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If I want to say that two things are equivalent in Latin, I can imagine two ways using essentially the same word:

  1. X et Y sunt aequivalentes.
  2. 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.

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    Have you not thought of using tantusdem? It seems to have exactly the quality that you are looking for. – Tom Cotton May 7 '17 at 9:51
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    A quick google has found Quint. Inst. I, 5: idem significant et tantundem valent. – Tom Cotton May 7 '17 at 10:02
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    @TomCotton Good finds, thanks! I had not heard of tantusdem before. I think it will help most modern mathematical readers if I use a phrase etymologically related to "equivalent", but tantusdem is indeed a good option to keep in mind. – Joonas Ilmavirta May 7 '17 at 20:52
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    @JoonasIlmavirta The word is rare enough that you should be able to do as you please. My only suggestion is to find what other mathematicians writing in Latin use and go with that. – C. M. Weimer May 7 '17 at 21:04
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    I don't think this question is a duplicate of the one about esse + pres. partic.. This one is more specific, seeking an idiom for logic or mathematics. – Ben Kovitz May 8 '17 at 17:15

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