Ius sine iustitia firmum manere non potest.

Ius is nominative singular neuter. It is the subject because it is the thing that cannot remain firm.

Its dictionary form is ius, iuris, a third-declension neuter noun.

Because sine always takes the ablative case. So sine iustitia means without justice.

Here iustitia is ablative singular.

They are related words, but they do not mean the same thing.

• ius = law, right, legal right, or what is lawful
• iustitia = justice, the quality or principle of being just

So in this sentence, the idea is that law/right cannot remain firm if it is separated from justice.

A learner often notices that Latin also has lex, meaning law.

The difference is roughly this:

• lex usually means a specific law, statute, or enacted rule
• ius is broader: law, right, justice in a legal sense, or the whole idea of what is legally right

So ius fits a general statement like this better than lex.

Because it agrees with ius.

Ius is:

• singular
• neuter
• nominative

So the adjective must also be:

• singular
• neuter
• nominative

That gives firmum.

Because Latin is describing what the law is like, not how it remains.

• firmum = firm, an adjective
• firmiter = firmly, an adverb

Here firmum is a predicate adjective with manere: to remain firm.

So the sentence means that ius remains firm, not that it remains firmly.

Because it depends on potest.

Latin uses a complementary infinitive after verbs like possum (to be able):

• potest manere = is able to remain / can remain

So manere is infinitive because it completes the meaning of potest.

Manere means to remain, to stay, or to continue to be.

In this sentence, it means something like:

• to remain firm
• to stay stable
• to endure in a firm state

So it is not just physical staying in one place; it can also describe continuing in a condition.

Non negates potest.

• potest = is able, can
• non potest = is not able, cannot

So firmum manere non potest means cannot remain firm.

Because Latin has no articles.

That means Latin does not have separate words for:

• the
• a/an

So ius can mean law, the law, or sometimes a law, depending on context. English has to choose what sounds best.

Yes, Latin word order is much more flexible than English word order.

This sentence could be rearranged in other ways and still mean essentially the same thing, for example:

• Ius firmum manere sine iustitia non potest
• Sine iustitia ius firmum manere non potest

The current order is natural and gives some emphasis to sine iustitia and to firmum manere as a unit: remain firm.

Yes. It is very natural to read firmum manere together as to remain firm.

This is a common Latin pattern:

• verb of remaining, becoming, seeming, etc.
• plus an adjective describing the subject

So firmum is not separate in sense from manere; together they express the state that ius is unable to keep.