I'm struggling, particularly, with determining the correct case for some of the words in the following expressions:
Here, is the word "invicta" in Ablative or Nominative case, and for what reason does it qualify for whichever is the correct classification?
Are both of these words in Nominative case?
Am I correct in believing that homines and sententiae are each Nominative here?
Thank you in advance for any guidance.
One can split up the process of finding the case to three steps:
Find all possible cases a word could possibly be. Also bear in mind that there might be several options for the base word, like supplici coming from either supplex or supplicium. Check the declension tables if you don't remember them by heart.
Analyze the grammatical context. Does the word go together with something else? How can you group things together? Go through all options from the previous step and see if they are at all possible.
Analyze the semantic context. What actually makes sense?
Let me apply these to your examples:
Natura est semper invicta
Both natura and invicta could be feminine singular nominative or ablative. In addition, the adjective invicta could be neuter plural nominative or accusative.
The only possible reading — unless there is some weird context — seems to be "something is something", and both somethings need to be in nominative. If one of the words is the feminine noun natura, the adjective is almost surely in the same form. Thus they must both be nominatives.
"Nature is always invincible" makes sense as a statement.
Absolutum dominium
The noun dominium is a neuter, so the form could be singular nominative or accusative. (Or perhaps a very rare plural genitive, but I will not entertain that option here.) The adjective or participle absolutum could be in these same forms or a masculine singular accusative.
The two words seem to go together, so the adjective is neuter. They are both nominative or both accusative.
There is no broader context to judge from, so the two options remain. But ablative was impossible already by the first test.
Quot homines tot sententiae
Homines could be plural nominative or accusative, sententiae singular dative or ablative or plural nominative. No ablative forms are possible.
The structure suggest nominatives; it appears to be "there are as many X as there are Y". However, as there is no explicit verb, this could in principle be a sentence fragment with a wholly different purpose.
Without further context, the reading with two nominatives makes by far the most sense.
