If I want to say that two things are equivalent in Latin, I can imagine two ways using essentially the same word:
- X et Y sunt aequivalentes.
- X et Y aequivalent.
Googling for the first option (without X et Y) produces numerous Latin texts with the phrase. Both intuition and L&S suggest that aequivalere is a verb that should have the same effect as the first option.
Option 1 has the benefit of matching the structure used in many other languages. However, using esse with a present participle (a present active periphrasis) looks a bit weird to me.
The phrase is particularly common in mathematics, but not confined to that one field. Here is an example sentence: "The following statements are equivalent." This sentence would then be followed by a list of statements.
Is there a difference between 1 and 2? Are there cases where one should be used instead of the other? Did the participle aequivalens get a meaning separate from its parent verb, so that it should not really be treated as its form? Is either option more idiomatic or otherwise better in your opinion? (If so, why?)
I am interested in using the phrase in today's world, but insights from any era are welcome.