How would I translate the phrase “child of freedom" in feminine form?
The Latin idiom (the appropriate way of stringing words together to express a thought) is different from that of English. It is very easy to come up with a literal translation: “freedom” is libertas, the female child is, you guessed it, daughter¹, filia. Put them together, libertatis filia (libertatis is the genitive case of libertas, meaning “of liberty”, as Rafael already explained). Problem solved!
Except it isn't.
In good Latin, abstract nouns cannot act in a personal context. The idea of liberty (which is an abstract noun) begetting or giving birth to a child would surprise a Roman. They probably could make sense of it, but it would sound like a writing of a freshman from barbarian Scythia, not of a native speaker of the refined literary language. This stands in a very big contrast with English, where we do not care too much about the semantic agent (the thing acting, in a wide sense) of a clause being animate, inanimate, or abstract. But Romans did. Only entities understood as animate can have children in Latin.
So how did they solve this conundrum? Sure thing, the ancient speakers faced it too, didn't they? Yes they did, and the answer is we should personify Freedom. One can be the child of someone called Freedom, or familiarly representing it. Indeed, freedom was a cherished thing in the ancient world; it was the Ancient Greek who gave us the word “democracy,” and the Roman the “republic.” There must be a goddess of freedom, standing for Freedom herself, and that would not be a minor deity! And there indeed was.
Not surprisingly, it was Artemis, an independent and unrestrained huntress, worshiped as Artemis Eleutheria, “Artemis the Freedom”, in the ancient Lycian city of Myra, where stood a great temple sacred to her². The Greek word ἐλευθερία thus stood for both the abstract concept of liberty and the goddess personifying it. The Romans also had a similar personification of Liberty, Libertas, which later inspired the French Marianne and American Columbia, the latter being represented in the Statue Of Liberty.
So which of the ladies is going to be the mom?
Romans had Libertas, Greek Eleutheria. The seemingly obvious idea is pick Libertas as the personification of Liberty, but I advise rejecting it. A motto is short and succinct by its nature, and because of this, when read, often presents an ambiguity. Libertas would not be perceived as a personal name here, because it is also a common Latin word for “liberty,” and this will push us back to square one. I would rather choose the Greek word for this purpose, so that it would clearly stand out, emphasizing the fact that the word was selected for a reason. That would certainly fall as a sweet touch on the educated Roman ear!
Therefore, my suggestion is Eleutheriae filia.³
¹ There appears to be no word for a child of indefinite sex in Latin. AFAICR, liberi is attested only in pl., and only rarely in sg. oblique cases. This development is paralleled by some other IE languages.
² Incidentally, Myra was also the birthplace of Santa Claus, or, to be precise, the historical St. Nicolas.
³ Greek feminine loanwords in -α decline like Latin words in -a, if only retaining the original long vowel of the ending in the nom.
Daughters of freedom could be:
- libertas means freedom, libertatis is the genitive, making it mean of freedom
- filius means son, in its feminine form, filia means daughter. Filiae is the plural form, daughters
- In Latin, word order is rather free—you could also say filiae libertatis—, but it's common to put the modifying genitive before the noun being modified.
The other answers here are okay, but they all appear to be fixated on providing one singular “correct” translation for such a broad phrase. As such, I will attempt to provide as many as possible, all fitting a variety of scenarios.
Before we begin to approach of freedom and the ways it can be interpreted, let’s simply start with child. In this case I would simply suggest puera, feminine form of puer. It retains the meaning of [female] child without carrying any other connotations, like filia, puella, and others do.
There are a number of ways freedom can be approached here. For the sake of simplicity, I will assume that you are simply referring to libertās, meaning civil liberty, freedom, freedom of speech, etc. There are other types of freedom however, licentia, vacātiō, immūnitās, and others. They may be worth looking into if you meant something different.
If you are simply talking about a child who embodies the qualities of freedom, then a genitive or ablative of description should suffice:
puera libertātis aut libertātis puera
puera libertāte aut libertāte puera
If you are talking about a more abstract idea, a child being “born” of freedom (e.g, a child born and raised into the ideas of a revolution), then I might suggest the ablative of source or material instead:
puera ex libertāte aut ex libertāte puera
On a somewhat different note, if you are attempting, through child of freedom, to refer to a freed child slave, then I might suggest the following:
puera lībera aut lībera puera
However, take these with a grain of salt – as far as I can tell, liberta usually referred to fully grown adult freewomen and puera lībera simply means free child. I am not sure of (a) the historicity of child slaves in Rome and (b) by extension, if there was such a way to express the concept of “a freed child slave”.