It's true that in Classical Latin, ille is a demonstrative pronoun (corresponding to that), not an article; indeed, articles as we know them in English do not exist in Classical Latin. However, that's not the entire story.
Ille in Classical Latin
The meaning of ille in Classical Latin is not so narrow as to exclude its use in these book titles. Allen and ...
This means "illa" definitely doesn't refer to "dies".
But it does!
The word dies can be feminine, and it is here.
The feminine gender is rarer but it is the typical choice for a special day like an appointment or a deadline.
That's why it was chosen here.
For details, see this question about gender variation in dies.
Two key mechanisms of disambiguation come to mind:
Using hic (latter) and ille (former) is one way. Simple example: "A and B meet. The former eats, the latter drinks." — A et B conveniunt. Ille est, hic bibit.
The pronoun se/suus usually refers to the subject of the sentence. Simple example: "B wrote a book. A compares his own book with B's." — ...
This is a really common stumbling block for those approaching Latin from the background of a language like English, so it merits a careful step-by-step explanation. I'll break my response into two steps:
Adjectives agree in case, number, and gender with the noun they modify.
Suus, -a, -um is an adjective.
Adjectives agree with their nouns
Let's start by ...
It is the feminine nominative and refers to dies. It means “that day.”
You do not say why you think you can definitely rule it out, but I guess you think dies is masculine, which is indeed the case. But it is also often feminine. Generally speaking, it is feminine only when referring to a set day, an appointed time. This does arguably apply to the day of ...
All forms of se, including suus, normally refer to the subject of the main clause of the sentence. Eius, however, normally does not refer to this subject, but to someone else. So the two words have different meanings.
Sextus Tarquinius crudelis est. Lucretia praevidet mortem suam.
"S.T. is cruel. Lucretia foresees her own death."
Sextus Tarquinius ...
Yes, the forms of vōs did originally resemble those of nōs. But there was a sound change in Latin whereby the sequence vo became ve; this is an example of dissimilation. Apparently this only occurred when the o was short, which is why it did not happen in the word vōs itself. Other examples are adversum, veto, which were originally advorsum, voto.
It is important to distinguish between syntactic gender and semantic gender. As we all know, a word like centuria, "group of ca. 100 soldiers", is syntactically feminine, but semantically it is masculine, since the Romans had no female soldiers. A feminine word is used to describe men. Or consider the feminine word virtus "manhood", from vir "man". There is ...
Of course, as with so much in Latin, there's more than one answer, none of them incorrect.
The first answer is yes, using hic and ille like this to mean "the latter" and "the former" is common and correct. Here's Cicero in De Amicitia:
Scitum est enim illud Catonis, ut multa: 'melius de quibusdam acerbos inimicos mereri quam eos amicos ...
When hic and ille are used like this, they refer to the distance of words: hic refers to the closest noun, ille the one that came first.
In your example, you have first pontus and then aer. Hic therefore refers to the one closer to the pronoun, and since aer is closer to hic than pontus, it must refer to that. Likewise, since pontus is further away than aer,...
In my opinion, the most likely translation of the sentece is:
Our sea has many docks
Mare Nostrum was a common name given by the Romans to the Mediterranean Sea around the I century AD, since the empire possesed all of its coast by that time.
Regarding your question in the title, yes adjectives and pronouns must agree in gender, number and case with the ...
Yep, it's called the reflexive adjective, suus, -a, -um. It declines like an adjective and goes with the noun it's modifying.
Marcus reads a book. Marcus librum legit.
Marcus reads his [i.e. someone else's] book. Marcus eius librum legit.
Marcus reads his own book. Marcus suum librum legit.
For the full set of rules on reflexives, see Allen &...
Yes, the meaning is different. αὐτός, when used in the nominative, is an emphatic pronoun meaning "he himself". So your second sentence would mean "He himself says...", with some implicit contrast such as "and not anyone else".
The oblique cases of αὐτός, however, are most often unemphatic and are the most common way of expressing the third-person pronoun "...
Lewis & Short have hidden this in their entry for qui/quae/quod (and not, as I would have thought, in the dedicated entry for quo) – II,E,2,b:
Quo, abl. neutr., with compp. (with or without hoc, eo, or tanto): quo … eo, by how much, by so much, the … the: “quo difficilius, hoc praeclarius,” Cic. Off. 1, 19, 64.
So the construction is quo + comparative. ...
quisquis and quicumque are relative pronouns, so they introduce a restricting clause:
Quisquis es, noster eris. Whoever you are, you will be one of us.
...scilicet omnibus quicumque terrae munere vescimur enaviganda. ... (which) all of us who feed on the bounty of the earth will surely have to sail through.
