The general place to look for etymological resources
One great resource is the Oxford English Dictionary, which is the most complete dictionary of the English language. The entries are all historically sourced, and one can observe the development of words over time that way.
Another useful resource to get older meanings of contemporary English words is Samuel Johnson's Dictionary, which was the first dictionary of English, compiled in the 18th century.
Specifically regarding the terms for the square of opposition
Every proposition in Aristotelian logic has a quantity and a quality. The quantities are affirmative and negative and the qualities are universal and particular.
- Universal Affirmative (A): "All trees are plants."
- Particular Affirmative (I): "Some tree is a plant."
- Universal Negative (E): "No dog is a plant."
- Particular Negative (O): "Some dogs are non-plans."
The letter names, A, E, I, O, are a mnemonic to help Latin-speaking school boys remember which kind of proposition is which. (The letters are taken from affirmo and nego, which mean "I affirm" and "I deny" respectively.)
Picture the propositions arranged as a square:
A - E
| / \ |
I ? O
Aristotelian logic is about the relationships among these four different kinds of propositions.
Here's one such rule. Subalternation: If you know a universal proposition (A or E) is true, then you also know that the proposition below it on the chart is true. So if "All trees are plants" is true, then it is also true that "Some tree is a plant." (Note, this is the biggest difference between Aristotle and modern logic. Modern logicians don't like that inference.) The rule is so-named, because you are inferring the one proposition from 'the other' (Latin "alter") and because the particular propositions are literally below (L. "sub") the universal propositions on the chart.
The name "subcontraries" is similar. A propositions and E propositions are contraries in that relation has logical implications. So the propositions below those propositions should be related too, and we should investigate the properties of that relation. So the medieval logicians just called that relationship subcontrariety because it was the version of contrariety for the propositions below.