduces a subordinate clause that gives the reason for the action in the main clause.

So:

• main clause: Medica novam medicinam puellae dat
• reason clause: quia vetus remedium non iam iuvat

In other words, the doctor gives the new medicine because the old remedy is no longer helping.

Because vetus is a different adjective from vetustus.

• vetus, veteris = old
• vetustus, -a, -um = also old, but a different word

In this sentence, the adjective used is vetus. It is a third-declension adjective, and its nominative singular form is vetus for masculine, feminine, and neuter.

So:

• vetus remedium = the old remedy

Also, remedium is neuter singular nominative here, because it is the subject of iuvat.

Non iam means no longer or not anymore.

So:

• non iam iuvat = no longer helps

This is a very common Latin way to express that something used to be true but is not true now.

Because its subject is remedium, which is singular.

• remedium = singular subject
• iuvat = third person singular present

So the agreement is normal: the old remedy helps / is helping.

Good question. Iuvare often takes a direct object, so you may expect something like the old remedy no longer helps the girl.

In this sentence, the person being helped is not stated explicitly. Latin often leaves out something that is easy to understand from the context. Here the understood object is most naturally the girl.

So the sense is:

• the old remedy no longer helps [her]

That omitted object is very normal in Latin when the meaning is already clear.