By contrast, quivis and quilibet are ...
I'd like to offer an addition, which was originally posted as a comment but requested to be turned into an answer by OP.
As explained in the other two answers, iste, ille and hic are used to refer back to the items of a previous enumeration. In that sense, "the former ... the latter" is a perfectly acceptable translation. However, in your example this ...
The case of a relative pronoun indicates its role inside the subordinate clause, not the main clause.
Since the servōs in the main clause are the subject of pārent in the subordinate clause, a nominative relative pronoun is needed: quī.
If that seems strange, here are three considerations that can help make it seem normal:
1. It works the same way in ...
You may be able to find nouna...nounb, isb...sed illea, but that's an unusual pairing, and you'd probably want to read it more literally, i.e. "he did X, but the former/latter did Y."
The most common pairing is nouna...nounb, hicb...illea. Allen & Greenough §297 have this to say about is in this usage:
Is is a weaker demonstrative than the others and ...
Adjectives always agree with the noun they are modifying in case, gender, and number. Since mea is the nominative feminine singular form of meus, mea, meum ("my" or "mine"), it goes with filia and parva which are also in the nominative feminine singular. Mea thus could not go with coronas pulchras, which is in the accusative feminine plural form.
In Latin, an adjective always agrees with the (pro)noun it modifies in gender, number, and case. Since Latin is inflected, position is not an important deciding factor, though it can be relevant.
Let's first parse the two nouns in your sentence:
coronas: feminine, plural, accusative
filia: feminine, singular, nominative
All that's left to do is find out ...
You are confusing gĕnu, -ūs ("knee") and gĕnus, -ĕris ("origin, lineage, stock").
The latter is a 3rd declension neuter noun, so the accusative singular is the same as the nominative singular. Hence, to fill in the blank:
Augustus affirmed that his lineage had arisen from Jupiter.
Quam here is being used as a normal relative, and could not be replaced with illam, since the relative clause quam non invenit umquam is the accusative subject of the verb esse in the accusative and infinitive construction introduced by putat in the main clause. A literal translation is: "[the one] whom (quam) he does not find anywhere, he believes to be ...
There isn't really an answer to the "why" question beyond the fact that in Proto-Indo-European, some of the case endings for pronouns were different from those for nouns, for unknown reasons. Among these is the nom./acc. sg. neuter ending, which was *-d instead of *-m. This is clear from cognates in other languages, e.g. Sanskrit neuter demonstrative tad, ...
Another use of the genitive that you've left out is subjective genitive, which is what this is. These are discussed in, e.g., Gildersleeve and Lodge, Latin grammar §363. Allen and Greenough, New Latin grammar §243, Note 1 treats them, not unreasonably, as a species of possessive genitive (where what is 'owned' is an action or state of being).
Death implies ...
Relative pronouns (like quis/quis/quid) don't agree with their antecedents for case; instead, it gets that from its position in the subordinate clause. Note that they still agree in gender and number, since it's supposed to be a stand-in for the noun.
Because the pronoun stands in for a nominative use, the subject of the clause -- i.e. "servi non parent" -- ...
"Nemine contradicente" is a kind of set expression in Latin. The plural forms are probably missing because it sounds goofy, in any language, to say "I spoke with no ones."
Ipse loquor Latine fluenter, et nullum problema habeo cum his formis. -Mentifex
It's for emphasis, and older than the use of ipse as an intensifier. From Allen & Greenough §143.d:
Emphatic forms of tu are tute and tutemet (tutimet). The other cases of the personal pronouns, excepting the genitive plural, are made emphatic by adding -met: as, egomet, vosmet.
NOTE.—Early emphatic forms are mepte and tepte.
Wiktionary has a list ...
The key confusion seems to be with quae.
It is here the singular feminine nominative relative pronoun.
I think it refers to resurrectio; there is also a reading which relates it to dies (Dominica).
It seems most likely that suae refers to Christians.
As pointed out in a comment below, this is somewhat unusual.
Usually suus refers to the subject ...
Eugene McCartney has an article in Classical Philology (XIV 3 July 1919) entitled "Greek and Latin Constructions in Implied Agreement" that mentions these constructions in its opening notes.
While talking about the "closeness of the relationship between the genitive of possession and the possessive adjective," he cites the coordination of the two in the ...
The general word for "his" (or "hers", or "its", or "theirs") in Latin is eius. This is the genitive singular of is/ea/id, "he/she/it". Those are three separate words, but conveniently they all share a genitive singular form.
However, I wouldn't use eius in this case, when the farmer has already been mentioned in the sentence. Because Latin uses reflexive ...