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What are the earliest known examples for attributing proofs as 'deep', 'elegant' or 'beautiful' (or their equivalents in other languages)?

Gauß for example called one of his results 'remarkable' Theorema Egregium -- are there earlier examples of such proof-attributes?

I thought of this when I saw the article Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals.

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  • $\begingroup$ @Matt: thanks for being faster with editing the question than I was. $\endgroup$
    – Manfred Weis
    Commented Feb 11, 2020 at 15:02
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    $\begingroup$ The Gauss example was not his calling his proof remarkable (elegant, etc.) but rather calling the phenomenon itself, an objective "fact of nature" as it were, remarkable. $\endgroup$
    – Todd Trimble
    Commented Feb 11, 2020 at 20:16

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Probably, one of the earliest examples is the famous appraisal made by Plutarch (c. AD 46 – c. 120) about Archimedes geometric work. The translation in English is as follows:

It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanations. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearances, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required [...] His discoveries were numerous and admirable; but he is said to have requested his friends and relations that, when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained.

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An early example is Proclus's Commentary on the First Book of Euclid, though "early" still means roughly 750 years after Euclid. This has been translated into English, and you can see a sample here: "He reduced to invincible demonstrations, such things as were exhibited by others with a weaker arm."

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    $\begingroup$ I'm saving that for when I need a really strong referee report (or reference letter, maybe). $\endgroup$
    – LSpice
    Commented Feb 11, 2020 at 20:58

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